remote sensing
Article
Change Detection in Synthetic Aperture Radar
Images Using a Multiscale-Driven Approach
Olaniyi A. Ajadi *, Franz J. Meyer and Peter W. Webley
Geophysical Institute, University of Alaska Fairbanks, 903 Koyukuk Drive, P.O. Box 757320, Fairbanks,
AK 99775, USA; fjmeyer@alaska.edu (F.J.M.); pwwebley@alaska.edu (P.W.W.)
* Correspondence: oaajadi@alaska.edu; Tel.: +1-270-293-9069
Academic Editors: Richard Gloaguen and Prasad S. Thenkabail
Received: 24 March 2016; Accepted: 2 June 2016; Published: 8 June 2016
Abstract: Despite the significant progress that was achieved throughout the recent years, to this
day, automatic change detection and classification from synthetic aperture radar (SAR) images
remains a difficult task. This is, in large part, due to (a) the high level of speckle noise that is
inherent to SAR data; (b) the complex scattering response of SAR even for rather homogeneous
targets; (c) the low temporal sampling that is often achieved with SAR systems, since sequential
images do not always have the same radar geometry (incident angle, orbit path, etc.); and (d) the
typically limited performance of SAR in delineating the exact boundary of changed regions. With
this paper we present a promising change detection method that utilizes SAR images and provides
solutions for these previously mentioned difficulties. We will show that the presented approach
enables automatic and high-performance change detection across a wide range of spatial scales
(resolution levels). The developed method follows a three-step approach of (i) initial pre-processing;
(ii) data enhancement/filtering; and (iii) wavelet-based, multi-scale change detection. The stand-alone
property of our approach is the high flexibility in applying the change detection approach to a wide
range of change detection problems. The performance of the developed approach is demonstrated
using synthetic data as well as a real-data application to wildfire progression near Fairbanks, Alaska.
Keywords: change detection; SAR; decision support; image decomposition; image analysis;
Bayesian inferencing
1. Introduction and Background
Multi-temporal images acquired by optical [1] or radar remote sensing sensors [2] are routinely
applied to the detection of changes on the Earth’s surface. As both of these two sensor types have
their own imaging and sensitivity characteristics, their performance in change detection varies with
the properties of the changing surface features [3]. In recent years, synthetic aperture radar (SAR)
data have gained increasing importance in change detection applications, because SAR is an active
sensor, operating without regard to weather, smoke, cloud cover, or daylight [4]. So SAR has shown
to be a valuable data source for the detection of changes related to river ice breakup [5], earthquake
damage [6], oil spill detection [7], flood [8], and forest growth assessment [9].
In this paper we are interested in developing an unsupervised change detection method from
series of SAR images. Despite extensive research that was dedicated to this topic throughout the last
decade [7], automation and robust change detection from a series of SAR images remains difficult for
the following reasons: (A) Due to the complicated nature of the surface backscatter response in SAR
data, most SAR-based change detection methods require repeated acquisitions from near-identical
vantage points. These repeated acquisitions provide a static background against which surface change
can be identified with reasonable performance [10]. This requirement severely limits the temporal
sampling that can be achieved with modern SAR sensors with revisit times in the order of tens of days,
Remote Sens. 2016, 8, 482; doi:10.3390/rs8060482
www.mdpi.com/journal/remotesensing
Remote Sens. 2016, 8, 482
2 of 27
and strongly limits the relevance of the method for many dynamic phenomena; (B) The multiplicative
speckle statistic associated with SAR images limits the change detection performance because it renders
the identification of a suitable detection threshold difficult and it adds noise to the detection result;
(C) The lack of automatic and adaptive techniques for the definition of change detection thresholds
has hindered the development of a fully automatic change detection approach. Finally; (D) the lack of
accuracy in delineating the boundary of changed regions has limited the performance of SAR data for
applications that require high location accuracy of change information.
Most of the recently proposed SAR-based change detection techniques utilize the concept of ratio
or difference images for suppressing background information and enhancing change information.
Published methods differ in their approach to extracting a final binary change detection map from
the image ratio or difference data. In [1], two automatic unsupervised approaches based on Bayesian
inferencing were proposed for the analysis of the difference image data. The first approach aims
to select an adaptive decision threshold to minimize the overall change detection error, using the
assumption that the pixels of the change map are spatially independent and that the gray value
probability density function (PDF) of the difference image map is composed of two Gaussian
distributions representing a change and a no-change class. This approach was further extended
in [11,12] by adding an expectation-maximization (EM) algorithm to estimate the statistical parameters
of the two Gaussian components. The second approach in [1], which utilizes a Markov random field
(MRF) model, is taking into account contextual information when analyzing the change map.
In [13], an MRF is used to model noiseless images for an optimal change image using the maximum
a posteriori probability computation and the simulated annealing (SA) algorithm. The SA algorithm
generates a random sequence of change images, such that a new configuration is established, which
depends only on the previous change image and observed images by using the Gibbs sampling
procedure [13].
A computationally efficient approach for unsupervised change detection is proposed in [14]. The
approach initially start by generating an h ˆ h non-overlapping image block from the difference image.
Eigenvector space is created using Principal Component Analysis (PCA) on the h ˆ h non-overlapping
image blocks. In addition, a feature vector space over the entire difference image is created by
projecting overlapping h ˆ h data blocks around each pixel onto eigenvector space. Furthermore, a
k-means algorithm is employed to cluster the feature vector space into two clusters and assigns each
pixel in the final change detection map to the cluster that minimizes the Euclidean distance between
the pixel’s feature vector and the mean feature vector of clusters [14].
Several recent publications have utilized wavelet techniques for change detection from SAR.
Analyzing an image in the wavelet domain helps to reduce the problems caused by the speckle noise.
Wavelet domain analysis has been applied to unsupervised change detection for SAR images [15–18].
In [15], a two-dimensional discrete stationary wavelet transform (2D-SWT) was applied to decompose
SAR ratio images into different scale-dependent images, each of which is characterized by a tradeoff
between speckle noise suppression and preservation of image details. The undecimated discrete
wavelet transform (UDWT) was proposed by [16] to decompose the difference image. For each pixel in
the difference image, a feature vector is extracted by locally sampling the data from the multiresolution
representation of the difference image [16]. The final change detection map is obtained using a binary
k-means algorithm to cluster the multi-scale feature vectors, while obtaining two disjoint classes:
change and no-change. Individual decompositions of each input image using the dual-tree complex
wavelet transform (DT-CWT) are used in [17]. Each input image is decomposed into a single low-pass
band and six directionally-oriented high-pass bands at each level of decomposition. The DT-CWT
coefficient difference resulting from the comparison of the six high-pass bands of each input image
determines classification of either change or no-change classes, creating a binary change detection
map for each band. These detection maps are then merged into a final change detection map using
inter-scale and intra-scale fusion. The number of decomposition scales (levels) for this method must
be determined in advance. This method boasts high performance and robust results, but has a high
Remote Sens. 2016, 8, 482
3 of 27
computational cost. In [18], a region-based active contour model with UDWT was applied to a
SAR difference image for segmenting the difference image into change and no-change classes. More
recently, [19] used a curvelet-based change detection algorithm to automatically extract changes from
SAR difference images.
Even though these papers have provided a solution to a subset of the limitations highlighted
above, not all the limitations are solved in a single paper. The work done by [1,11,12] does not
provide an effective way to select the number of scales needed for the EM algorithm in order to avoid
over- or under-estimation of the classification. Also, the noise filtering methods employed do not
preserve the detailed outline of a change feature. The disadvantages of the method in [13] are its high
computational complexity and reduced performance in the presence of speckle noise. Although the
method in [14] achieves a good result with low computational cost, the performance of the employed
PCA algorithm decreases when the data is highly nonlinear. While [15–19] provided promising results
in a heterogeneous image, the various methods have several disadvantages. They do not consider
image acquisitions from multiple geometry, are not fully preserving the outline of the changed regions,
and require manual selection of detection thresholds.
To improve upon previous work, we developed a change detection approach that is automatic,
more robust in detecting surface change across a range of spatial scales, and efficiently preserves
the boundaries of change regions. In response to the previously identified limitation (A), we utilize
modern methods for radiometric terrain correction (RTC) [10,20,21] to mitigate radiometric differences
between SAR images acquired from different geometries (e.g., from neighboring tracks). We show
in this paper that the application of RTC technology allows combining multi-geometry SAR data
into joint change detection procedures with little reduction in performance. Thus, we show that the
addition of RTC results in improved temporal sampling with change detection information and in an
increased relevance of SAR for monitoring dynamic phenomena.
To reduce the effects of speckle on image classification (limitation (B)), we integrate several recent
image processing developments in our approach: We use modern non-local filtering methods [22]
to effectively suppress noise while preserving most relevant image details. Similarly, we perform a
multi-scale decomposition of the input images to generate image instances with varying resolutions
and signal-to-noise ratios. We use a 2D-SWT in our approach to conduct this decomposition.
To fully automate the classification operations required in the multi-scale change detection
approach (limitation (C)), we model the probability density function of the change map at each
resolution level as a sum of two or more Gaussian distributions (similar to [11]). We developed an
automatic method to identify the number of Gaussian processes that make up our data and then use
probabilistic Bayesian inferencing with EM algorithm and mathematical morphology to optimally
separate these processes.
Finally, to accurately delineate the boundary of the changed region (limitation (D)), we utilize
measurement level fusion techniques. These techniques used the posterior probability of each class
at each multi-scale image to compose a final change detection map. Here we tested five different
techniques including (i) product rule fusion; (ii) sum rule fusion; (iii) max rule fusion; (iv) min rule
fusion; and (v) majority voting rule fusion.
These individual methods are combined in a multi-step change detection approach consisting of
a pre-processing step, a data enhancement and filtering step, and the application of the multi-scale
change detection algorithm. The details of the proposed approach are described in Section 2. A
performance assessment using a synthetic dataset and an application to wildfire mapping is shown in
Sections 3 and 4, respectively. A summary of the presented work is shown in Section 5.
2. Change Detection Methodology
The work presented here is motivated by the challenges associated with change detection and
the desire to develop an improved algorithm for unsupervised change detection in SAR images that
can provide change information at high temporal sampling rates. We aim at using information at
Remote Sens. 2016, 8, 482
4 of 27
Remote Sens.resolution
2016, 8, 482 levels to obtain high accuracy change detection maps in both heterogeneous4 and
of 27
different
homogeneous regions, contributing to a change detection method that is applicable to a wide range
presented in Figure 1. The overall contribution of our methodology has two components. First, we
of change situations. To achieve this goal, a multi-step processing workflow was developed that is
developed a set of new techniques that are utilized within our change detection workflow to
presented in Figure 1. The overall contribution of our methodology has two components. First, we
streamline processing and improve detection performance. As part of these techniques we (1)
developed a set of new techniques that are utilized within our change detection workflow to streamline
developed an efficient way to improve classification performance by combining EM algorithms with
processing and improve detection performance. As part of these techniques we (1) developed an
mathematical morphology—this is a novel contribution to this field of research; (2) we integrated a
efficient way to improve classification performance by combining EM algorithms with mathematical
low computational complexity way to achieve high accuracy in preserving the boundary of changed
morphology—this is a novel contribution to this field of research; (2) we integrated a low computational
regions using measurement level fusion techniques; and (3) we combine modern non-local filtering
complexity way to achieve high accuracy in preserving the boundary of changed regions using
and 2D-SWT to provide robustness against noise. The second contribution comes from a novel way
measurement level fusion techniques; and (3) we combine modern non-local filtering and 2D-SWT to
of combining our own technology with other published processing procedures to arrive at a new,
provide robustness against noise. The second contribution comes from a novel way of combining our
efficient and highly flexible change detection workflow that can be applied to a wide range of change
own technology with other published processing procedures to arrive at a new, efficient and highly
detection problems.
flexible change detection workflow that can be applied to a wide range of change detection problems.
0
Figure
thethe
original
log-ratio
image,
XkLRX is the
kth
Figure 1.
1. Workflow
Workflowof
ofthe
theproposed
proposedapproach.
approach.Here,
Here,XLR
X is is
original
log-ratio
image,
is the
K´1
decomposed
image,
andand
XLRX is the
highest
decomposed
level.
kth decomposed
image,
is the
highest
decomposed
level.
requires
some
parameters
to
It is worth
worth mentioning
mentioningthat
thatthe
theautomatic
automaticprocess
processofofour
ourapproach
approach
requires
some
parameters
be be
set set
beforehand.
The The
parameters
that need
to be set
include
(i) the neighborhood
size of the
filtering
to
beforehand.
parameters
that need
to be
set include
(i) the neighborhood
size
of the
step; (ii)step;
the number
of multi-scale
decomposition
levels;levels;
(iii) the
element
of the
filtering
(ii) the number
of multi-scale
decomposition
(iii)structuring
the structuring
element
of
morphological
filter;
and,and,
finally,
(iv) (iv)
the maximum
number
of allowed
change
classes.
Please
note
the
morphological
filter;
finally,
the maximum
number
of allowed
change
classes.
Please
that while
we identified
optimal
settings
for these
parameters,
we found
that the
performance
of our
note
that while
we identified
optimal
settings
for these
parameters,
we found
that
the performance
algorithm does not critically depend on the exact choice for these variables. This is true for the
following reasons: (i) as non-local means filtering is conducted very early in the workflow, the impact
of changes in the neighborhood size is mitigated by subsequent processing steps such as multi-scale
Remote Sens. 2016, 8, 482
5 of 27
of our algorithm does not critically depend on the exact choice for these variables. This is true for
the following reasons: (i) as non-local means filtering is conducted very early in the workflow, the
impact of changes in the neighborhood size is mitigated by subsequent processing steps such as
multi-scale decomposition and the application of mathematical morphology. Hence, we found that
varying the neighborhood size from its optimal value changed system performance only slowly; (ii) in
empirical tests it was found that using six decomposition levels was a good compromise between
processing speed and classification accuracy. Adding additional levels (beyond six) did not result
in significant performance improvement but added computational cost. Reducing the number of
layers leads to a slow decrease of change detection performance, yet this reduction of performance
does not become significant unless the number of bands drops below four; (iii) from an analysis of a
broad range of data from different change detection projects we found (1) that a 20 ˆ 20 pixel-sized
structuring element of the morphological filter led to the most consistent results; and (2) that change
detection performance changed slowly with deviation from the 20 pixel setting. Hence, while 20 pixels
was found to be optimal, the exact choice of the window size is not critical for change detection
success; finally, (iv) the maximum number of allowable change classes is a very uncritical variable as
it merely sets an upper bound for a subsequent algorithm that automatically determines the number
of distinguishable classes in a data set (see Section 2.3.3). By presetting this variable to 20 classes we
ensure that almost all real life change detection scenarios are captured. There is no need to change
this variable unless unusually complex change detection situations with more than 20 radiometrically
distinguishable change features are expected
2.1. SAR Data Pre-Processing
The ultimate goal of the pre-processing step is to perform image normalization, i.e., to suppress
all image signals other than surface change that may introduce radiometric differences between the
acquisitions used in the change detection analysis. Such signals are largely related to (i) seasonal
growth or (ii) topographic effects such as terrain undulation that arise if images were not acquired from
near-identical vantage points. In order to enable a joint change detection analysis of SAR amplitude
images acquired from different observation geometries, we attempt to mitigate relative geometric and
radiometric distortions. In a calibrated SAR image, the radar cross-section (RCS) of a pixel can be
modeled as [4]:
σ “ σ0 pθi q ˆ Aσ pθi q
(1)
where Aσ is the (incidence angle–dependent) surface area covered by a pixel, θi is the local incidence
angle, and σ0 is the normalized RCS. According to (1), images acquired from different geometries will
differ due to the look angle dependence of both σ0 and Aσ .
In areas that are dominated by rough surface scattering and for moderate differences ∆θi of
observation geometries, we can often assume that ∆σ0 p∆θi q ! ∆Aσ p∆θi q [4]. Under these conditions,
the geometric dependence of σ can largely be removed by correcting for ∆Aσ p∆θi q. This correction is
called radiometric terrain correction [20], which is completed by the following steps:
‚
‚
In the first step, geometric image distortions related to the non-nadir image geometry are removed
by applying a “geometric terrain correction” step [10] using a digital elevation model (DEM).
Secondly, to remove radiometric differences between images, we use radiometric terrain
normalization [10]. This normalization also utilizes a DEM to estimate, pixel by pixel, and
compensate Aσ pθi q, for the radiometric distortions.
In areas dominated by rough surface scattering, the application of RTC allows for combining
SAR data acquired from moderately different incidence angles into joint change detection procedures
with little reduction in performance. Hence, it can lead to significant improvements in the temporal
sampling with change detection data.
An example of the effect of geometric and radiometric terrain correction is shown in Figure 2.
Figure 2a shows an original ALOS PALSAR image over the Tanana Flats region in Alaska while the
Remote Sens. 2016, 8, 482
6 of 27
image after geometric and radiometric terrain correction is presented in Figure 2b. The normalized
data is now largely free of geometric influences, reducing differences between images acquired from
different
Remote Sens.geometries
2016, 8, 482 and enhancing the performance of change detection from multi-geometry data.
6 of 27
Figure 2.
Figure
2. Example
Example of
of (a)
(a) image
image affected
affected by
by radiometric
radiometric and
and geometric
geometric distortions;
distortions; (b)
(b) radiometric
radiometric and
and
geometric normalized
normalized image
image enabling
enabling change
change detection
detection analysis
analysis from
from multiple
multiple geometries.
geometries.
geometric
It is worth mentioning that the RTC utilized in our approach is most effective when dealing with
It is worth mentioning that the RTC utilized in our approach is most effective when dealing
natural environments that are dominated by rough surface scattering. For these target types, the
with natural environments that are dominated by rough surface scattering. For these target types,
surface scattering properties change slowly with incidence angle and differences in measured radar
the surface scattering properties change slowly with incidence angle and differences in measured
brightness are dominated by geometric effects. However, RTC will be less useful for areas dominated
radar brightness are dominated by geometric effects. However, RTC will be less useful for areas
by targets with very oriented scattering characteristics (e.g., urban environments). For these regions,
dominated by targets with very oriented scattering characteristics (e.g., urban environments). For
RTC correction may not lead to significant reduction of radiometric differences between images from
these regions, RTC correction may not lead to significant reduction of radiometric differences between
different incidence angles. Furthermore, limitations exist for regions with complex small-scale
images from different incidence angles. Furthermore, limitations exist for regions with complex
topography, if this topography is not sufficiently captured in the available DEM.
small-scale topography, if this topography is not sufficiently captured in the available DEM.
2.2. Data
2.2.
Data Enhancement
Enhancement
2.2.1. Logarithmic Scaling and Ratio Image Formation
To suppress
suppress image
image background
background structure and improve the detectability
detectability of potential surface
changes from SAR data, a ratio image is formed between a newly acquired image Xii and a reference
R.. Using
image XR
Using ratio
ratio images
images in
in change
change detection
detection was
was first
first suggested
suggested by
by [3] and has since been the
basis of many change detection
detection methods
methods [12,23,24].
[12,23,24]. The
The reference
reference image
image X
XRR and image Xii are selected
such that the effects of seasonal variations as well as spurious changes of surface reflectivity on the
change detection product are minimized. Before ratio image formation, all data are geometrically and
radiometrically calibrated
calibratedfollowing
followingthe
theapproach
approachininSection
Section2.1.
2.1.The
The
resulting
ratio
image
then
radiometrically
resulting
ratio
image
cancan
then
be
be modeled
as [3]:
modeled
as [3]:
Oir “=xTir
(2)
(2)
where
and Tir is
where Oir isis the
the observed
observed intensity
intensity ratio,
ratio, x isis aamultiplicative
multiplicative speckle
speckle contribution,
contribution, and
is the
the
underlying
true
intensity
ratio.
The
observed
intensity
ratio
image
has
the
disadvantage
that
the
underlying true intensity ratio. The observed intensity ratio image has the disadvantage that the
multiplicative
noise is
is difficult
difficultto
toremove.
remove.Therefore,
Therefore,aalogarithmic
logarithmicscaling
scalingisisapplied
appliedtoto Oir, ,resulting
resultingin:
in:
multiplicative noise
(`
)+
10 pxq
10log(
′ “=10log
X 1LR
10log
pTir q )
(3)
The application of logarithmic scaling and ratio image formation helps to transform our data
The application of logarithmic scaling and ratio image formation helps to transform our data
into a near normal distribution which closely resembles a Gaussian distribution. To suppress the
into a near normal distribution which closely resembles a Gaussian distribution. To suppress
now-additive noise in the log-scaled ratio image ( ` ) , ˘we applied a fast non-local means
the now-additive noise in the log-scaled ratio image X 1 LR , we applied a fast non-local means
filtering procedure.
filtering procedure.
2.2.2. Fast Non-Local Means Filtering Approach
As we are interested in developing a flexible change detection method that can be applied to a
wide range of change situations, we are interested in preserving the original image resolution when
filtering the data. Non-local means filters are ideal for this task as they identify similar image patches
Remote Sens. 2016, 8, 482
7 of 27
2.2.2. Fast Non-Local Means Filtering Approach
As we are interested in developing a flexible change detection method that can be applied to a
wide range of change situations, we are interested in preserving the original image resolution when
filtering the data. Non-local means filters are ideal for this task as they identify similar image patches
in a dataset and use those patches to optimally suppress noise without sacrificing image resolution.
The non-local means concept was first published in [25]. The algorithm uses redundant information to
reduce noise, and restores the original noise-free image by performing a weighted average of pixel
values, considering the spatial and intensity similarities between pixels [22]. Given the log-ratio image
1 (see Section 2.2), we interpret its noisy content over a discrete regular grid, Ω.
XLR
X 1LR “
X 1LR px, yq | px, yq P Ω
(
(4)
The restored image content X LR pxi , yi q at pixel pxi , yi q is then computed as a weighted average
of all of the pixels in the image, according to:
`
˘
X LR xi , x j “
ÿ
`
˘
w pi, jq X 1LR x j , y j
(5)
px j y j qPΩ
`
˘
The weight w pi, jq measures the similarities between two pixels pxi , yi q and x j , y j and is
given by:
1 ´ spi,jq
w pi, jq “
e h2
(6)
D piq
where h controls the amount of filtering, D piq is the normalization constant, and s pi, jq is the weighted
Euclidean distance (gray-value distance) of two neighborhood pixels (Pi and Pj ) that are of equal size.
According to [25], the similarity between two neighborhood pixels (Pi and Pj ) is based on the similarity
of their intensity gray level. Neighborhoods having similar gray-level pixels will have larger weights
in the average. To compute the similarity of the intensity gray level, we estimated s pi, jq as follow:
s pi, jq “ k Pi ´ Pj k2a
(7)
The standard deviation of the Gaussian kernel is denoted as a. To ensure that the averaging in
Equations (5)–(7) is more robust, we set the neighborhood size for weight computation to 5 ˆ 5 pixels
and the size of the searching region to 13 ˆ 13 pixels. We referred to Ω as the searching window. The
optimal neighborhood sizes were determined in empirical tests. These tests also showed that the
choice of neighborhood size does not critically affect the filtering performance. We implemented the
modern non-local filtering methods to effectively suppress the noise while preserving most relevant
details in the image.
2.3. Change Detection Approach
The workflow of our change detection approach is shown in the lower frame of the sketch in
Figure 1 and includes three key elements. In an initial step, a multi-scale decomposition of the input
ratio images is conducted using a 2D-SWT and resulting in K image instances. Secondly, a multi-scale
classification is performed at each of the K levels, resulting in K classification results per pixel. In
our approach, the classifications are performed automatically and adaptively using an EM algorithm
with mathematical morphology. Finally, in a third step, we conduct a measurement level fusion of the
classification results to enhance the performance of our change detection.
2.3.1. Multi-Scale Decomposition
As previously mentioned, often our ability to detect change in SAR images is limited by substantial
noise in full resolution SAR data. Here, we utilize multi-scale decomposition of our input images
Remote Sens. 2016, 8, 482
8 of 27
to generate image instances with varying resolutions and signal-to-noise ratios, and also to further
reduce residual noise that remains after an initial non-local means filtering algorithm (Section 2.2)
was applied.
Multi-scale decomposition is an elegant way to optimize noise reduction while preserving the
desired geometric detail [2]. In our approach, 2D-SWTs are used to decompose the log-ratio images [26].
Figure
3 shows
Remote Sens.
2016, 8,that
482 in our implementation of the wavelet decomposition we apply a set of high-pass
8 of 27
and low-pass filters first to the rows and then to the columns of an input image at resolution level
klevel
´ 1, resulting
in fourindecomposition
imagesimages
at resolution
level k. level
The four
decomposition
images
− 1, resulting
four decomposition
at resolution
. The
four decomposition
LL and (2) three high-frequency detail images (X LH , X HL , and
include
(1) a lower
image X LR
images include
(1) resolution
a lower resolution
image
and (2) three high-frequency detail LR
images
,
LR (
HH ), where the superscripts LL, LH, HL, HH indicate in which order low-pass (L) and high-pass (H)
X LR
, and
), where the superscripts
,
,
,
indicate in which order low-pass ( ) and
filters
were( applied.
high-pass
) filters were applied.
Figure 3.
3. Multi-scale
Multi-scale decomposition
decomposition of
of input
input log-ratio
log-ratio image
image X into
into aa lower
lower resolution
resolution and
and detail
detail
Figure
LR
images; X LL isisthe
thelower
lowerresolution
resolutionimage
imageand
and(X
( LH , ,X HL,, X HH) )are
the high frequency detail images,
images;
LR
LR
LR
LR are the high frequency detail images,
which
captures
horizontal,
vertical
and
diagonal
directions,
respectively.
which captures horizontal, vertical and diagonal directions, respectively.
We chose the discrete stationary wavelet transform (
) over the discrete wavelet transform
We chose the discrete stationary wavelet transform (SWT) over the discrete wavelet transform
(
), as the
is computationally more efficient, shift invariant, and un-decimated (
(DWT), as the SWT is computationally more efficient, shift invariant, and un-decimated (SWT adjusts
adjusts the filters (up-sampling) at each level by padding them with zero in order to preserve the
the filters (up-sampling) at each level by padding them with zero in order to preserve the image size).
image size). To gain a greater flexibility in the construction of wavelet bases, we select a wavelet
To gain a greater flexibility in the construction of wavelet bases, we select a wavelet decomposition
decomposition filter from the biorthogonal wavelet family. The biorthogonal wavelet was selected
filter from the biorthogonal wavelet family. The biorthogonal wavelet was selected because of its
because of its symmetric capabilities, which is often desirable since it exhibits the property of linear
symmetric capabilities, which is often desirable since it exhibits the property of linear phase, which
phase, which is needed for image reconstruction. Another reason for using the biorthogonal wavelet
is needed for image reconstruction. Another reason for using the biorthogonal wavelet was that,
was that, rather than having one wavelet and one scaling function, biorthogonal wavelets have two
rather than having one wavelet and one scaling function, biorthogonal wavelets have two different
different wavelet functions and two scaling functions that may produce different multiresolution
wavelet functions and two scaling functions that may produce different multiresolution analyses. In
analyses. In addition, the biorthogonal wavelet has good compact support, smoothness and good
addition, the biorthogonal wavelet has good compact support, smoothness and good localization.
localization. We choose the fifth-order filter, which has a filter length of 12. The fifth-order filter was
We choose the fifth-order filter, which has a filter length of 12. The fifth-order filter was selected
selected to avoid distortions along the image boundary. Using
, the log-ratio image
is
to avoid distortions along the image boundary. Using SWT, the log-ratio image X LR is recursively
recursively decomposed into six resolution levels. Empirical analysis suggested six to be the optimum
decomposed into six resolution levels. Empirical analysis suggested six to be the optimum level for
level for multi-scale decomposition.
multi-scale decomposition.
To reduce computation time, we focused only on the lower resolution images LL per
To reduce computation time, we focused only on the lower resolution images X LR
per
decomposition level. Discarding the detail images is allowed as the information contents at a certain
decomposition level. Discarding the detail images is allowed as the information contents at a certain
resolution level are recovered at a higher level. Hence, the exclusion of the detail images does not
resolution level are recovered at a higher level. Hence, the exclusion of the detail images does not affect
affect the change detection approach. The final multi-scale decomposition
image stack then
the change detection approach. The final multi-scale decomposition X MS image stack then contains
contains the lower resolution images at each level, as below:
the lower resolution images at each level, as below:
(8)
..,
………..,
!=
)
K´1
k
X MS “ X 0LR .., X LR
. . . . . . . . . .., X LR
(8)
2.3.2. Classification by Expectation-Maximization (EM) Algorithm with Mathematical Morphology
2.3.2. Classification by Expectation-Maximization (EM) Algorithm with Mathematical Morphology
After the multi-scale decomposition, each decomposed image is inserted into a mathematical
After
theframework.
multi-scaleMathematical
decomposition,
each decomposed
into a mathematical
morphology
morphology
defines aimage
familyisofinserted
morphological
filters, which
morphology
framework.
Mathematical
morphology
defines
a
family
of
morphological
filters,
are nonlinear operators that aim at emphasizing spatial structures in a gray-level image.
Forwhich
more
details on mathematical morphology the reader is referred to [27]. Morphological filters are defined
by a structuring element ( ), which is based on a moving window of a given size and shape centered
( , ). In image processing, erosion
( , ) and dilation
( , ) are the basic
on a pixel
operators used, and are defined as follows [27]:
analyses. In wavelet addition, the biorthogonal wavelet has good compact support, smoothness and good . In addition, the contains the lower resolution images at each level, as below: biorthogonal has good compact support, smoothness and good Figure 3. Multi‐scale decomposition of input log‐ratio image into a lower resolution and detail ime, we focused only on wavelet the scaling lower resolution images per tion level are recovered at a higher level. Hence, the exclusion of the detail images does not different functions and that two scaling functions that may produce different multiresolution ent wavelet functions and two functions may produce different multiresolution localization. We choose the fifth‐order filter, which has a filter length of 12. The fifth‐order filter was ion. We choose the fifth‐order filter, which has a filter length of 12. The fifth‐order filter was We chose the discrete stationary wavelet transform (
) over the discrete wavelet transform
..,
………..,
(8)
images; is the lower resolution image and (
, decomposition ,
) are the high frequency detail images, g the detail images is allowed as the information contents at a certain the change detection approach. The final multi‐scale compact image stack analyses. In the addition, the has biorthogonal wavelet has good support, smoothness and good is ses. In addition, the biorthogonal wavelet good compact support, smoothness and good selected to avoid distortions along the image boundary. Using log‐ratio image to avoid distortions along image boundary. Using , the log‐ratio image then is , the (
), as the is computationally more efficient, shift invariant, and un‐decimated (
which captures horizontal, vertical and diagonal directions, respectively. t a higher level. Hence, the exclusion of the detail images does not ns the lower resolution images at each level, as below: localization. We choose the fifth‐order filter, which has a filter length of 12. The fifth‐order filter was zation. We choose the fifth‐order filter, which has a filter length of 12. The fifth‐order filter was recursively decomposed into six resolution levels. Empirical analysis suggested six to be the optimum ely decomposed into six resolution levels. Empirical analysis suggested six to be the optimum adjusts the filters (up‐sampling) at each level by padding them with zero in order to preserve th
then proach. The final multi‐scale decomposition image 2.3.2. Classification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology selected to avoid distortions along the stack image boundary. Using is ed to avoid distortions along the image boundary. Using , the log‐ratio image , the is log‐ratio image level for multi‐scale decomposition. multi‐scale decomposition. (8)
) over the discrete wavelet transform . . , size). … …To … .gain .,
image a greater flexibility in the construction of wavelet bases, we select a wavel
We chose the discrete stationary wavelet transform (
Remote
Sens.
2016,
8,
482
9 of 27
mages at each level, as below: recursively decomposed into six resolution levels. Empirical analysis suggested six to be the optimum sively decomposed into six resolution levels. Empirical analysis suggested six to be the optimum decomposition of input log‐ratio image into a lower resolution and detail To reduce computation time, we focused only on the lower resolution images per reduce computation time, we focused only on the lower resolution images per After the multi‐scale decomposition, each decomposed image is inserted into a mathematical decomposition filter from the biorthogonal wavelet family. The biorthogonal wavelet was selecte
(
), as the is computationally more efficient, shift invariant, and un‐decimated (
level for multi‐scale decomposition. or multi‐scale decomposition. wer resolution image and (
decomposition level. Discarding the detail images is allowed as the information contents at a certain osition level. Discarding the detail images is allowed as the information contents at a certain (8)
) are the high frequency detail images, . . , morphology framework. Mathematical morphology defines a family of morphological filters, which … … … . ,. , ,
because of its symmetric capabilities, which is often desirable since it exhibits the property of linea
adjusts the filters (up‐sampling) at each level by padding them with zero in order to preserve the Classification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology To time, reduce time, we focused only on images the lower resolution images per ontal, vertical and diagonal directions, respectively. To reduce computation we computation focused only on the lower resolution per resolution level are recovered at a higher level. Hence, the exclusion of the detail images does not on level are recovered at a higher level. Hence, the exclusion of the detail images does not are
nonlinear
operators
that
aimconstruction at emphasizing
spatial structures
a gray-level
image.
are nonlinear operators that aim at emphasizing spatial structures in a gray‐level image. For more phase, which is needed for image reconstruction. Another reason for using the biorthogonal wavel
image Remote Sens. 2016, 8, 482 size). To gain a greater flexibility in the of wavelet bases, we in
select a wavelet 9 of 27 For more
Remote Sens. 2016, 8, 482 decomposition level. Discarding the detail images is allowed as the information contents at a certain mposition level. Discarding the detail images is allowed as the information contents at a certain affect the change detection approach. The final multi‐scale decomposition image then 9 of 27 e decomposition filter from the biorthogonal wavelet family. The biorthogonal wavelet was selected change detection approach. The final multi‐scale decomposition image stack then After the multi‐scale decomposition, each decomposed image is inserted into a mathematical details on mathematical morphology the reader is referred to [27]. Morphological filters are defined details
on
mathematical
morphology
the reader
is referred
to [27].
Morphological
filters
arestack defined
was that, rather than having one wavelet and one scaling function, biorthogonal wavelets have tw
on‐Maximization (EM) Algorithm with Mathematical Morphology Remote Sens. 2016, 8, 482 9 of 27 ete stationary wavelet transform (
) over the discrete wavelet transform resolution level are recovered at a higher level. Hence, the exclusion of the detail images does not ution level are recovered at a higher level. Hence, the exclusion of the detail images does not Remote Sens. 2016, 8, 482 9 of 27 contains the lower resolution images at each level, as below: the lower resolution images at each level, as below: hology framework. Mathematical morphology defines a family of morphological filters, which , which is based on a moving window of a given size and shape centered by
a structuring
element
pSq,
which
isopening based
on
aand moving
window
of a given
size
and
shape
different wavelet functions two scaling functions that may produce different multiresolutio
because of its symmetric capabilities, which is often desirable since it exhibits the property of linear ,opening and closing , closing , and centered
The by a structuring element two morphological filters used are ,
and ,
, and The two morphological filters used are Remote Sens. 2016, 8, 482 9 of 27 computationally more efficient, shift invariant, and un‐decimated (
Remote Sens. 2016, 8, 482 affect approach. the change detection approach. decomposition The final multi‐scale decomposition image stack then the change detection The final multi‐scale image stack then mposition, each decomposed image is inserted into a mathematical nlinear operators that aim at emphasizing spatial structures in a gray‐level image. For more on a pixel , jq.
. In image processing, erosion ,…are .and dilation , jqq
are the basic jqq
pXcompact on a pixelthey are the concatenation of erosion and dilation. They are defined as follows: X LR pi,
In
processing,
are
the basic
analyses. In the wavelet has good support, smoothness goo
phase, which is needed for image reconstruction. Another reason for using the biorthogonal wavelet LR
LR
they are the concatenation of erosion and dilation. They are defined as follows: (8)
(8)
. . , pXused …pi,
…
.and
, , dilation
are biorthogonal . The . , image
……
…addition, . . , used erosion
, pi,
and closing , and , and two morphological filters opening 8, 482 2016, 8, 482 9 of 27 9 of 27 ampling) at each level by padding them with zero in order to preserve the and closing ,
, and The two morphological filters opening contains the lower resolution images at each level, as below: ns the lower resolution images at each level, as below: matical morphology defines a family of morphological filters, which Remote Sens. 2016, 8, 482 s on mathematical morphology the reader is referred to [27]. Morphological filters are defined operators used, and are defined as follows [27]: operators
used,
and
are
defined
as
follows
[27]:
localization. We choose the fifth‐order filter, which has a filter length of 12. The fifth‐order filter wa
was that, rather than having one wavelet and one scaling function, biorthogonal wavelets have two ,
and closing , and The two morphological are opening they are the concatenation of erosion and dilation. They are defined as follows: ,
and
two morphological filters used are opening , 9 of 27 greater flexibility in the construction of wavelet bases, we filters select used a The wavelet Remote Sens. 2016, 8, 482 they are the concatenation of erosion and dilation. They are defined as follows: Remote Sens. 2016, 8, 482 m at emphasizing spatial structures in a gray‐level image. For more Remote Sens. 2016, 8, 482 ,. . , distortions ,…, …the . different (11), the log‐ratio ructuring element , which is based on a moving window of a given size and shape centered , (8)
Using 9 of 27 (11)
(8)
.
.
,
…
.
,
.
.
,
…
…
…
selected to avoid along image boundary. image different wavelet functions and two scaling functions that may produce multiresolution ,
,
and and closing closing ,
,
, and , and morphological wo morphological filters filters used used are opening are opening they are the concatenation of erosion and dilation. They are defined as follows: they are the concatenation of erosion and dilation. They are defined as fo
,
,
,
∀
∈
,
(9)
m the biorthogonal wavelet family. The biorthogonal wavelet was selected 2.3.2. Classification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology ,
and (9)
closing ,
The pi,
two morphological filters used are opening assification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology ology the reader is referred to [27]. Morphological filters are defined Remote Sens. 2016, 8, 482 pixel ,
. In image processing, erosion ,
and dilation ,
are the basic pX
jqq
“
min
tX
pi,
jq
,
x
u
@
x
P
S
pi,
jq
,
,
(11)
s
s
Remote Sens. 2016, 8, 482 9 of 27 LR
LR
recursively decomposed into six resolution levels. Empirical analysis suggested six to be the optimum
analyses. In addition, the biorthogonal wavelet has opening good compact smoothness and good ,
, closing (11) , and 9 of 27 9 of he concatenation of erosion and dilation. They are defined as follows: ncatenation of erosion and dilation. They are defined as follows: , are and The two morphological filters are support, Remote Sens. 2016, 8, 482 Remote Sens. 2016, 8, 482 Remote Sens. 2016, 8, 482 Remote Sens. 2016, 8, 482 ,opening and , closing , and 9 of 27 The two morphological filters used are c capabilities, which is often desirable since it exhibits the property of linear , , 9 of 27 and closing The two used morphological filters used they are the concatenation of erosion and dilation. They are defined as follows: hich is based on a moving window of a given size and shape centered Remote Sens. 2016, 8, 482 9 of 27 ors used, and are defined as follows [27]: , , opening , 9 of 27 , (11) ,
,
(12)
After the multi‐scale decomposition, each decomposed image is inserted into a mathematical er the multi‐scale decomposition, each decomposed image is inserted into a mathematical level for multi‐scale decomposition. localization. We choose the fifth‐order filter, which has a filter length of 12. The fifth‐order filter was ,
,
(12)
Remote Sens. 2016, 8, 482 Remote Sens. 2016, 8, 482 9 of 27 ,
,
,
∀
∈
,
(10)
2.3.2. Classification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology they are the concatenation of erosion and dilation. They are defined as follows: Classification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology for image reconstruction. Another reason for using the biorthogonal wavelet they are the concatenation of erosion and dilation. They are defined as follows: ,
and closing ,
The two morphological filters used are opening they are the concatenation of erosion and dilation. They are defined as follows: ocessing, erosion ,
and dilation ,
are the basic pX
pi,
jqq
“
max
tX
pi,
jq
,
x
u
@
x
P
S
pi,
jq
(10)
Remote Sens. 2016, 8, 482 s
s
,
and closing ,
, and The two morphological filters used are opening LR
LR
, along ,
,, boundary. , computation (11) ,(11)
logy framework. Mathematical morphology defines a family of morphological filters, which To reduce time, we only on the lower images p
selected to avoid morphology framework. Mathematical morphology defines a family of morphological filters, which distortions the image Using , are the log‐ratio image is ,focused (12)
, closing , opening ∀ used used ∈ filters ,are (9)
, opening ,and closing and ,,, closing ,and and , resolution closing , ,and , and ,
, , and , an
The two The ,morphological two The morphological two The morphological two filters morphological filters used are opening filters opening used opening are ,
,
(12)
ving one wavelet and one scaling function, biorthogonal wavelets have two ,
and closing , and The two morphological filters used are they are the concatenation of erosion and dilation. They are defined as follows: The effect of opening on a gray‐level image tends to suppress regions that are brighter than the as follows [27]: The effect of opening on a gray‐level image tends to suppress regions that are brighter than the they are the concatenation of erosion and dilation. They are defined as follows: After the multi‐scale decomposition, each decomposed image is inserted into a mathematical After the multi‐scale decomposition, each decomposed image is inserted into a mathematical Remote Sens. 2016, 8, 482 9 of 27 , closing , p pX LR
are nonlinear operators that aim at emphasizing spatial structures in a gray‐level image. For more and , pi,
, , and The two morphological filters used are opening (11)
inear operators that aim at emphasizing spatial structures in a gray‐level image. For more , used , , p , pX LR, pi,
(11)
decomposition level. Discarding the detail images is allowed as the information contents at a certa
recursively decomposed into six resolution levels. Empirical analysis suggested six to be the optimum ,closing , jqqq,
, (12)
, jqqq
and , and The two morphological filters are opening The
two
morphological
filters
used
are
opening
and
closing
and
Remote Sens. 2016, 8, 482 9 of 27 they are the concatenation of erosion and dilation. They are defined as follows: they are the concatenation of erosion and dilation. They are defined as follows: they are the concatenation of erosion and dilation. They are defined as follows: they are the concatenation of erosion and dilation. They are defined as follows: ons and two scaling functions that may produce different multiresolution , to and closing ,
The two morphological filters used are opening they are the concatenation of erosion and dilation. They are defined as follows: surroundings while closing suppresses regions that are darker than the surroundings. In order surroundings while closing suppresses regions that are darker than the surroundings. In order to The effect of opening on a gray‐level image tends to suppress regions that are brighter than the morphology framework. Mathematical morphology defines a family of morphological filters, which hology framework. Mathematical morphology defines a family of morphological filters, which details on mathematical morphology the reader is referred to [27]. Morphological filters are defined n mathematical morphology the reader is referred to [27]. Morphological filters are defined The effect of opening on a gray‐level image tends to suppress regions that are brighter than the they are the concatenation of erosion and dilation. They are defined as follows: ,
,
,
∀
∈
,
resolution level are recovered at a higher level. Hence, the exclusion of the detail images does n
level for multi‐scale decomposition. (9)
,
,
,
,
(12)
(12)
,
,
,
∀
∈
,
ote Sens. 2016, 8, 482 9 of 27 (10)
they
are
the
concatenation
of
erosion
and
dilation.
They
are
defined
as
follows:
,
,
they are the concatenation of erosion and dilation. They are defined as follows: ,
,
,
,
(11)
he biorthogonal wavelet has good compact support, smoothness and good they are the concatenation of erosion and dilation. They are defined as follows: preserve the spatial structures of our original image, opening by reconstruction followed with closing closing , , and The two closing morphological filters used are opening preserve the spatial structures of our original image, opening by reconstruction followed with closing surroundings while closing suppresses regions In order The effect of opening on a gray‐level image tends to suppress regions that are brighter than the onlinear operators that aim at emphasizing spatial structures in a gray‐level image. For more , the ,The effect of opening on a gray‐level image tends to suppress region
,The , final , that are darker , images , , , and the surroundings. (11),to (11)
(11) to (1
by a structuring element , which is based on a moving window of a given size and shape centered cturing element , which is based on a moving window of a given size and shape centered surroundings while suppresses regions that are darker than In order than and closing and The two morphological filters affect the change detection approach. multi‐scale image the
To reduce are nonlinear operators that aim at emphasizing spatial structures in a gray‐level image. For more computation time, we focused on lower resolution ,decomposition per , ,only ,used (11)
, the surroundings. (12), stack , , are opening (12)
,
,
the fifth‐order filter, which has a filter length of 12. The fifth‐order filter was by reconstruction was applied. The sequence of first doing opening by reconstruction followed by ,
,
(11)
they are the concatenation of erosion and dilation. They are defined as follows: by reconstruction was applied. The sequence of first doing opening by reconstruction followed by preserve the spatial structures of our original image, opening by reconstruction followed with closing surroundings while closing suppresses regions that are darker than the surroundings. In order to effect of opening on a gray‐level image tends to suppress regions that are brighter than the of opening on a gray‐level image tends to suppress regions that are brighter than the ,
,
surroundings while closing suppresses regions that are darker than the
(11)
details on mathematical morphology the reader is referred to [27]. Morphological filters are defined s on mathematical morphology the reader is referred to [27]. Morphological filters are defined on a pixel ,
. In image processing, erosion ,
and dilation ,
are the basic ,
and closing ,
, and The two morphological filters used are opening el ,
. In image processing, erosion ,
and dilation ,
are the basic ,
,
,
∀
∈
,
pX
pi,
jqq
“
p
pX
pi,
jqqq
(11)
preserve the spatial structures of our original image, opening by reconstruction followed with closing The effect of opening on a gray‐level image tends to suppress regions that are brighter th
(10)
Remote Sens. 2016, 8, 482 they are the concatenation of erosion and dilation. They are defined as follows: contains the lower resolution images at each level, as below: decomposition level. Discarding the detail images is allowed as the information contents at a certain LR
, ,
, , rtions along the image boundary. Using , the log‐ratio image LR
is closing by reconstruction is reconstruction particularly designed to reduce noise in detection masks ,the surroundings. (12) without closing by is particularly designed to order reduce noise in without detection masks by reconstruction was applied. The sequence of first doing opening by reconstruction followed by preserve the spatial structures of our original image, opening by reconstruction followed with closing while ngs while closing closing suppresses regions suppresses regions that are darker that are darker than than the surroundings. In , order In to to preserve the spatial structures of our original image, opening by reconstru
by a structuring element , which is based on a moving window of a given size and shape centered The effect of opening on a gray‐level image tends to suppress regions that are brighter than the tructuring element , which is based on a moving window of a given size and shape centered The effect of opening on a gray‐level image tends to suppress regions that are brighter than the operators used, and are defined as follows [27]: by reconstruction was applied. The sequence of first doing opening by reconstruction followed by surroundings while closing suppresses regions that are darker or
y are the concatenation of erosion and dilation. They are defined as follows: The effect of opening on a gray‐level image tends to suppress regions that are bri
s used, and are defined as follows [27]: resolution level are recovered at a higher level. Hence, the exclusion of the detail images does not ,
,
,
,
,
,
,
,
than the surroundings. (12) (12)(11) (12)In (1
,achieving … . . , boundary , in , it , is [27]. (12)
d into six resolution levels. Empirical analysis suggested six to be the optimum .
.
,
…
…
incurring loss of details in mask outlines [27]. Hence, relevant for ,
,
(11) , (
incurring loss of details mask outlines Hence, it is relevant for achieving boundary closing by reconstruction is particularly designed to reduce noise in detection masks without by reconstruction was applied. The sequence of first doing opening by reconstruction followed by patial structures of our original image, opening by reconstruction followed with closing he spatial structures of our original image, opening by reconstruction followed with closing by reconstruction was applied. The sequence of first doing opening by on a pixel ,
. In image processing, erosion ,
and dilation ,
are the basic surroundings while closing suppresses regions that are darker than the surroundings. In order to ,
,
pixel ,
. In image processing, erosion ,
and dilation ,
are the basic pX
pi,
jqq
“
p
pX
pi,
jqqq
(12)
(12)
,
and closing The two morphological filters used are opening surroundings while closing suppresses regions that are darker than the surroundings. In order to LR
LR
,
,
(12)
closing by reconstruction is particularly designed to reduce noise in detection masks without preserve the spatial structures of our original image, opening by reconstruction followed with c
surroundings while closing suppresses regions that are darker than the surrounding
The effect of opening on a gray‐level image tends to suppress regions that are brighter
affect the change The effect of opening on a gray‐level image tends to suppress regions that are brighter than the detection approach. The , final decomposition image then ,
,∈
for achieving ,∈, particularly , reconstruction ,
∀
noise , stack (9)reduce ,closing , of multi‐scale ∀details (9)
omposition. preservation. The method requires an original image and a marker image. If the marker image ,reconstruction (11)
preservation. The method requires an original image and a marker image. If the marker image incurring loss in , closing mask outlines [27]. Hence, it is relevant boundary by is designed to relevant reduce in detection masks without truction was applied. The sequence of first doing opening by reconstruction followed by ion was applied. The sequence of first doing opening by reconstruction followed by The effect of opening on a gray‐level image tends to suppress regions that are brighter than the The effect of opening on a gray‐level image tends to suppress regions that are brighter than the The effect of opening on a gray‐level image tends to suppress regions that are brighter than the The effect of opening on a gray‐level image tends to suppress regions that are brighter than th
by is particularly designed to noise In
in
preserve the spatial structures of our original image, opening by reconstruction followed with closing operators used, and are defined as follows [27]: tors used, and are defined as follows [27]: they are the concatenation of erosion and dilation. They are defined as follows: preserve the spatial structures of our original image, opening by reconstruction followed with closing incurring loss of details in mask outlines [27]. Hence, it is for achieving boundary by reconstruction was applied. The sequence of first doing opening by reconstruction follow
preserve the spatial structures of our original image, opening by reconstruction followe
surroundings while closing suppresses regions that are darker than the surroundings. The effect of opening on a gray‐level image tends to suppress regions that are brighter than the contains the lower resolution images at each level, as below: surroundings while closing suppresses regions that are darker than the surroundings. In order to The
effect
of
opening
on
a
gray-level
image
tends
to
suppress
regions
that
are
brighter
than
the
The effect of opening on a gray‐level image tends to suppress regions that are brighter than the tation time, we focused only on the lower resolution images per ,
,
(12)
The effect of opening on a gray‐level image tends to suppress regions that are brighter than the ,
, and the is obtained after erosion has been initially applied to the original image preservation. The method requires an original image and a marker image. If the marker image incurring loss of details in mask outlines [27]. Hence, it is relevant for achieving boundary y construction reconstruction is particularly is particularly designed designed to reduce to reduce noise noise in detection in detection masks masks without without surroundings surroundings surroundings while surroundings while closing closing suppresses regions while while suppresses regions closing closing suppresses regions suppresses regions that are darker that are darker that are darker than that are darker the surroundings. than the surroundings. than the surroundings. than In the surroundings. order In order to In to order In order to incurring loss of details in mask outlines [27]. Hence, it is relevan
by reconstruction was applied. The sequence of first doing opening by reconstruction followed by 2.3.2. Classification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology
, detection , and the masks is obtained after erosion has been initially applied to the original image ,the surroundings. , In reduce (12) w
by reconstruction was applied. The sequence of first doing opening by reconstruction followed by preservation. The method requires an original image and a marker image. If the marker image closing by particularly in preserve the spatial structures of our original image, opening by reconstruction followed wit
surroundings while closing suppresses regions that are darker than to noise preserve the spatial structures of our original image, opening by reconstruction followed with closing ,…
,, darker
∈ designed , ,surroundings.
(9)
, while
,,. by reconstruction was applied. The sequence of first doing opening by reconstructio
∀ ,…∈regions
is , that are darker (9)
, ∀ than ∀than to order (10)
, while ,The effect of opening on a gray‐level image tends to suppress regions that are brighter th
∀reconstruction , that are darker surroundings
closing
suppresses
that
than
the
In
order
to
(10)
closing suppresses regions the surroundings. order to scarding the detail images is allowed as the information contents at a certain ,∈the surroundings. , In order (8)
,are
. it ,, relevant …∈for . to . ,preservation. The method requires an original image and a marker surroundings while closing suppresses regions In to preservation. The method requires an original image and a marker image. If the marker image loss of details of closing details in surroundings mask in mask outlines outlines [27]. [27]. Hence, Hence, it is is relevant achieving for achieving boundary boundary preserve the spatial structures of our original image, opening by reconstruction followed with closing preserve the spatial structures of our original image, opening by reconstruction followed with closing preserve the spatial structures of our original image, opening by reconstruction followed with closing preserve the spatial structures of our original image, opening by reconstruction followed with closin
closing by reconstruction is particularly designed to reduce noise in detection masks without ,
,
(12)
,
, and the is obtained after erosion has been initially applied to the original image original image is reconstructed by a series of iterative dilations of , then the resulting filter is by reconstruction is particularly designed reduce noise in detection masks without incurring loss of details in mask outlines [27]. Hence, it is relevant for achieving closing by reconstruction is particularly designed to reduce noise in detection m
by reconstruction was applied. The sequence of first doing opening by reconstruction foll
preserve the spatial structures of our original image, opening by reconstruction followed with closing surroundings while closing suppresses regions that are darker than the surroundings. or
original image is reconstructed by a series opening
of iterative dilations of followed
, then ,the , and the is obtained after erosion has been initially applied to the original image The effect of opening on a gray‐level image tends to suppress regions that are brighter than the by reconstruction was applied. The sequence of first doing opening by reconstruction followed by After the multi‐scale decomposition, each decomposed image is inserted into a mathematic
preserve
the spatial
structures
of our original
image,
by reconstruction
withresulting closing filter is In bou
preserve the spatial structures of our original image, opening by reconstruction followed with closing overed at a higher level. Hence, the exclusion of the detail images does not The effect of opening on a gray‐level image tends to suppress regions that are brighter than the preserve the spatial structures of our original image, opening by reconstruction followed with closing The method requires an original image and a marker on. The method requires an original image and a marker image. If the marker image image. If the marker image by reconstruction was applied. The sequence of first doing opening by reconstruction followed by by reconstruction was applied. The sequence of first doing opening by reconstruction followed by by reconstruction was applied. The sequence of first doing opening by reconstruction followed by by reconstruction was applied. The sequence of first doing opening by reconstruction followed b
incurring loss of details in mask outlines [27]. Hence, it is relevant for achieving boundary ,
, and the is obtained after erosion has been initially applied to the original image opening by reconstruction : incurring loss of details in mask outlines [27]. Hence, it is relevant for achieving boundary is obtained after erosion has been initially applied to the original image preservation. The method requires an original image and a marker image. If the marker
loss of in opening
mask [27]. Hence, it filter is the relevant for filter achiev
by is designed to masks reduce noise in is detection masks
by reconstruction was applied. The sequence of first doing opening by reconstruction followed by preserve the spatial structures of our original image, opening by reconstruction followed with c
opening by reconstruction : of
image is reconstructed by a ,doing
series iterative dilations of , without then resulting is ,sequence
, particularly ∀of ∈of outlines , detection surroundings while closing suppresses regions that are darker than the surroundings. In order to (10)
, original , incurring ,by ∀reconstruction details ∈ of ,stack (10)
by multi‐scale reconstruction is closing particularly to reduce noise in morphology framework. Mathematical morphology defines a family of morphological filters, whic
by
reconstruction
applied.
The
first
by
reconstruction
followed
by
original image is was
reconstructed a series iterative dilations , then the resulting The effect of opening on a gray‐level image tends to suppress regions that are brighter than the by reconstruction was applied. The sequence of first doing opening by reconstruction followed by tion approach. closing The final decomposition designed image then surroundings while suppresses regions that are darker than the surroundings. In masks order to by reconstruction was applied. The sequence of first doing opening by reconstruction followed by , noise ,in masks closing closing by reconstruction by closing reconstruction closing by reconstruction is by particularly reconstruction is closing particularly is designed particularly is designed particularly to reduce designed to reduce designed noise to reduce in masks to detection reduce in noise detection noise masks detection in without detection without masks without withou
preservation. The method requires an original image and a marker image. If the marker image 2.3.2. Classification by Expectation‐Maximization (EM) Algorithm with Mathematical Morphology ,
,
, and the , and the d after erosion has been initially applied to the original image er erosion has been initially applied to the original image preservation. The method requires an original image and a marker image. If the marker image preservation. The method requires an original image and a marker image. If the incurring loss of details in mask outlines [27]. Hence, it is relevant for achieving closing by reconstruction is particularly designed to reduce noise in detection without by reconstruction was applied. The sequence of first doing opening by reconstruction follow
opening by reconstruction : original image is reconstructed by a series of iterative dilations of , then the resulting filter is original image is reconstructed by a series of iterative dilations of preserve the spatial structures of our original image, opening by reconstruction followed with closing ,
, ab
is obtained after erosion has been initially applied to the original image incurring loss of details in mask outlines [27]. to
Hence, is relevant for achieving boundary are nonlinear operators that aim at emphasizing spatial structures in a gray‐level image. For mo
opening by reconstruction : designed
closing
by
reconstruction
is
particularly
reduce
noise
in
detection
masks
without
incurring
roundings while closing suppresses regions that are darker than the surroundings. In order to closing by reconstruction is in particularly designed to reduce noise in detection masks without ution images at each level, as below: preserve the spatial structures of our original image, opening by reconstruction followed with closing ,mask , it is ,[27]. (13)
closing by reconstruction is particularly designed to reduce noise in detection masks without ,
,
,
(13)
incurring incurring loss incurring of loss details incurring of details loss of mask loss in details of outlines details in outlines mask [27]. in mask outlines Hence, outlines Hence, it [27]. it relevant [27]. Hence, is relevant Hence, it for is achieving it relevant for is achieving relevant for boundary achieving for boundary achieving boundary boundar
,
, and the is obtained after erosion has been initially applied to the original image preservation. The method requires an original image and a marker 9 of 27 image. If the mark
incurring loss details in mask outlines [27]. Hence, it is relevant for filter achieving closing by reconstruction is particularly designed to reduce noise detection masks wf
, boundary is obtained after erosion has been initially applied to the original image opening by reconstruction : is
e mage is reconstructed is After the multi‐scale decomposition, each decomposed image is inserted into a mathematical reconstructed by of a by series a series of iterative of iterative dilations dilations of of , then , opening by reconstruction then the resulting the resulting filter is : , and the by reconstruction was applied. The sequence of first doing opening by reconstruction followed by is obtained after erosion has been initially applied to the original image Remote Sens. 2016, 8, 482 preservation. The method requires an original image and a marker image. If the marker image details on mathematical morphology the reader is referred to [27]. Morphological filters are define
loss
of
details
in
mask
outlines
[27].
Hence,
it
relevant
achieving
boundary
preservation.
original image is reconstructed by a series of is iterative dilations of in , then the resulting The effect of opening on a gray‐level image tends to suppress regions that are brighter th
serve the spatial structures of our original image, opening by reconstruction followed with closing incurring loss of details in in mask outlines [27]. Hence, it it is boundary by reconstruction was applied. The sequence of first doing opening by reconstruction followed by incurring loss of details mask outlines [27]. Hence, is relevant relevant for achieving boundary ,,for
, it is ,achieving (13)
preservation. The method requires an original image and a marker preservation. The method requires an original image and a marker preservation. The method requires an original image and a marker preservation. The method requires an original image and a marker for image. If the marker image image. If the marker image image. If the marker image image. If the marker imag
(8)
.
.
,
…
…
…
.
.
,
,
,
(13)
preservation. The method requires an original image and a marker image. If the marker image incurring loss of details in mask outlines [27]. Hence, relevant for achieving construction y reconstruction : : initially applies dilation to the original image, Moreover, closing by reconstruction original image is reconstructed by a series of iterative dilations of , then the resulting filter is closing by reconstruction is particularly designed to reduce noise in detection masks without ,bou
is obtained after erosion has been initially applied to the original image original is obtained after erosion has been initially applied to the original image image is reconstructed by a series of iterative dilations of q image.
, then resulting filter is : initially applies dilation the original image, Moreover, closing by reconstruction by a structuring element , which is based on a moving window of a given size and shape centere
morphology framework. Mathematical morphology defines a family of morphological filters, which opening by reconstruction p ,designed The method
requires
an
original
image
and
a marker
Ifthe marker
image
is
obtained
original image is reconstructed by to a series of noise iterative dilations of , without then the res
surroundings while closing suppresses regions that are darker than the surroundings. In , to , and the reconstruction was applied. The sequence of first doing opening by reconstruction followed by preservation. The method requires an original image and a marker the
image. If the marker image closing by reconstruction is particularly reduce in detection masks preservation. The method requires an original image and a marker image. If the marker image ,
,
(13)
,
,
or
,
,
, and the ,
, and the ,
, and the ,
, and th
is obtained after erosion has been initially applied to the original image is obtained after erosion has been initially applied to the original image is obtained after erosion has been initially applied to the original image is obtained after erosion has been initially applied to the original image ,
and closing ,
, and The two morphological filters used are opening preservation. The method requires an original image and a marker image. If the marker opening by reconstruction : then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: incurring loss of details in mask outlines [27]. Hence, it is relevant for achieving boundary ,
, and the is obtained after erosion has been initially applied to the original image opening by reconstruction : initially applies dilation to the original image, Moreover, closing by reconstruction on a pixel ,
. In image processing, erosion ,
and dilation ,
are the bas
then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: are nonlinear operators that aim at emphasizing spatial structures in a gray‐level image. For more opening by reconstruction : after
erosion
has
been
initially
applied
to
the
original
image
p
“
pX
pi,
jqqq,
and
the
original
original image is reconstructed by a series of iterative dilations of , then the resulting
preserve the spatial structures of our original image, opening by reconstruction followed with c
ing by reconstruction is particularly designed to noise in without LRis 9 of 27 loss details outlines [27]. masks Hence, it relevant for achieving boundary detection initially applies to resulting the , original image, Moreover, closing by reconstruction original image is reconstructed series iterative dilations of , dilation then the is , and the is obtained after erosion has been initially applied to the original image ,incurring ,
, in of mask ,of by , a , reduce (13)
,, then , and the is obtained after erosion has been initially applied to the original image ,(13)
,filter original image, , of Remote Sens. 2016, 8, 482 9 of 27 they are the concatenation of erosion and dilation. They are defined as follows: original original image image original is reconstructed original is image reconstructed image is reconstructed by of
is a iterative
reconstructed series by a series of by iterative of a series by iterative a dilations series of , iterative dilations of of iterative dilations of dilations of , reconstruction then , the then resulting the resulting , the filter the then resulting filter is the resulting is filter is dila
preservation. The method requires an original image and a marker dilation image. If the marker image , filter , an
is obtained after erosion has been initially applied to the original image xpectation‐Maximization (EM) Algorithm with Mathematical Morphology initially applies to Moreover, closing by reconstruction details on mathematical morphology the reader is referred to [27]. Morphological filters are defined then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: operators used, and are defined as follows [27]: initially applies Moreover, closing by opening by reconstruction : image
is
reconstructed
by
a
series
dilations
of
,
then
the
resulting
filter
is
opening
by
original is reconstructed by a series of iterative dilations of then the resulting filter is by reconstruction was applied. The sequence of first doing opening by reconstruction follow
urring loss of image details in mask outlines [27]. Hence, it is relevant for achieving boundary ens. 2016, 8, 482 9 of 27 preservation. The method requires an original image and a marker image. If the marker image opening by reconstruction then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: , , , the the (14)filter (13)
original image is reconstructed by a : ,a series of of iterative is is ,, of of , , , then ,, ,, dilations (13)
resulting (14)
original image is reconstructed by series iterative dilations , then resulting filter ,
,
opening by reconstruction opening by reconstruction opening by reconstruction opening by reconstruction : : : : : initially applies dilation dilation to by original image, the original image, r, closing over, closing by reconstruction by reconstruction , , then , and the is obtained after erosion has been initially applied to the original image by a structuring element , which is based on a moving window of a given size and shape centered then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: ,original Moreover, closing and closing , to , and ogical filters used are opening opening by reconstruction qq:
reconstruction
p p initially applies image is reconstructed by a series of iterative of dilation the resulting fi
closing by reconstruction particularly to dilations reduce noise in detection masks w
then reconstructs the original image by applying a series of iterative eros
servation. The method requires an original image and a marker is image. If the marker image to the original i
reconstruction ,the , designed , and the is obtained after erosion has been initially applied to the original image le decomposition, each decomposed image is inserted into a mathematical , t, , and , , initially applies , , (11)
opening by reconstruction Remote Sens. 2016, 8, 482 Remote Sens. 2016, 8, 482 9 of 27
closing The two morphological filters used , ∀ , , ∈ , , ,and (14) (
opening by reconstruction : opening ,are the basic t : are ,
,
,
,
,
,
(14)
(13)
on a pixel ,
. In image processing, erosion ,
and dilation nstructs the original image by applying a series of iterative erosion. The resulting filter is: cts the original image by applying a series of iterative erosion. The resulting filter is: ,
and closing ,
, and e two morphological filters used are opening opening by reconstruction ploss pi,
jqqq
“, mint
,reconstruction (13)
incurring of by in Hence, is relevant for dilation achieving bou
tion of erosion and dilation. They are defined as follows: pX
of . It is worth mentioning that in this Both filtering processes stop when : outlines initially applies dilation to the original image, Moreover, closing by reconstruction details initially applies the Moreover, closing by image reconstruction LR
LR
original is reconstructed series iterative the filter is to mask Xdilation pi,
dilations Both filtering processes stop when it initially applies the o
Moreover, closing by then reconstructs the original image by applying a series of iterative erosion. The resulting filt
,,jquto , and the btained after erosion has been initially applied to the original image . Mathematical morphology defines a family of morphological filters, which ,a by , dilations [27]. ,, . It is worth mentioning that in this original image, (13)
, resulting ,of , ,, then (13)
(13)
original image is reconstructed , , then the (13)
resulting is they are the concatenation of erosion and dilation. They are defined as follows: , of (14)
, (1
,filter ,
, , of , ,iterative , a series operators used, and are defined as follows [27]: preservation. The method requires an original image and a marker image. If the marker e the concatenation of erosion and dilation. They are defined as follows: paper, we used a fixed square shape ,
with a size of 20 × 20 pixels. From an analysis of a broad ,
,
,
then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: (13)
opening by reconstruction : then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: paper, we used a fixed square shape with a size of 20 × 20 pixels. From an analysis of a broad dilation Both filtering processes stop when ,. It is worth mentioning that in this filter , resulting initially applies dilation by reconstruction then reconstructs the original image by applying a series of iterative erosion. The resul
, the , toto ,the
∀,. It is worth mentioning that in this (13)
∈
, closing (1
,and and closing , origin
, , and
The two The morphological two morphological filters used used are opening are that aim at emphasizing spatial structures in a gray‐level image. For more ginal image is reconstructed by a closing
of reconstruction iterative , then is the filters (11)
Both filtering processes stop when initially applies original image, Moreover, closing ,dilation
qq,, : initially
Moreover,
by
applies
original
image,
then
(12) to the , opening by reconstruction ,series , p p, of , Moreover, closing , , dilations (14)
(14)
,Moreover, closing , by reconstruction
,,opening ,original image, ,original image, , to the , the initially applies dilation initially applies initially applies dilation initially applies dilation to the to dilation dilation to original image, the original imag
Moreover, closing Moreover, closing by Moreover, closing reconstruction by reconstruction by reconstruction by reconstruction range of data from different change detection projects, we found (1) that most consistent results were ,
,
(11)
,
, an
is obtained after erosion has been initially applied to the original image range of data from different change detection projects, we found (1) that most consistent results were paper, we used a fixed square shape ,
with a size of 20 × 20 pixels. From an analysis of a broad . It is worth mentioning that in this Both filtering processes stop when initially applies to the original image, Moreover, closing by reconstruction . It is w
Both filtering processes stop when then reconstructs the original image by applying a series of iterative erosion. The resulting morphology the reader is referred to [27]. Morphological filters are defined they are the concatenation of erosion and dilation. They are defined as follows: they are the concatenation of erosion and dilation. They are defined as follows: ∀series
, , erosion.
ning by reconstruction (9)
paper, we used a fixed square shape then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: reconstructs
the: original
image
by applying
The, to resulting
filter
, ,by ,, iterative
the , (11)
∈initially applies dilation original image, Moreover, closing reconstruction , , , ,, awith a size of 20 × 20 pixels. From an analysis of a broad , of
(14) is:,
(13) (13)
dilation to the Moreover, closing by reconstruction , (14)
then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: achieved with a 20 pixel window; and (2) that change detection performance changed slowly with , a series of , dilations original image, , ,initially applies The effect of opening on a gray‐level image tends to suppress regions that are brighter than the achieved with a 20 pixel window; and (2) that change detection performance changed slowly with range of data from different change detection projects, we found (1) that most consistent results were paper, we used a fixed square shape ,initially applies with a size of 20 × 20 pixels. From an analysis of a broad then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: then reconstructs the original image by applying a series of iterative erosion. The resulting filter is:
original Moreover, closing image . It is worth mentioning that in this . It is worth mentioning that in this ring processes stop when paper, we used a fixed square shape , . It is worth mentioning that with a size of 20 × 20 pixels. F
dilation to the original ifi
by reconstruction then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: t filtering processes stop when , which is based on a moving window of a given size and shape centered is reconstructed by iterative of , then the resulting range of data from different change detection projects, we found (1) that most consistent results were Both filtering processes stop when then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: ,
,
(12)
,
,
,
then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: ,
,
,
,
(11)
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice t
t
,
,
,
(13)
,
,
,
(14)
surroundings while closing suppresses regions that are darker than the surroundings. In order to achieved with a 20 pixel window; and (2) that change detection performance changed slowly with d a fixed square shape used a fixed square shape ,deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice range of data from different change detection projects, we found (1) that most consistent results were with a size of 20 × 20 pixels. From an analysis of a broad ,Both filtering processes stop when ,with a size of 20 × 20 pixels. From an analysis of a broad ,pi,
, . It is worth mentioning that in this , then reconstructs the original image by applying a series of iterative erosion. The resulting filte
Remote Sens. 2016, 8, 482 Remote Sens. 2016, 8, 482 9 of 27 ,LR,pi,
, ,, X ,: LR
mage processing, erosion and dilation , jqqq
are the basic opening by reconstruction p reconstruction pX
“, maxt
(14)
∀
∈ . It is worth mentioning that in this Both filtering processes stop when initially applies Moreover, closing by achieved with a 20 pixel window; and (2) that change detection performance changed slowly with paper, we used a fixed square shape , ,initially applies with a size of 20 × 20 pixels. From an analysis of a
dilation original image, . It is worth mentioni
Both filtering processes stop when , range of data from different change detection projects, we found (1) that m
,jqu
9 of 27 ,to the (12)
, dilation , ,(10)
(14)
(14)
(14) (1
to the original image, Moreover, closing by reconstruction ,
,
(12)
,
,
,
(14)
of the window size is not critical for change detection success. The new multi‐scale decomposition preserve the spatial structures of our original image, opening by reconstruction followed with closing of the window size is not critical for change detection success. The new multi‐scale decomposition deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice achieved with a 20 pixel window; and (2) that change detection performance changed slowly with rom different change detection projects, we found (1) that most consistent results were ata from different change detection projects, we found (1) that most consistent results were paper, we used a fixed square shape , with a size of 20 × 20 pixels. From an analysis of a broad , , achieved with a 20 pixel window; and (2) that change detection perform
, , , with a size of 20 × 20 pixels. From an analy
, ,
(14)
defined as follows [27]: paper, we used a fixed square shape with a size of 20 × 20 pixels. From an analysis of a broad then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: ing on a gray‐level image tends to suppress regions that are brighter than the (14)
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice range of data from different change detection projects, we found (1) that most consistent result
paper, we used a fixed square shape . It is worth mentioning th
, Both filtering processes stop when initially applies original image, Moreover, closing by reconstruction dilation t to the . It is worth mentioning that in this Both filtering processes stop when then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: ,is
, in this
,,, and t “
t´
1 and
t´
1closing ,
The effect of opening on a gray‐level image tends to suppress regions that are brighter than the stack now contains morphological filtered images at each level in , as below: by reconstruction was applied. The sequence of first doing opening by reconstruction followed by ,
,
,
,
,
and closing and ,
, ,
and The two The morphological two morphological filters filters used used are opening are opening Both
filtering
processes
stop
when
“
.
It
worth
mentioning
that
(12)
stack now contains morphological filtered images at each level in , as below: of the window size is not critical for change detection success. The new multi‐scale decomposition deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice with a 20 pixel window; and (2) that change detection performance changed slowly with a 20 pixel window; and (2) that change detection performance changed slowly with . It is worth mentioning that in this . It is worth mentioning that in this . It is worth mentioning that in this . It is worth mentioning that in th
Both filtering processes stop when Both filtering processes stop when Both filtering processes stop when Both filtering processes stop when deviation from the 20 pixel setting. Hence, while 20 pixels was found to range of data from different change detection projects, we found (1) that most consistent results were range of data from different change detection projects, we found (1) that most consistent results were osing suppresses regions that are darker than the surroundings. In order to e effect of opening on a gray‐level image tends to suppress regions that are brighter than the of the window size is not critical for change detection success. The new multi‐scale decomposition achieved with a 20 pixel window; and (2) that change detection performance changed slowl
range of data from different change detection projects, we found (1) that most consisten
paper, we used a fixed square shape ,
with a size of 20 × 20 pixels. From an analysis o
. It is worth mentioning that in this Both filtering processes stop when n reconstructs the original image by applying a series of iterative erosion. The resulting filter is: , with a size of 20 × 20 pixels. From an analysis of a broad , paper, we used a fixed square shape ,
,
∀
∈
,
(9)
. It is worth mentioning that in this Both filtering processes stop when surroundings while closing suppresses regions that are darker than the surroundings. In order to ,
,
,
(14)
. It is worth mentioning that in this Both filtering processes stop when closing by is particularly designed to ,ˆreduce noise detection masks without paper,
we
used
areconstruction fixed
square
shape
S. .pi,
size
20
pixels.
From
an
analysis. It is worth mentioning that of, as below: a broad
they are the concatenation of erosion and dilation. They are defined as follows: they are the concatenation of erosion and dilation. They are defined as follows: stack now contains morphological filtered images at each level in of the window size is not critical for change detection success. The new multi‐scale decomposition m the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice paper, we used a fixed square shape paper, we used a fixed square shape paper, we used a fixed square shape , jq with
with a size of 20 × 20 pixels. From an analysis of a broad , …by a…with a size of 20 × 20 pixels. From an analysis of a broad with a size of 20 × 20 pixels. From an analysis of a broad with a size of 20 × 20 pixels. From an analysis of a broa
achieved with a 20 pixel window; and (2) that change detection performance changed slowly with , in (14)
achieved with a 20 pixel window; and (2) that change detection performance changed slowly with uctures of our original image, opening by reconstruction followed with closing ndings while closing suppresses regions that are darker the surroundings. order paper, we used a fixed square shape stack now contains morphological filtered images at each level in deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact achieved with a 20 pixel window; and (2) that change detection performance change
range of data from different change detection projects, we found (1) that most consistent res
paper, we used a fixed square shape ,Both filtering processes stop when with a size of 20 × 20 pixels. From an analysis of a broad , than …of the window size is not critical for change detection success. The new
.reconstruction . , ,of. . 20
, as below: initially applies dilation to the Moreover, closing (15)original i
, (15)
,, …In ……
. . , to range of data from different change detection projects, we found (1) that most consistent results were The effect of opening on a gray‐level image tends to suppress regions that are brighter than the
The effect of opening on a gray‐level image tends to suppress regions that are brighter tha
paper, we used a fixed square shape , , outlines with a size of 20 × 20 pixels. From an analysis of a broad preserve the spatial structures of our original image, opening by reconstruction followed with closing paper, we used a fixed square shape with a size of 20 × 20 pixels. From an analysis of a broad incurring loss of details in mask [27]. Hence, it is relevant for achieving boundary range
of
data
from
different
change
detection
projects,
we
found
(1)
that
most
consistent
results
were
stack now contains morphological filtered images at each level in , as below: w size is not critical for change detection success. The new multi‐scale decomposition ndow size is not critical for change detection success. The new multi‐scale decomposition range of data from different change detection projects, we found (1) that most consistent results were range of data from different change detection projects, we found (1) that most consistent results were range of data from different change detection projects, we found (1) that most consistent results were range of data from different change detection projects, we found (1) that most consistent results we
stack now contains morphological filtered images at each level in deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice ,
,
,
(14)
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice applied. The sequence of first doing opening by reconstruction followed by e the spatial structures of our original image, opening by reconstruction followed with closing of the window size is not critical for change detection success. The new multi‐scale decompo
range of data from different change detection projects, we found (1) that most consistent results were paper, we used a fixed square shape with a size of 20 × 20 pixels. From an analysis of a then reconstructs the original image by applying a series of iterative erosion. The resulting filte
…
(15)
(11)
…. It is worth mentioning that in this … . . . It is worth mentioning that in this , (11)
,The importance of opening and closing by reconstruction is that it filters out darker and brighter , Both filtering processes stop when , surroundings ∀ surroundings , while ∈ achieved with a 20 pixel window; and (2) that change detection performance changed slo
(10)
achieved with a 20 pixel window; and (2) that change detection performance changed slowly with , , deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, th
, suppresses regions …… . . , . ,. , that are darker while closing closing than the surroundings. than the surroundings. In order In ord
to
range of data from different change detection projects, we found (1) that most consistent results were (15)
. . , , suppresses regions by reconstruction was applied. The sequence of first doing opening by reconstruction followed by …that are darker Both filtering processes stop when range of data from different change detection projects, we found (1) that most consistent results were The importance of opening and closing by reconstruction is that it filters out darker and brighter preservation. The method requires an original image and a marker image. If the marker image achieved
with
a reduce 20
pixelrange of data from different change detection projects, we found (1) that most consistent results
window;
and (2) that
change
detection
performance
changed slowly with
w contains morphological filtered images at each level in now contains morphological filtered images at each level in , as below: , as below: achieved with a 20 pixel window; and (2) that change detection performance changed slowly with achieved with a 20 pixel window; and (2) that change detection performance changed slowly with achieved with a 20 pixel window; and (2) that change detection performance changed slowly with achieved with a 20 pixel window; and (2) that change detection performance changed slowly wi
of the window size is not critical for change detection success. The new multi‐scale decomposition of the window size is not critical for change detection success. The new multi‐scale decomposition tion is particularly designed to noise in detection masks without nstruction was applied. The sequence of first doing opening by reconstruction followed by stack now contains morphological filtered images at each level in , as below: of the window size is not critical for change detection success. The new multi‐scale d
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exa
achieved with a 20 pixel window; and (2) that change detection performance changed slowly with paper, we used a fixed square shape ,
with a size of 20 × 20 pixels. From an analysis of a broad (15)
.
.
,
…
…
…
.
.
,
.
.
,
…
…
…
.
.
,
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice preserve the spatial structures of our original image, opening by reconstruction followed with closing
particularly Hence,
while
. It is worth mentioning that in this Both filtering processes stop when achieved with a 20 pixel window; and (2) that change detection performance changed slowly with elements smaller than , while preserving the original boundaries of structures in our image. closing by is obtained after erosion has been initially applied to the original image reconstruction is preserve the spatial structures of our original image, opening by reconstruction followed with cl
to reduce noise in ,to
detection masks without , with a size of 20 × 20 pixels. From an analysis of a broad achieved with a 20 pixel window; and (2) that change detection performance changed slowly with elements smaller than , designed , while preserving the original boundaries of structures in our image. The importance of opening and closing by reconstruction is that it filters out darker and brighter deviation
from
the, designed 20
pixel
setting.
pixels
was
found
be optimal,
the
of
, ,choice
, and the , exact
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choic
paper, we used a fixed square shape stack now contains morphological filtered images at each level in , as below: The importance of opening and closing by reconstruction is that it filters out darker and brighter stack now contains morphological filtered images at each level in , as below: ails mask outlines [27]. Hence, it is relevant for achieving boundary by in reconstruction is deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice particularly to reduce noise in 20detection masks without stack now contains morphological filtered images at each level in , as below: of the window size is not critical for change detection success. The new multi‐scale decom
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice achieved with a 20 pixel window; and (2) that change detection performance changed slowly
range of data from different change detection projects, we found (1) that most consistent results were (15)
(15)
.
.
,
.
.
,
…
…
…
…
.
…
.
,
…
.
.
,
of the window size is not critical for change detection success. The new multi‐scale decomposition by reconstruction was applied. The sequence of first doing opening by reconstruction followed by
by reconstruction was applied. The sequence of first doing opening by reconstruction followe
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice er, we used a fixed square shape ,
with a size of 20 × 20 pixels. From an analysis of a broad Note that morphological filtering leads to a quantization of the gray‐value space such that each image X
.
.
,
…
…
…
.
.
,
incurring loss of details in mask outlines [27]. Hence, it is relevant for achieving boundary range of data from different change detection projects, we found (1) that most consistent results were ,
,
,
,
(12)
(12)
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice Note that morphological filtering leads to a quantization of the gray‐value space such that each image elements smaller than ,
, while preserving the original boundaries of structures in our image. The importance of opening and closing by reconstruction is that it filters out darker and brighter The importance of opening and closing by reconstruction is that it fil
the
window
size
is
not
critical
for
change
detection
success.
The
new
multi-scale
decomposition
of the window size is not critical for change detection success. The new multi‐scale decomposition of the window size is not critical for change detection success. The new multi‐scale decomposition of the window size is not critical for change detection success. The new multi‐scale decomposition of the window size is not critical for change detection success. The new multi‐scale decompositio
MD
,
, while preserving the original boundaries of structures in our image. original image is reconstructed by a series of iterative dilations of , then the resulting filter is hod requires an original image and a marker image. If the marker image ng loss of details elements smaller than in mask outlines [27]. Hence, it is relevant for achieving boundary stack now contains morphological filtered images at each level in , as below: of the window size is not critical for change detection success. The new multi‐scale decomposition deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact c
achieved with a 20 pixel window; and (2) that change detection performance changed slowly with stack now contains morphological filtered images at each level in (15)masks th .detection . .reduce . . , designed ………
. . , to , as below: closing closing by Both filtering processes stop when reconstruction by reconstruction particularly designed reduce to noise noise in detection wi
, while preserving the original boundaries …(15)
. It is worth mentioning that . ,. , , while preserving the original boundaries of structures in our image. …is …particularly …at
.is . ,each
th without
ge of data from different change detection projects, we found (1) that most consistent results were in preservation. The method requires an original image and a marker of the window size is not critical for change detection success. The new multi‐scale decomposition can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
masks ,, as below: …
…
. , in image. If the marker image achieved with a 20 pixel window; and (2) that change detection performance changed slowly with of the window size is not critical for change detection success. The new multi‐scale decomposition in Note that morphological filtering leads to a quantization of the gray‐value space such that each image can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
elements smaller than mportance of opening and closing by reconstruction is that it filters out darker and brighter rtance of opening and closing by reconstruction is that it filters out darker and brighter elements smaller than , below:
stack
now
contains
morphological
filtered
images
level , as below: in X MS
, as
opening by reconstruction stack now contains morphological filtered images at each level in stack now contains morphological filtered images at each level in stack now contains morphological filtered images at each level in of the window size is not critical for change detection success. The new multi‐scale decompo
stack now contains morphological filtered images at each level in , as below: , as below: , as below: Note that morphological filtering leads to a quantization of the gray‐value space such that each image The importance of opening and closing by reconstruction is that it filters out darker and br
: vation. The method requires an original image and a marker image. If the marker image stack now contains morphological filtered images at each level in ,
, and the n has been initially applied to the original image deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice The effect of opening on a gray‐level image tends to suppress regions that are brighter than the The effect of opening on a gray‐level image tends to suppress regions that are brighter than the incurring incurring loss of loss details of details in mask in mask outlines outlines [27]. [27]. Hence, Hence, it relevant is for for achieving boundary
boun
, with a size of 20 × 20 pixels. From an analysis of a th stack now contains morphological filtered images at each level in , as below: ieved with a 20 pixel window; and (2) that change detection performance changed slowly with , a lossless normalization is applied, leading to a float value between 0 and 255, such that: achieving . ., as below: , it is …
…, and the . . ,relevant deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice stack now contains morphological filtered images at each level in level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: in paper, we used a fixed square shape can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
Note that morphological filtering leads to a quantization of the gray‐value space such that each image smaller than ler than level in , The importance of opening and closing by reconstruction is that it filters out darker and brighter , while preserving the original boundaries of structures in our image. , in , while preserving the original boundaries of structures in our image. , …
is obtained after erosion has been initially applied to the original image (15)
th The importance of opening and closing by reconstruction is that it filters out darker and brighter . Note that morphological filtering leads to a quantization of the gray‐value
.,
……..,
!that are darker )
of the window size is not critical for change detection success. The new multi‐scale decomposition can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
elements smaller than ,…
, while preserving the original boundaries of structures in our i
The importance of opening and closing by reconstruction is that it filters out darke
stack now contains morphological filtered images at each level in , as below: ,
, and the ned after erosion has been initially applied to the original image surroundings surroundings while while closing closing suppresses regions suppresses regions that are darker than the surroundings. than the surroundings. In order In order to to (15)
(15)
(15)
(1
.
.
,
.
.
…
,
…
…
…
.
.
.
…
,
.
,
…
.
.
,
.
…
,
…
…
…
.
.
…
,
…
.
.
,
nstructed by a series of iterative dilations of , then the resulting filter is preservation. The method requires an original image and a marker preservation. The method requires an original image and a marker image. If the marker image
image. If the marker i
range of data from different change detection projects, we found (1) that most consistent results
K
´
1
0
k
th
iation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice (15)
.
.
,
…
…
…
.
.
,
of the window size is not critical for change detection success. The new multi‐scale decomposition , dilations , the resulting filter is (15)
level in phological filtering leads to a quantization of the gray‐value space such that each image morphological filtering leads to a quantization of the gray‐value space such that each image Xa MD
X MD
..,
. . can be normalized into the gray‐value range of [0, 255] without lo
. . .…. ..,.. ,.of .., X ,MD
(15) (13)
,“ , while preserving the original boundaries of structures in our image. elements smaller than , can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
, while preserving the original boundaries of structures in our image. original image elements smaller than is in reconstructed by , a lossless normalization is applied, leading to a float value between 0 and 255, such that: series of iterative , then level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: Note that morphological filtering leads to a quantization of the gray‐value space such that each
elements smaller than The importance of opening and closing by reconstruction is that it filters out darker and
. in . .X
, . ,MD
…
(15)
……the … …55 . . , while preserving the original boundaries of structures ,
The importance of opening and closing by reconstruction is that it filters out darker and brighter stack now contains morphological filtered images at each level in , as below: preserve the spatial structures of our original image, opening by reconstruction followed with closing preserve the spatial structures of our original image, opening by reconstruction followed with closing tion : l image is reconstructed by a series of iterative dilations of , then resulting filter is achieved with a 20 pixel window; and (2) that change detection performance changed slowly
th . .th, he window size is not critical for change detection success. The new multi‐scale decomposition … … … . . , (16)
, (16) , and the
,
, an
is obtained after erosion has been initially applied to the original image is obtained after erosion has been initially applied to the original image stack now contains morphological filtered images at each level in , as below: 55 level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: normalized into the gray‐value range of [0, 255] without loss of information. At the k
n be normalized into the gray‐value range of [0, 255] without loss of information. At the k
The importance of opening and closing by reconstruction is that it filters out darker and brighter The importance of opening and closing by reconstruction is that it filters out darker and brighter The importance of opening and closing by reconstruction is that it filters out darker and brighter The importance of opening and closing by reconstruction is that it filters out darker and bright
level in , , while preserving the original boundaries of structures in ou
, a lossless normalization is applied, leading to a float value b
Note that morphological filtering leads to a quantization of the gray‐value space such that each image Note that morphological filtering leads to a quantization of the gray‐value space such that each image opening by reconstruction : Note that morphological filtering leads to a quantization of the gray‐value space such th
in can be normalized into the gray‐value range of [0, 255] without loss of information. At The importance of opening and closing by reconstruction is that it filters out darker and brighter elements smaller than , elements smaller than , while preserving the original boundaries of structures in our image. by reconstruction was applied. The sequence of first doing opening by reconstruction followed by by reconstruction was applied. The sequence of first doing opening by reconstruction followed by initially applies dilation to the original image, Moreover, closing by reconstruction g by reconstruction : The importance of opening and closing by reconstruction is that it filters out darker and brighter deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact lossless normalization is applied, leading to a float value between 0 and 255, such that: stack now contains morphological filtered images at each level in , as below: The importance of opening and closing by reconstruction is that it filters out darker and brighter th
55 of th
The
importance
opening
and
closing
by, reconstruction
is
that
filters
out
darker
brighter
dilations .(13)
, a . .series ……
…
.it
. ,iterative , a lossless normalization is applied, leading to a float value between 0 and 255, such that: elements smaller than elements smaller than elements smaller than elements smaller than ,,image , while preserving the original boundaries of structures in our image. , while preserving the original boundaries of structures in our image. , reconstructed , while preserving the original boundaries of structures in our image. , while preserving the original boundaries of structures in our imag
original is reconstructed is by a .series by iterative , then , the then resulting the (15)
resulting filter is
in can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
(15)
(16)fil
in Note that morphological filtering leads to a quantization of the gray‐value space such that each image can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
55 level in , a lossless normalization is applied, leading to a float value between 0 and 255, suc
in can be normalized into the gray‐value range of [0, 255] without loss of informa
Note that morphological filtering leads to a quantization of the gray‐value space such that ea
elements smaller than , while preserving the original boundaries of structures in our image. The importance of opening and closing by reconstruction is that it filters out darker and br
,then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: ,image , oforiginal of and
, of …of …
… . .dilations , without (16)
closing closing by reconstruction by reconstruction is ,particularly is particularly designed designed to reduce to reduce noise noise in detection in detection masks masks without elements smaller than , ,jq,
, while preserving the original boundaries of structures in our image. of the window size is not critical for change detection success. The new multi‐scale decompo
,
,
,
(13)
elements smaller than , while preserving the original boundaries of structures in our image. 55 elements
smaller
than
S
pi,
while
preserving
the
original
boundaries
of
structures
in
our
image.
Note
55 Note that morphological filtering leads to a quantization of the gray‐value space such that each image Note that morphological filtering leads to a quantization of the gray‐value space such that each image Note that morphological filtering leads to a quantization of the gray‐value space such that each image Note that morphological filtering leads to a quantization of the gray‐value space such that each imag
opening by reconstruction opening by reconstruction : : level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: After the mathematical morphology the posterior probability one “no‐
level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: (15) of level in , a lossless normalization is applied, leading to a float value between 0 and in …
can be normalized into the gray‐value range of [0, 255] without loss of information. Note that morphological filtering leads to a quantization of the gray‐value space such that each image elements smaller than , step, , while preserving the original boundaries of structures in our i
it . .outlines , [27]. …step, …morphology . we . , Hence, ,the , calculate ,[27]. After mathematical we calculate the posterior probability of one “no‐(16)
th
(13)boundary in of can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
th, as below: incurring incurring loss of loss details details in The importance of opening and closing by reconstruction is that it filters out darker and brighter mask in mask outlines Hence, it is relevant is relevant for achieving for achieving boundary Note that morphological filtering leads to a quantization of the gray‐value space such that each image leads
stack now contains morphological filtered images at each level in The importance of opening and closing by reconstruction is that it filters out darker and brighter th th Note that morphological filtering leads to a quantization of the gray‐value space such that each image initially applies dilation to the original image, g by reconstruction 55 55 that morphological
filtering
to
a
quantization
of
the
gray-value
space
such
that
each
image
in
in in can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
in in can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
th change” and potentially several “change” classes at every one of the resolution levels, resulting in (16)
(16)
,
,
,
(14) of 55 level in , a lossless normalization is applied, leading to a float value between 0 and 255, s
in can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
Note that morphological filtering leads to a quantization of the gray‐value space such that each change” and potentially several “change” classes at every one of the resolution levels, resulting in After the morphology mathematical step, we calculate the posterior probability one “no‐
elements smaller than , , while preserving the original boundaries of structures in our image. morphology initially applies dilation to the original image, Moreover, closing by reconstruction level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: th th
preservation. The method requires an original image and a marker preservation. The method requires an original image and a marker image. If the marker image , image. If the marker image After the mathematical step, we calculate the posterior probability of one “no‐
,
,
,
,
,
(13)
in can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
The importance of opening and closing by reconstruction is that it filters out darker and brighter th
elements smaller than ,
, while preserving the original boundaries of structures in our image. in can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
The initially applies dilation to the original image, oreover, closing by reconstruction riginal image by applying a series of iterative erosion. The resulting filter is: X MD
can be
normalized
into
the
gray-value
range
ofassumed [0,
255]
without
of
information.
At the
kcalculate level in level in level in level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: , a lossless normalization is applied, leading to a float value between 0 and 255, such that: , a lossless normalization is applied, leading to a float value between 0 and 255, such that: , a lossless normalization is applied, leading to a float value between 0 and 255, such tha
55 55 posterior probabilities per pixel. various classes are to calculate be a loss
mixture of Gaussian . . , the …
…
. . , a (16)
55 (16)
level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: in can be normalized into the gray‐value range of [0, 255] without loss of information. At posterior probabilities per pixel. The various classes are assumed to …
be mixture Gaussian change” and potentially several “change” classes at every one of the resolution levels, resulting in After the mathematical morphology step, we posterior probability of one “no‐
After the mathematical morphology step, we of the poster
Note that morphological filtering leads to a quantization of the gray‐value space such that each image then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: change” and potentially several “change” classes at every one of the resolution levels, resulting in ,
, and the ,
, and the is obtained after erosion has been initially applied to the original image is obtained after erosion has been initially applied to the original image level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: ments smaller than ,
, while preserving the original boundaries of structures in our image. to a float value
. It is worth mentioning that in this Both filtering processes stop when level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: constructs the original image by applying a series of iterative erosion. The resulting filter is: level
in Xdensity distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio ,Note that morphological filtering leads to a quantization of the gray‐value space such that each image a step, lossless
normalization
isposterior applied,
leading
between
0 and
255,
such
that:
MD
density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio 55 initially applies be initially applies dilation dilation to the to original image,
the original im
Moreover, closing Moreover, closing by reconstruction by reconstruction level in , a lossless normalization is applied, leading to a float value between 0 and 255, such
posterior probabilities per pixel. The classes are assumed to be a mixture of th
Gaussian change” and potentially several “change” classes at every one of the resolution levels, resulting in mathematical the mathematical morphology morphology step, we calculate we calculate posterior the probability probability of various one of assumed one “no‐
“no‐
change” and potentially several “change” classes at every one of the re
in can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
thof 55 ,paper, we used a fixed square shape , per the (14)
posterior probabilities pixel. The various classes are to a mixture of Gaussian After the mathematical morphology step, we calculate the posterior probability The importance of opening and closing by reconstruction is that it filters out darker and br
(16)
e that morphological filtering leads to a quantization of the gray‐value space such that each image in , can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
on
,
with a size of 20 × 20 pixels. From an analysis of a broad original original image image is reconstructed is reconstructed by a series by a series of iterative of iterative dilations dilations of of , then , the then resulting the resulting filter filter is is 55 55 55 55 ,
,
,
(14)
´
¯
data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio (16)
(16)
(16)
(1
55 then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: then reconstructs the original image by applying a series of iterative erosion. The resulting filte
data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio After posterior probabilities per The various classes are assumed to (16)
be a mixture of Gaussian nd potentially several “change” classes at every one of the otentially several “change” classes at every one of the we resolution levels, resulting in the resolution levels, resulting in posterior probabilities per pixel. The various are assumed to
the mathematical morphology we calculate the posterior probability of one “no‐
level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: After density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio the range of data from different change detection projects, we found (1) that most consistent results were mathematical step, calculate the posterior probability one “no‐
thof , morphology ,pixel. , After (14)
change” and potentially several “change” classes at every one of the classes resolution levels, resul
morphology step, calculate the posterior probabilit
elements smaller than , step, , while preserving the original boundaries of structures in our i
55 k mathematical k
can be normalized into the gray‐value range of [0, 255] without loss of information. At the k
we level in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: 55 (16)
opening by reconstruction opening by reconstruction : : X
´
min
X
(16)
data is near normal and closely resembles a Gaussian distribution. Hence, our assumption of . It is worth mentioning that in this cesses stop when MD
MD
55 data is near normal and closely resembles a Gaussian distribution. Hence, our assumption of data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio robabilities or probabilities per pixel. per pixel. The The various various classes classes are assumed are assumed to be to a be mixture a mixture of Gaussian of Gaussian density distributions. While an approximation, assuming Gaussian char
change” and potentially several “change” classes at every one of the resolution levels, resulting in k
change” and potentially several “change” classes at every one of the resolution levels, resulting in data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio posterior probabilities The various are to be a probability mixture of (14)
Ga
change” and potentially several “change” classes at every one of the resolution leve
the step, mathematical morphology we , calculate of Note that morphological filtering leads to a quantization of the gray‐value space such that each per pixel. Both filtering processes stop when el in , a lossless normalization is applied, leading to a float value between 0 and 255, such that: ` kwe ` . It is worth mentioning that in this XAfter ˆ
(16)
the mathematical morphology calculate probability of the one achieved with a 20 pixel window; and (2) that change detection performance changed slowly with ,˘˘posterior ,55 step, classes , posterior “no‐
, , assumed MD “ . It is worth mentioning that in this k the Gaussian characteristics is only weakly affecting the performance of our change detection approach. square shape , After probabilities with a size of 20 × 20 pixels. From an analysis of a broad mathematical The normal th filtering processes stop when max
X
´
min
X
Gaussian characteristics is only weakly affecting the performance of our change detection approach. data is near and closely resembles a Gaussian distribution. Hence, our assumption of data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio stributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio utions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio After After the mathematical the After After the mathematical morphology the mathematical morphology step, morphology step, we morphology calculate we step, calculate the step, we posterior calculate the we posterior calculate probability the posterior probability the posterior of probability one of “no‐
probability one “no‐
of one of “no‐
one “n
data is not uncommon. Previous research [3] has found that the statisti
55 posterior probabilities per pixel. The various classes are assumed to be a mixture of Gaussian ,
,
,
,
,
,
After posterior per pixel. various classes are assumed to be a mixture of Gaussian (13)
(13)
MD
MD
(16)
data is near normal and closely resembles a Gaussian distribution. Hence, our assumption of density distributions. While an approximation, assuming Gaussian characteristics for SAR log
posterior probabilities per pixel. The various classes are assumed to be a mixtur
change” and potentially several “change” classes at every one of the resolution levels, res
the mathematical morphology step, we calculate the posterior probability of one “no‐
in can be normalized into the gray‐value range of [0, 255] without loss of information. At paper, we used a fixed square shape , with a size of 20 × 20 pixels. From an analysis of a broad 55 of one “no‐
change” and potentially several “change” classes at every one of the resolution levels, resulting in deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice (16)
After the mathematical morphology step, we calculate the posterior probability Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these processing erent change detection projects, we found (1) that most consistent results were we used a fixed square shape ,
with a size of 20 × 20 pixels. From an analysis of a broad After the mathematical morphology step, we calculate the posterior probability of one “no‐
Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these processing Gaussian characteristics is only weakly affecting the performance of our change detection approach. data is change” and potentially several “change” classes at every one of the near normal and closely resembles a Gaussian assumption of of of common. Previous research [3] has found that the statistical distribution of log‐ratio t uncommon. Previous research [3] has found that the statistical distribution of log‐ratio change” and potentially several “change” classes at every one of the change” and potentially several “change” classes at every one of the change” and potentially several “change” classes at every one of the distribution. resolution levels, resulting in calculate resolution levels, resulting in resolution levels, resulting in posterior resolution levels, resulting data is per near normal and a our Gaussian distribution. density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio The various to closely a resembles . It is worth mentioning that in this
Hence, Both filtering processes stop when Both filtering processes stop when Gaussian characteristics is only weakly affecting the performance of our change detection approach. data is not uncommon. Previous research [3] has found that the statistical distribution of log
density distributions. While an approximation, assuming Gaussian characteristics for
After posterior probabilities pixel. classes are assumed to probability be a mixture change” and potentially several “change” classes at every one of the resolution levels, resulting in the mathematical morphology step, we the one
level in , a lossless normalization is applied, leading to a float value between 0 and 255, suc
55 range of data from different change detection projects, we found (1) that most consistent results were posterior probabilities per pixel. The various classes are assumed be mixture of . It is worth mentioning that i
Gaussian of the window size is not critical for change detection success. The new multi‐scale decomposition (16)
change” and potentially several “change” classes at every one of the original image, resolution levels, resulting in The initially applies The initially applies dilation dilation to the to the original image, Moreover, closing Moreover, closing by reconstruction by reconstruction steps and, depending on the results of this study, may modify our approach in the future. To el window; and (2) that change detection performance changed slowly with f data from different change detection projects, we found (1) that most consistent results were change” and potentially several “change” classes at every one of the resolution levels, resulting in steps and, depending on the results of this study, may modify our approach in the future. To Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these processing Gaussian characteristics is only weakly affecting the performance of our change detection approach. normal ear normal and and closely closely resembles resembles a Gaussian a Gaussian distribution. distribution. Hence, Hence, our our assumption assumption of of posterior posterior probabilities posterior probabilities posterior per probabilities pixel. per probabilities pixel. per various pixel. per various classes pixel. The classes various The are various assumed are classes assumed classes to are be assumed to are a mixture be assumed a mixture to of be Gaussian to a of mixture be Gaussian a mixture of Gaussian of Gaussia
Gaussian characteristics is only weakly affecting the performance of our data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio paper, we used a fixed square shape paper, we used a fixed square shape ,
with a size of 20 × 20 pixels. From an analysis of a broad
,
with a size of 20 × 20 pixels. From an analysis of a b
Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these processing data is near normal and closely resembles a Gaussian distribution. Hence, our assumpt
data is not uncommon. Previous research [3] has found that the statistical distributio
density distributions. While an approximation, assuming Gaussian characteristics for SAR
posterior probabilities per pixel. The various classes are assumed to be a mixture of Gaussian change” and potentially several “change” classes at every one of the resolution levels, result
achieved with a 20 pixel window; and (2) that change detection performance changed slowly with After the mathematical morphology step, we calculate the posterior probability of one “no‐
density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio stack now contains morphological filtered images at each level in , as below: density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio posterior probabilities per pixel. The various classes are assumed to be a mixture of of Gaussian After the mathematical morphology step, we calculate the posterior probability of one then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: then reconstructs the original image by applying a series of iterative erosion. The resulting filter is: automate the calculation of the posterior probabilities, we employ an EM approach. The importance pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice ed with a 20 pixel window; and (2) that change detection performance changed slowly with posterior probabilities per pixel. The various classes are assumed to be a mixture Gaussian automate the calculation of the posterior probabilities, we employ an EM approach. The importance steps and, depending on the results of this study, may modify our approach in a the future. To Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these processing acteristics is only weakly affecting the performance of our change detection approach. characteristics is only weakly affecting the performance of our change detection approach. density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐rat
Still, we are currently assessing the benefits of using non‐Gaussian desc
data is near normal and closely resembles a Gaussian distribution. Hence, our assumption of “no‐
data is data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio near normal and closely a distribution. Hence, our assumption of range of data from different change detection projects, we found (1) that most consistent results were
range of data from different change detection projects, we found (1) that most consistent results
55 steps and, depending on the results of this study, may modify our approach in the future. To Gaussian characteristics is only weakly affecting the performance of our change detection app
data is Gaussian near normal and closely resembles a resolution levels, resulting in Gaussian distribution. Hence, our a
data is not uncommon. Previous research [3] has found that the statistical distribution of
density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio resembles posterior probabilities per pixel. The various classes are assumed to be mixture of Gau
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice change” and potentially several “change” classes at every one of the density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio After the mathematical morphology step, we calculate the posterior probability of one “no‐
change” and potentially several “change” classes at every one of the resolution levels, resulting in of integrating mathematical morphology into our EM algorithm framework is to suppress the effect not critical for change detection success. The new multi‐scale decomposition on from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio (15)
.
.
,
…
…
…
.
.
,
of integrating mathematical morphology into our EM algorithm framework is to suppress the effect automate the calculation of the posterior probabilities, we employ an EM approach. The importance steps and, depending on the results of this study, may modify our approach in the future. To urrently assessing the benefits of using non‐Gaussian descriptions in these processing re currently assessing the benefits of using non‐Gaussian descriptions in these processing data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio data is not uncommon. Previous research [3] has found that the statistical distribution of log‐rat
steps and, depending on the results of this study, may modify our Gaussian characteristics is only weakly affecting the performance of our change detection approach. Gaussian characteristics is only weakly affecting the performance of our change detection approach. achieved with a 20 pixel window; and (2) that change detection performance changed slowly with
achieved with a 20 pixel window; and (2) that change detection performance changed slowly
automate the calculation of the posterior probabilities, we employ an EM approach. The importance Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these proc
data is near normal and a Gaussian distribution. our assuma
data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio density distributions. While an approximation, assuming Gaussian characteristics for SAR log
of the window size is not critical for change detection success. The new multi‐scale decomposition , Gaussian characteristics is only weakly affecting the performance of our change detect
, per various , distribution. resembles ,The ,, closely probabilities pixel. various classes are assumed to be a mixture of Hence, Gaussian (14)
(14)
data is near posterior normal and closely resembles a Gaussian Hence, our assumption of nge” and potentially several “change” classes at every one of the resembles resolution levels, resulting in data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio posterior probabilities per pixel. The classes are assumed to be a mixture of Gaussian of background clutter that may constitute false positives after applying the EM algorithm. ns morphological filtered images at each level in , as below: window size is not critical for change detection success. The new multi‐scale decomposition data is not uncommon. Previous research [3] has found that the statistical distribution of log‐ratio of background clutter that may constitute false positives after applying the EM algorithm. of integrating mathematical morphology into our EM algorithm framework is to suppress the effect automate the calculation of the posterior probabilities, we employ an EM approach. The importance pending , depending on the on results the results of this of this study, study, may may modify modify our our approach approach in the in future. the future. To To data is data near is normal near data normal data is and near is closely and near normal closely normal resembles and resembles closely and a closely Gaussian a Gaussian resembles distribution. a Gaussian distribution. a Gaussian Hence, distribution. Hence, distribution. our assumption our Hence, assumption Hence, our of assumption our of assumption of automate the calculation of the posterior probabilities, we employ an EM
Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these processing deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact choice
deviation from the 20 pixel setting. Hence, while 20 pixels was found to be optimal, the exact c
of integrating mathematical morphology into our EM algorithm framework is to suppress the effect steps and, depending on the results of this study, may modify our approach in the Still, we are currently assessing the benefits of using non‐Gaussian descriptions in the
Gaussian characteristics is only weakly affecting the performance of our change detection a
data is near normal Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these processing and closely resembles a the Gaussian distribution. Hence, our assumption of data is not uncommon. Previous research [3] has found that the statistical distribution of log
stack now contains morphological filtered images at each level in , as below: The importance of opening and closing by reconstruction is that it filters out darker and brighter density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio Gaussian characteristics is only weakly affecting the performance of our change detection approach. After mathematical morphology step, we calculate the posterior probability of futu
one
posterior probabilities per pixel. The various classes are assumed to be a mixture of Gaussian data is near normal and closely resembles a Gaussian distribution. Hence, our assumption of density distributions. While an approximation, assuming Gaussian characteristics for SAR log‐ratio ack now contains morphological filtered images at each level in , as below: data is near normal and closely resembles a Gaussian distribution. Hence, our assumption of of integrating mathematical morphology into our EM algorithm framework is to suppress the effect calculation of the posterior probabilities, we employ an EM approach. The importance the calculation of the posterior probabilities, we employ an EM approach. The importance Gaussian characteristics is only weakly affecting the performance of our change detection approach. Gaussian characteristics is only weakly affecting the performance of our change detection approach. Gaussian characteristics is only weakly affecting the performance of our change detection approach. Gaussian characteristics is only weakly affecting the performance of our change detection approac
of steps the results depending may modify . It is worth mentioning that in this Both filtering processes stop when Both filtering processes stop when of integrating mathematical morphology into our EM algorithm framew
and, on of . It is worth mentioning that in this this study, may modify our approach the future. To assumpti
steps and, depending the this study, our approach in the future. To in of the window size is not critical for change detection success. The new multi‐scale decomposition
of the window size is not critical for change detection success. The new multi‐scale decompo
of background clutter that may constitute false positives after applying the EM algorithm. automate the calculation of the posterior probabilities, we employ an EM approach. The impo
and, on the results this study, may modify our approach in t
Still, we are currently assessing the benefits of using non‐Gaussian descriptions in these pr
Gaussian characteristics is only weakly affecting the performance of our change detection approach. data near normal and closely resembles a of Gaussian distribution. Hence, our (15)
is . . ,steps …on …of background clutter that may constitute false positives after applying the EM algorithm. …
.depending . ,results Remote Sens. 2016, 8, 482
10 of 27
After the mathematical morphology step, we calculate the posterior probability of one “no-change”
and potentially several “change” classes at every one of the K resolution levels, resulting in K
posterior probabilities per pixel. The various classes are assumed to be a mixture of Gaussian density
distributions. While an approximation, assuming Gaussian characteristics for SAR log-ratio data
is not uncommon. Previous research [3] has found that the statistical distribution of log-ratio data
is near normal and closely resembles a Gaussian distribution. Hence, our assumption of Gaussian
characteristics is only weakly affecting the performance of our change detection approach. Still, we
are currently assessing the benefits of using non-Gaussian descriptions in these processing steps and,
depending on the results of this study, may modify our approach in the future. To automate the
calculation of the posterior probabilities, we employ an EM approach. The importance of integrating
mathematical morphology into our EM algorithm framework is to suppress the effect of background
clutter that may constitute false positives after applying the EM algorithm.
The EM algorithm focuses on discrimination between the posterior probability of one no-change
pωu q and potentially several change classes pωc q. For each level in X MD , we model the probability
density function ppX MD q of the normalized image series X MD as a mixture of N density distributions.
This mixture contains the probability density functions, denoted ppX MD |ωc q and ppX MD |ωu q, and the
prior probability, Ppωc q and Ppωu q. At the kth level in X MD , the probability density function (PDF) is
modeled as:
´ 1´
´
¯ Nÿ
¯
(17)
p X kMD “
ppX kMD |wcn qP pwcn q ` ppX kMD |ωu qP pωu q
n“1
ř
The first summand in Equation (17) ( nN “´ 11 ppX kMD |wcn qP pwcn qq represents the mixture of N ´ 1
change PDFs described by their respective likelihood ppX kMD |wcn q and prior probabilities P pwcn q, while
the second summand describes the PDF of a single no-change class. It is worth noting that all PDFs
in Equation (17) are assumed to be of Gaussian nature, such that the mean µωc and variance σω2 c
are sufficient to define the density function associated with the change classes ωc , and mean µωu
and variance σω2 u can be used to describe the density function related with the no-change classes
ωu . The parameters in Equation (17) are estimated using an EM algorithm. Given X kMD is the kth
level image in X MD , we inferred which class pωi “ pωc , ωu qq each pixel in X kMD belongs to, using
`
˘
θs “ µωc , σω2 c , µωu , σω2 u which is our current (best) estimate for the full distribution, and θ as our
improved estimate. The expectation step at the sth iteration is calculated by the conditional expectation:
”
´
¯ı ÿ ´
¯
´
¯
Q pθ|θs q “ E In P ωi , X kMD |θ|X kMD , θs “
P ωi |X kMD , θs In P ωi , X kMD |θ
(18)
The maximization step maximizes Q pθ|θs q to acquire the next estimate:
θps ` 1q “ argmaxQ pθ|θs q
(19)
θ
The iterations cease when the absolute differences between the previous and current variables
are below a tolerance value (ε). In our paper, we empirically set the tolerance value ε to 10´6 .
Once the iterations cease, the final optimal θps ` 1q is used to calculate the posterior probability
using Bayes’ formula. The EM algorithm (see Algorithm 1) is applied separately to all K levels
of the multi-scale
decomposition series,
X MD , resulting in a stack of posterior probability maps
!
)
PPMD “ PP0 , . . . .PPk , . . . ., PPK ´ 1 of depth K where each map contains the posterior probability
of change and no-change classes, respectively. Our EM algorithm is illustrated as follows:
iterations cease, the final optimal Ѳ is used to calculate the posterior probability using Bayes’ formula. The algorithm (see algorithm 1) is applied separately to all levels of the multi‐scale decomposition series, , resulting in a stack of posterior probability maps of depth where each map contains the posterior probability of change ,….
,….,
and no‐change classes, respectively. Our EM algorithm is illustrated as follows: Remote
Sens. 2016, 8, 482
11 of 27
Algorithm 1. (Expectation‐Maximization) Algorithm 1. (Expectation-Maximization)
Begin initialize Ɵ°, ε, s = 0 Begin
initialize θ˝ , ε, s = 0
do s ← s + 1 do s Ð s + 1
E step: compute Q(Ɵ|Ɵs) E step: compute Q(θ|θs )
M step: Ɵs+1 ← argmax Q(Ɵ|Ɵs) M step: θs+1 Ð argmax Q(θ|θs )
s+1|Ɵs) − Q(Ɵ
s|Ɵ
s−1) ≤ ε s |θ
s´1 ) ď ε
until Q(Ɵ
until Q(θs+1
|θs ) ´ Q(θ
s+1
return Ӫ ← Ɵ
return Ð θ s+1 end end
2.3.3. Selection of Number of Change Classes 2.3.3.
Selection of Number of Change Classes
In order
order toto execute
execute the
the expectation
expectation maximization
maximization algorithm
algorithm from
from Section
Section 2.3,
2.3, the
the number
number ofof In
change classes that are present in an image has to be known. Selection of classes is a difficult task, change
classes that are present in an image has to be known. Selection of classes is a difficult task,
and care should be taken to avoid over‐ or under‐classifying the data. Various methods have been and
care should be taken to avoid over- or under-classifying the data. Various methods have been
proposed for selecting number of classes to fitbest the and
data, and examples include the pNq to best
proposed
for
selecting
thethe number
of classes
the fit data,
examples
include the
penalty
penalty method [28], the cross‐validation method [29] and the minimum description length approach method
[28], the cross-validation method [29] and the minimum description length approach [30]. In
Remote
Sens. 2016,
8, 482
of 27
[30]. In our paper, we developed a selection approach that identifies the number of required classes our
paper,
we developed
a selection approach that identifies the number of required classes pNq11using
a sum of square error (SSE) approach. The SSE approach utilized the measured data PDF, which is
( ) using a sum of square error (SSE) approach. The SSE approach utilized the measured data PDF,
the statistical distribution of the highest decomposition level image, and the estimated PDF, which is
which is the statistical distribution of the highest decomposition level image, and the estimated PDF,
the statistical distribution estimated after applying the EM algorithm to the highest decomposition
which is the statistical distribution estimated after applying the EM algorithm to the highest
level image. The highest decomposition level image was used because at this level, most of the noise
decomposition level image. The highest decomposition level image was used because at this level,
in the image was filtered out. This approach seeks to minimize the sum of the square of the differences
most of the noise in the image was filtered out. This approach seeks to minimize the sum of the square
between the measured data PDF and the estimated PDF, as follows:
of the differences between the measured data PDF and the estimated PDF, as follows:
NN
ÿ
SSE “
pmii ´ f ii q2
(20)
(20)
=
(
− )
i“2
where NN isisthe
number
of classes,
mii is theisoriginal
measured
PDF and
f ii isand
the estimated
where
theoverall
overall
number
of classes,
the original
measured
PDF
is the
PDF.
An
example
of
the
dependence
of
SSE
on
the
number
of
classes
used
in
f
is
shown
in
Figure
estimated PDF. An example of the dependence of
on the number of classesii used in
is shown4.
Initially,
start with
classes
change (one
and one
no-change
and calculate
thecalculate
SSE. For
in
Figure we
4. Initially,
wetwo
start
with (one
two classes
change
and oneclass)
no-change
class) and
each
extra
class
that
is
added
into
the
procedure,
its
corresponding
SSE
is
estimated.
Plotting
each
the SSE. For each extra class that is added into the procedure, its corresponding SSE is estimated.
class
sequentially
against
its
corresponding
SSE
leads
to
a
continuous
decrease
of
approximation
error
Plotting each class sequentially against its corresponding SSE leads to a continuous decrease of
as NN gets larger.
approximation
error as NN gets larger.
Figure
Figure 4.
4. Selection
Selectionof
ofclasses
classesused
usedfor
for final
final classification.
classification.
The data from Section 4 is used in this example and SSE was carried out using a maximum of 20
classes, with each classes being added sequentially. The knee point on the curve in Figure 4 suggests
that 3 is a good candidate for .
2.3.4. Measurement Level Fusion
Remote Sens. 2016, 8, 482
12 of 27
The data from Section 4 is used in this example and SSE was carried out using a maximum
of 20 classes, with each classes being added sequentially. The knee point on the curve in Figure 4
suggests that 3 is a good candidate for N.
2.3.4. Measurement Level Fusion
We developed a measurement level fusion technique to accurately delineate the boundary of the
changed region by using the posterior probability of each class at each multi-scale image to compose a
final change detection map (M). We developed and tested five measurement level fusion methods that
are briefly explained below:
1.
Product rule fusion: This fusion method assumes conditionally statistical independence, and
each pixel is assigned to the class that maximizes the posterior conditional probability, creating a
change detection map. Each pixel is assigned to the class such that
ωi “ argmax
K !
ź
K !
)
)
ź
Ppωi |X kMD pi, jqq “ argmax
PPi
ωi εtωc ,ωu u i “ 0
2.
(21)
ωi εtωc ,ωu u i “ 0
Sum rule fusion: This method is very useful when there is a high level of noise leading to
uncertainty in the classification process. This fusion method assumes each posterior probability
map in X MD does not deviate much from its corresponding prior probabilities. Each pixel is
assigned to the class such that
K !
)
ÿ
ωi “ argmax
PPi
(22)
ωi εtωc ,ωu u i “ 0
3.
Max rule fusion: Approximating the sum in Equation (22) by the maximum of the posterior
probability, we obtain
K !
)
ωi “ argmax max PPi
(23)
ωi εtωc ,ωu u i “ 0
4.
Min rule fusion: This method is derived by bounding the product of posterior probability. Each
pixel is assigned to the class such that
K !
)
PPi
min
ωi εtωc ,ωu u i “ 0
ωi “ argmax
5.
(24)
Majority voting rule fusion: This method assigns a class to the pixel that carries the highest
number of votes. Each pixel in each posterior probability map pPPMD q is converted to binary, i.e.,
$
’
K
’
(
’
& 1, i f max
PPi
∆ibn “
’
i“0
’
’
%
0, otherwise
K
ř
ωi “ argmax
∆ibn
(25)
ωi εtωc ,ωu u i “ 0
The measurement level fusion with the lowest overall error, highest accuracy, and highest kappa
coefficient is selected as the best fusion method and is used as our final change detection map. The
next section shows how the best fusion method was selected.
Remote Sens. 2016, 8, 482
13 of 27
3. Performance Assessment Using Synthetic Data
To assess the performance of the developed change detection approach under both controlled
and uncontrolled conditions, we have conducted two types of validation studies, both of which are
presented in this paper. In this section, we summarize change detection results on a synthetic dataset to
evaluate the performance and limitations of the technique under controlled conditions. Subsequently,
in the next section, we show an application of the developed change detection technique to wildfire
mapping. An area in Alaska is chosen and the change detection results are compared to ground truth
measurements for validation.
3.1. Description of Synthetic Dataset
A synthetic dataset of size 1152 ˆ 1152 pixels was generated from two SAR images acquired
over the same area but at different times, and “change patches” were artificially introduced into the
second of these images. A post-event image was generated by adding 2 dB to the radar cross-section
of certain locations to form the change patches. Our approach was tested on synthetic data, because
with synthetic data, we can control every aspect of the data, and also evaluate the accuracy with
absoluteRemote
reliability.
the
Sens. 2016,The
8, 482purpose of analyzing the synthetic dataset was to assess, more accurately,
13 of 27
robustness of the proposed approach and also to select the best measurement level fusion.
with synthetic data, we can control every aspect of the data, and also evaluate the accuracy with
It is worth mentioning that, with the exception of the border pixels, moderate changes in speckle
absolute reliability. The purpose of analyzing the synthetic dataset was to assess, more accurately,
noise dothe
not
significantly
impact our
classification
This
ismeasurement
due to the mitigating
robustness
of the proposed
approach
and also toresult.
select the
best
level fusion. effects of the
wavelet decomposition
and
due
to
the
way
decisions
at
different
decomposition
levels
are merged
It is worth mentioning that, with the exception of the border pixels, moderate changes
in speckle
noise
do
not
significantly
impact
our
classification
result.
This
is
due
to
the
mitigating
effects
of
the
in our approach. In homogeneous areas (e.g., within the change patches), the higher decomposition
wavelet
decomposition
and
due
to
the
way
decisions
at
different
decomposition
levels
are
merged
levels carry the majority of the weight in the classification of these areas. As most speckleinnoise is
our approach. In homogeneous areas (e.g., within the change patches), the higher decomposition
removed
at these higher decomposition levels, the classification result within homogeneous areas is
levels carry the majority of the weight in the classification of these areas. As most speckle noise is
very robust to speckle noise. Only in heterogeneous areas (the boundary pixels of our simulated data),
removed at these higher decomposition levels, the classification result within homogeneous areas is
where lower
decomposition
levelsOnly
contribute
more to areas
the final
classification
very robust
to speckle noise.
in heterogeneous
(the boundary
pixelsresult,
of our residual
simulatedspeckle
noise may
have
a
measurable
effect
on
performance.
As
there
are
only
very
few
boundary
data), where lower decomposition levels contribute more to the final classification result, residual pixels
speckle
may ahave
a measurable
effect on of
performance.
As there arewe
only
very few
boundary
and as we
onlynoise
applied
very
moderate change
radar cross-section,
believe
that
neglecting the
pixels of
and
as we is
only
applied a very
moderateFigure
change5aofshows
radar the
cross-section,
wegenerated
believe thatbetween
recalculation
speckle
a well-justified
decision.
ratio image
neglecting the recalculation of speckle is a well-justified decision. Figure 5a shows the ratio image
the synthetic pre-event image and the post-event images, while Figure 5b depicts the ground truth
generated between the synthetic pre-event image and the post-event images, while Figure 5b depicts
change the
map.
The faint change signatures in Figure 5a indicate that a challenging change detection
ground truth change map. The faint change signatures in Figure 5a indicate that a challenging
situation
was
change generated.
detection situation was generated.
Figure 5. (a) Ratio image calculated from pre- and post-event images; (b) ground truth change map.
Figure 5. (a) Ratio image calculated from pre- and post-event images; (b) ground truth change map.
3.2. Performance Evaluation for Selecting Best Fusion Method
3.2. Performance Evaluation for Selecting Best Fusion Method
For selecting the best performing fusion method, quantitative measurements are derived from
binary change
detection
map obtained
the different
measurement
level fusion
Forthe
selecting
the best
performing
fusion using
method,
quantitative
measurements
aretechniques.
derived from the
In generating
the confusion
matrix which
the accuracy
of our classification
result,techniques.
the
binary change
detection
map obtained
usingshows
the different
measurement
level fusion
following defined quantities are computed: (i) the false alarm ( ), which signifies the no-change
In generating the confusion matrix which shows the accuracy of our classification result, the
pixels incorrectly classified as change. The false alarm rate (
) is computed in percentage as
following defined
quantities are computed:
(i) the false alarm pFAq, which signifies the no-change
=
/ × 100%, where
is the total number of unchanged pixels in the ground truth change
detection map; (ii) the missed alarm ( ), which signifies the changed pixels incorrectly classified
as no-change. The missed alarm rate (
) is computed in percentage as
=
/ × 100%,
where
is the total number of changed pixels in the ground truth change detection map; (iii) the
overall error ( ), which is the percentage ratio of incorrect classification made (addition of both the
false alarm rate and missed alarm rate). Hence,
=( +
)/( + ) × 100%; (iv) the overall
Remote Sens. 2016, 8, 482
14 of 27
pixels incorrectly classified as change. The false alarm rate pFARq is computed in percentage as
FAR “ FA{N1 ˆ 100%, where N1 is the total number of unchanged pixels in the ground truth change
detection map; (ii) the missed alarm pMAq, which signifies the changed pixels incorrectly classified
as no-change. The missed alarm rate pMARq is computed in percentage as MAR “ MA{N0 ˆ 100%,
where N0 is the total number of changed pixels in the ground truth change detection map; (iii) the
overall error pOEq, which is the percentage ratio of incorrect classification made (addition of both
the false alarm rate and missed alarm rate). Hence, OE “ pFA ` MAq { pN1 ` N0 q ˆ 100%; (iv) the
overall accuracy pOAq, which is calculated by adding the number of pixels classified correctly and
dividing it by the total number of pixels. Therefore OA “ 100% ´ OE; and (v) the kappa coefficient,
which measures the agreement between classification pixels and ground truth pixels [31]. A kappa
value of 1 represents perfect agreement while a value of 0 represents no agreement. Table 1 shows
the quantitative performance of each of the measurement level fusion techniques. It can be seen that
product rule fusion achieved the best performance with an overall accuracy of 98.97%.
Table 1. Overall accuracy, overall error, kappa coefficient, false positive and false negative of the
measurement level fusion using Figure 5a.
Product rule fusion
Sum rule fusion
Max rule fusion
Min rule fusion
Majority voting rule fusion
Overall
Accuracy (%)
Overall
Error (%)
Kappa
Coefficient
False
Positive (%)
False
Negative (%)
98.973
98.941
98.952
67.256
98.826
1.035
1.058
1.042
32.743
1.173
0.906
0.904
0.905
0.157
0.891
0.361
0.380
0.365
34.076
0.340
11.532
11.626
11.582
11.972
14.157
3.3. Comparison to Alternative Change Detection Methods
To evaluate the performance of our proposed algorithm relative to the state-of-the-art, we
conducted an extensive qualitative (Figure 6) and quantitative (Table 2) comparison of the results of
our change detection approach to results of other recently published change detection methods. The
following alternative methods were used in the comparison: (a) Method A: our proposed approach is
used without fast non-local means filtering; (b) Method B: our proposed approach is used without
2D-SWT and measurement level fusion—the approach utilized mathematical morphology and the
EM algorithm for classification; (c) Method C: our proposed approach is used without morphological
filtering; (d) Method D: our proposed approach is used without the EM algorithm—the approach
employed the thresholding algorithm proposed by [32] and majority voting rule fusion for classification;
(e) Method E: semi-supervised change detection, based on using a kernel-based abnormal detection
into the wavelet decomposition of the SAR image [33]; (f) Method F: image denoising using fast
discrete curvelet transform via wrapping with the EM algorithm to produce the change detection
map [34]; (g) Method G: using UDWT to obtain a multiresolution representation of the log-ratio image,
then identifying the number of reliable scales, and producing the final change detection map using
fusion at feature level (FFL_ARS) on all reliable scales [15]; (h) Method H: implementing probabilistic
Bayesian inferencing with the EM algorithm to perform unsupervised thresholding over the images
generated by the dual-tree complex wavelet transform (DT-CWT) at various scales, and moreover,
using intra- and inter-scale data fusion to produce the final change detection map [12]; (i) Method
I: obtaining a multiresolution representation of the log-ratio image using UDWT, then applying the
Chan–Vese (region-based) active contour model to the multiresolution representation to give the
final change detection map [18]. Based on Table 2 and Figure 6, one can observe that the change
detection result from Method G showed the lowest performance of all tested methods with an overall
accuracy of 68.412% and a kappa coefficient of 0.162. The low performance of this approach is due to
the effectiveness of the method employed to select the optimal resolution level (reliable scale). The
result of Method G was computed by averaging the reliable scales for every pixel which led to the
low performance. Thus, most reliable scales contain a large amount of both geometrical details and
Remote Sens. 2016, 8, 482
15 of 27
speckle components (lowest decomposition level) and a low amount of geometrical details and speckle
components (highest decomposition level). The proposed method yields the best performance with an
overall accuracy of 98.973% and a kappa coefficient of 0.906. It is worth mentioning that the aim of
Methods A–D is to show the importance of each element in our proposed approach (see gray shade
area in Table 2).
Remote Sens. 2016, 8, 482
15 of 27
Figure 6. Change detection map showing: (a) proposed approach without fast non-local means filter;
Figure 6. Change
detection map showing: (a) proposed approach without fast non-local means filter;
(b) proposed approach without 2D-SWT; (c) proposed approach without morphological filtering; (d)
(b) proposed
approach
without
2D-SWT;
(c)(e)proposed
approach
morphological
proposed approach
without EM
algorithm;
SVM approach;
(f) imagewithout
denoising using
fast discrete filtering;
curvelet
transform
via wrapping
EM algorithm;
(g) FFL_ARS
approach;
DT-CWT
with intra-using fast
(d) proposed
approach
without
EM with
algorithm;
(e) SVM
approach;
(f) (h)
image
denoising
and
inter-scale
data
fusion
approach;
(i)
UDWT
with
Chan–Vese
active
contour
model
approach.
discrete curvelet transform via wrapping with EM algorithm; (g) FFL_ARS approach; (h) DT-CWT with
intra- and inter-scale
data fusion approach; (i) UDWT with Chan–Vese active contour model approach.
Table 2. Overall accuracy, overall error, kappa coefficient, false positive and false negative of our
proposed approach with alternative methods using Figure 5a.
Table 2. Overall accuracy, overall
error, kappa
coefficient,
false positive
and falseFalse
negative of our
Overall
Overall
Kappa
False
proposed approach with alternative
methods
using
Figure
5a.
Accuracy (%)
Error (%)
Coefficient
Positive (%)
Negative (%)
Proposed approach
98.973
Method A Overall 98.038
Method Accuracy
B
(%)98.024
Method C
98.352
Proposed approach
Method D 98.973 98.647
Method A Method E 98.038 93.583
Method B Method F 98.024 94.763
Method C Method G 98.352 68.412
Method D Method H 98.647 94.527
Method E Method I 93.583 95.549
Method F
Method G
Method H
Method I
94.763
68.412
94.527
95.549
1.035
1.961
Overall
1.975
Error (%)
1.648
1.0351.353
1.9616.416
1.9755.236
1.648
31.587
1.3535.473
6.4164.450
5.236
31.587
5.473
4.450
0.906
0.844
Kappa
0.827
Coefficient
0.836
0.906
0.878
0.844
0.575
0.827
0.594
0.836
0.162
0.878
0.519
0.575
0.659
0.594
0.162
0.519
0.659
0.361
1.843 False
1.127
Positive (%)
0.109
0.694 0.361
5.708 1.843
3.741 1.127
32.7730.109
2.953 0.694
3.409 5.708
3.741
32.773
2.953
3.409
11.532
3.806
False
15.201 Negative (%)
25.622
11.532
9.942
3.806
17.453
15.201
28.547
25.622
13.101
9.942
44.750
17.453
20.678
28.547
13.101
44.750
20.678
The study area for this real-data experiment is situated around the Tanana Flats region of Alaska,
just east of the communities of Healy, Clear, Anderson and Nenana, and approximately 26 miles
southwest of Fairbanks, Alaska (Figure 7). The topography of the area is relatively flat and is
comprised of low-vegetation tundra and taiga regions with an interspersed network of small streams.
Remote Sens. 2016, 8, 482
16 of 27
The forest vegetation of the area is diverse, containing white spruce, black spruce, aspen and birch.
During the hot summer climate, this area is very prone to wildfires.
2 each year
4. Performance
Analysis through
Application
to Wildfire
Mapping
In Alaska, wildfires
affect thousands
of km
[35]. The dry conditions, increased
lightning strikes, and higher-than-normal temperatures cause atmospheric effects that impact the
4.1. Description of Area
strength of wildfires [35]. The strongest occurrences of wildfires in Alaska happen in the mid-summer
months,
occurrences
annually.
According
to the around
Alaska the
interagency
coordination
center,
The and
study
area for thisvary
real-data
experiment
is situated
Tanana Flats
region of Alaska,
the mapped
firecommunities
in our study area
is called
theAnderson
Survey Line
fire,
which started
in the year 2001.
This
just
east of the
of Healy,
Clear,
and
Nenana,
and approximately
26 miles
fire, causedofby
lightning,
consumed
796 km2, and
lasted
four
monthsflat
from
June to 14
southwest
Fairbanks,
Alaska
(Figurean7).area
Theof
topography
of the
area is
relatively
and20
is comprised
October
2001. During
the and
winter
of regions
the yearwith
2002,anthe
fire scar disappears
and
thisstreams.
is likely due
the
of
low-vegetation
tundra
taiga
interspersed
network of
small
The to
forest
freezing of of
thethe
soils
and
the addition
of a seasonal
snow cover
Section
4.5).
Bybirch.
the beginning
of
vegetation
area
is diverse,
containing
white spruce,
black(see
spruce,
aspen
and
During the
the
year
2004,
the
trees
in
the
fire
scar
area
have
regenerated.
hot summer climate, this area is very prone to wildfires.
Figure 7. Study area for wildfire mapping.
4.2. Description of SAR and Reference Data Used in
this Study
In Alaska, wildfires affect thousands of km2 each year [35]. The dry conditions, increased lightning
strikes,
higher-than-normal
temperatures
cause transmit
atmospheric
that impact
strength of
Weand
obtained
eight, HH-polarized
(horizontal
andeffects
horizontal
receivethe
polarization),
wildfires
[35].
The strongest
of wildfires
Alaska
the mid-summer
months,
Radarsat-1
images
acquiredoccurrences
between 2000
and 2004inover
thehappen
area ofininterest.
Only acquisitions
and
occurrences
vary
annually.
According
to theimages
Alaska were
interagency
center,
theinmapped
between
April and
October
of preand post-fire
used tocoordination
avoid seasonal
effects
change
fire
in our For
study
area
called
the Survey the
Lineacquisition
fire, whichisstarted
in the
year 2001. This
fire, caused
detection.
ease
of is
visual
comparison,
not shown
successively
according
to the
by
lightning,
consumed
area
of post-fire
796 km2 ,images.
and lasted
four images
months(images
from 20showing
June to 14
2001.
year
but according
to thean
preand
Pre-fire
noOctober
fire scar)
are
During
thefirst,
winter
ofare
theshown
year 2002,
the fire8a–d,
scar while
disappears
and thisimages
is likely(images
due to the
freezing
the
displayed
and
in Figure
the post-fire
showing
fireofscar)
soils
and
the addition
a seasonal snow cover (see Section 4.5). By the beginning of the year 2004, the
can be
found
in Figureof8e–h.
trees in the fire scar area have regenerated.
4.2. Description of SAR and Reference Data Used in this Study
We obtained eight, HH-polarized (horizontal transmit and horizontal receive polarization),
Radarsat-1 images acquired between 2000 and 2004 over the area of interest. Only acquisitions
between April and October of pre- and post-fire images were used to avoid seasonal effects in change
detection. For ease of visual comparison, the acquisition is not shown successively according to the
year but according to the pre- and post-fire images. Pre-fire images (images showing no fire scar) are
Remote Sens. 2016, 8, 482
17 of 27
displayed first, and are shown in Figure 8a–d, while the post-fire images (images showing fire scar)
can be
found in Figure 8e–h.
Remote Sens. 2016, 8, 482
17 of 27
Figure 8. Pre-fire image acquired on: (a) 21 June 2000; (b) 6 June 2001; (c) 23 October 2002; (d) 13 April
Figure 8. Pre-fire image acquired on: (a) 21 June 2000; (b) 6 June 2001; (c) 23 October 2002;
2004. Post-fire image acquired on: (e) 3 August 2001; (f) 7 October 2001; (g) 22 August 2002; (h) 6 June
(d) 13 April 2004. Post-fire image acquired on: (e) 3 August 2001; (f) 7 October 2001; (g) 22 August 2002;
2003. The triangular gray area in F denotes no data available.
(h) 6 June 2003. The triangular gray area in F denotes no data available.
Remote Sens. 2016, 8, 482
18 of 27
Each image has a size of 3584 ˆ 5056 pixels, corresponding to an area of 44.8 ˆ 63.2 square
kilometers. The pixel spacing in each image is 12.5 ˆ 12.5 m with a range resolution of 26.8 m and an
azimuth resolution of 24.7 m. The eight Radarsat-1 images were used to generate seven different ratio
images, and were used for the analysis of seven different detection scenarios (scenarios 1–7 in Table 3).
Table 3 shows the seven independent scenarios that we investigated to analyze the performance of
our approach. The image acquisitions highlighted in gray in Table 3 are the post-fire images, while
the rest of the acquisitions are pre-fire images. Three of the analyzed scenarios are “negative tests”
as they do not include fire activity and test our ability to correctly identify no-change scenarios. The
four remaining scenarios include change signatures related to wildfires and allow us to quantify our
ability to correctly detect fire perimeters. Table 4 shows the incidence angle of all the individual
image acquisitions. The image acquisitions highlighted in gray in Table 4 are images with a different
incidence angle. All the images were radiometrically corrected using the Alaska IFSAR DEM which
has a resolution of 5 m. The images were calibrated and co-registered as well, with ASF MapReady
software, then geocoded to latitude and longitude [21]. Notice that the pre- and post-fire comparisons
in scenarios 2 and 5 collated images with different incidence angles. These comparisons were included
to test our approach’s ability to increase temporal resolution through the combination of images of
varying geometry (see Section 2.1).
Table 3. Combination of image acquisitions used to generate the ratio images.
Image 1 (X1)
Image 2 (X2)
Scenarios
Change
Figure
21 June 2000
6 June 2001
6 June 2001
6 June 2001
6 June 2001
6 June 2001
6 June 2001
6 June 2001
23 October 2002
13 April 2004
3 August 2001
7 October 2001
22 August 2002
6 June 2003
scenario 1
scenario 2
scenario 3
scenario 4
scenario 5
scenario 6
scenario 7
Negative
Negative
Negative
Positive
Positive
Positive
Positive
11a
11b
11c
10
11d
11e
11f
Table 4. Incidence angle of all the individual image acquisitions.
Image Acquisitions
Incidence Angle
21 June 2000
6 June 2001
23 October 2002
13 April 2004
3 August 2001
7 October 2001
22 August 2002
6 June 2003
27.207˝
27.238˝
33.736˝
27.375˝
27.236˝
22.796˝
27.296˝
27.336˝
To validate achieved detection results, we used a fire area history map generated by the Alaska
Fire Service as ground truth. The fire area history map was prepared using ground-based GPS, which,
although effective, suffers from the limitation that everything inside the fire area history map is
considered to be wildfire. We modified the fire area history map by using optical imagery to visually
digitizing areas that are not actually affected by wildfire. Other limitations the Alaska Fire Service
faced include time and safety.
4.3. Description of Classification Processes
Based on several experiments, the performance of our approach was measured qualitatively
and quantitatively by comparing detections to a fire area history map. To execute the classification
process, ratio images (scenarios 1–7) previously shown in Table 3 were filtered and decomposed into
Remote Sens. 2016, 8, 482
19 of 27
six resolution levels. As previously described, 2D-SWT using the biorthogonal wavelets procedure
was employed.
Remote Sens. 2016, 8, 482
19 of 27
As an example of the decomposition process, Figure 9 shows the decomposed images for scenario
the decomposition
9 shows
theeach
decomposed
images
for how
4. LookingAsatan
theexample
highest of
resolution
images in process,
Figure 9 Figure
(top left
panel of
sub-Figure),
we see
scenariobetween
4. Looking
at the highest
images is
ininitially
Figure 9 low
(topdue
left panel
each sub-Figure),
the contrast
background
andresolution
change regions
to theofsignificant
noise in the
seecontrast
how the is
contrast
between background
and change
regions is decomposition
initially low due to
the significant
data. we
This
continuously
improving with
the increasing
level.
This is due to
noise in the data. This contrast is continuously improving with the increasing decomposition level.
a continuous improvement of noise suppression through the K levels. At the same time, the loss of
This is due to a continuous improvement of noise suppression through the
levels. At the same
contrast and detail level can be observed for higher decomposition levels, which is particularly strong
time, the loss of contrast and detail level can be observed for higher decomposition levels, which is
at theparticularly
border between
background
and the
changed
area. and changed area.
strong the
at the
border between
background
Figure
9. SWT
decomposition
of scenario
4 from
level (level
(level1–6)
1–6)ofofdecomposition
decomposition is
Figure
9. SWT
decomposition
of scenario
4 fromlevel
level11to
to6.6. Each
Each level
is showing
the resolution
lower resolution
(LL) image
three
detail
(high
frequency)images
images (LH,
showing
the lower
(LL) image
(top (top
left)left)
andand
the the
three
detail
(high
frequency)
(LH, HL,
HH).
0 is the original
SAR image.
HL, HH).
Level
0 isLevel
the original
SAR image.
per pixel and to produce the final classification map . Table 5 shows the quantitative comparison
of each fusion method to confirm our choice of product rule fusion as the best-performing method.
It is evident that product rule fusion gave a better result with an overall accuracy of 99.932% and a
kappa coefficient of 0.997. Figure 10 shows a qualitative comparison of the burned area detected by
our algorithm to the available fire area information (red outlines in Figure 10) retrieved from the
Remote Sens. 2016, 8, 482
20 of 27
archives of the Alaska interagency coordination center.
Table
5. Overall
accuracy,
overall K
error,
kappa coefficient,
false
positive the
andposterior
false negative
of the of
For every
of the
decomposed
resolution
levels, we
calculate
probability
measurement
level
fusion
using
scenario
4.
one “no-change”, one “negative change” and one “positive change” class, resulting in K posterior
probabilities per pixel. Product rule
fusion is then
used to Kappa
fuse the K classification
results
achieved
Overall
Overall
False
False
per pixel and to produce the final
classification
map
M. Table
5 showsPositive
the quantitative
comparison
Accuracy
(%) Error
(%)
Coefficient
(%) Negative
(%)
rule fusion
99.932
0.269method.
of each Product
fusion method
to confirm our
choice of 0.067
product rule0.997
fusion as the0.021
best-performing
Sumthat
ruleproduct
fusion rule fusion
98.991
1.008
0.967
2.543 and a
It is evident
gave a better
result with
an overall 0.653
accuracy of 99.932%
Max
rule
fusion
97.609
2.390
0.924
2.476
2.020 by our
kappa coefficient of 0.997. Figure 10 shows a qualitative comparison of the burned area detected
Min rule fusion
98.273
1.726
0.944
1.815
1.342
algorithm to the available fire area information (red outlines in Figure 10) retrieved from the archives
Majority voting rule fusion
98.842
1.158
0.961
0.417
4.359
of the Alaska interagency coordination center.
Figure
Figure 10.
10. Overlay
Overlay of
of the
the change
change detection
detection map
map resulting
resulting from
from product
product rule fusion applied to scenario
4 with fire area history.
history.
A good
automatic
detection
and ground
truth information
can be of
observed.
Table
5. match
Overallbetween
accuracy,the
overall
error, kappa
coefficient,
false positive
and false negative
the
Particularly
note (1)
the
“cleanness”
of the4.detection result outside of the burn scar and (2) the close
measurement
level
fusion
using scenario
preservation of the burn scar boundary that was achieved. Both properties indicate our method’s
Overall
Overall
Kappasuppression
False
False
ability to simultaneously achieve
high performance
noise
and outline preservation.
Accuracy (%)
Error (%)
Coefficient
Positive (%)
Negative (%)
Classification results for the remaining six scenarios are shown in Figure 11. These results show good
Product rule fusion
99.932
0.067
0.997
0.021
0.269
performance
for both the “negative”
and the1.008
“positive” tests.
As expected,
no extended 2.543
change was
Sum rule fusion
98.991
0.967
0.653
identifiedMax
forrule
thefusion
scenarios that did
not
span
a
forest
fire.
Some
change
was
identified
along
97.609
2.390
0.924
2.476
2.020a stream
Min
rule
fusion
98.273
1.726
0.944
1.815
1.342
that crosses the area. This change is likely real and due to changes of river flow patterns or water
Majority voting rule fusion
98.842
1.158
0.961
0.417
4.359
level variations. Even though three classes (see Section 2.3.3) were used for the classification in areas
with negative change, none of the classes have a mean similar to that of a fire scar class. All “positive”
A good match between the automatic detection and ground truth information can be observed.
Particularly note (1) the “cleanness” of the detection result outside of the burn scar and (2) the close
preservation of the burn scar boundary that was achieved. Both properties indicate our method’s ability
to simultaneously achieve high performance noise suppression and outline preservation. Classification
results for the remaining six scenarios are shown in Figure 11. These results show good performance
for both the “negative” and the “positive” tests. As expected, no extended change was identified
for the scenarios that did not span a forest fire. Some change was identified along a stream that
crosses the area. This change is likely real and due to changes of river flow patterns or water level
variations. Even though three classes (see Section 2.3.3) were used for the classification in areas with
Remote Sens. 2016, 8, 482
21 of 27
negative
change,
none
Remote
Sens. 2016,
8, 482of the classes have a mean similar to that of a fire scar class. All “positive”
21 of 27 tests
reliably identify the burn scar and retrace its boundary. Figure 11b,d showed that the classification
reliably
identify
the burn
and retrace
its boundary.
11b,d showed
that
the this
of firetests
scars
was not
inhibited
by thescar
varying
geometry
of the pre-Figure
and post-fire
images.
Thus,
classification
of
fire
scars
was
not
inhibited
by
the
varying
geometry
of
the
preand
post-fire
images.
approach is able to increase the temporal sampling of our image acquisitions. The benefit of radiometric
Thus, this approach is able to increase the temporal sampling of our image acquisitions. The benefit
normalization for combining data with different observation geometry is quantified by comparing
of radiometric normalization for combining data with different observation geometry is quantified
scenario 5 with and without radiometric and geometric normalization. Employing radiometric and
by comparing scenario 5 with and without radiometric and geometric normalization. Employing
geometric
normalization
to scenario
5 gave an
overall accuracy
97.78%
and a kappa
coefficient
radiometric
and geometric
normalization
to scenario
5 gave an of
overall
accuracy
of 97.78%
and a of
0.924.kappa
Whencoefficient
radiometric
and geometric
normalization
is not normalization
employed weishave
an overallwe
accuracy
of 0.924.
When radiometric
and geometric
not employed
have of
87.08%
a kappa
coefficient
0.585.
an and
overall
accuracy
of 87.08%ofand
a kappa coefficient of 0.585.
Figure 11. Change detection map resulting from product rule fusion applied to (a) scenario 1; (b)
Figure 11. Change detection map resulting from product rule fusion applied to (a) scenario 1;
scenario 2; (c) scenario 3; (d) scenario 5; (e) scenario 6; (f) scenario 7.
(b) scenario 2; (c) scenario 3; (d) scenario 5; (e) scenario 6; (f) scenario 7.
4.4. Comparison to Reference Change Detection Techniques
4.4. Comparison to Reference Change Detection Techniques
Change detection results obtained from different approaches for scenario 4 are analyzed
quantitatively
in Table
6 and obtained
qualitatively
in Figure
12. Our
proposed for
approach
yields
Change
detection
results
from
different
approaches
scenario
4 an
areoverall
analyzed
accuracy ofin99.932%,
overall
error of 0.067%,
and a 12.
kappa
coefficient
of 0.997.
The performance
of
quantitatively
Table 6anand
qualitatively
in Figure
Our
proposed
approach
yields an overall
accuracy of 99.932%, an overall error of 0.067%, and a kappa coefficient of 0.997. The performance of
Remote Sens. 2016, 8, 482
22 of 27
our approach without a fast non-local means filter gave a good result as well. However, the accuracy
was reduced as a result of a false positive, causing the overall accuracy and kappa coefficient to
drop to 98.402% and 0.946%, respectively. The performance decreased when wavelet transform was
not utilized in our approach, giving an overall accuracy of 97.823% and a kappa coefficient of 0.927.
Furthermore, without the application of the morphological filter the performance dropped, giving an
overall accuracy of 97.963% and a kappa coefficient of 0.932. Also, in the absence of the EM algorithm
in our approach, the accuracy dropped to 97.550% and the kappa coefficient dropped to 0.916. Given
the results of Methods A–D (see gray shade area in Table 6), it is evident that each individual processing
step is important for the effectiveness of our approach. With regard to other published techniques,
Method E gave a lower accuracy when compared with our approach, with an overall accuracy of
93.816% and a kappa coefficient of 0.808. The lower accuracy is likely due to the region of interest
definition which leads to spectral confusion and resulted in several numbers of false positives and
false negatives in the final change detection result. The curvelet method (Method F) effectively filtered
the ratio image; however, it only relies on the EM algorithm to classify the fire scar. The method has an
overall accuracy of 93.054% and a kappa coefficient of 0.745. According to Method G, no filtering was
done, along with the absence of the EM algorithm. The thresholding of fire scars was done manually,
and this reduced the effectiveness of the method. Method G has an overall accuracy of 94.986% and a
kappa coefficient of 0.830. The degradation in the accuracy of the change detection result from Method
H, with respect to the proposed approach, is mainly because of the DT-CWT used. The DT-CWT is
fairly robust to speckle noise, and the down-sampling process used is not able to detect the changes
whose spatial supports are lost through the multi-scale decomposition. Method H gave an overall
accuracy of 89.078% and a kappa coefficient of 0.605. Method I showed a decent detection with an
overall accuracy of 96.587% and a kappa coefficient of 0.891. This is mainly due to the effective contour
definition that partitions the ratio image into change and no-change.
It is worth mentioning that all the methods used for comparative analysis were sent through
the identical pre-processing chain including SAR data pre-processing, ratio image formation and
logarithmic scaling, fast non-local means filtering and mathematical morphology filtering. While the
fire scars are correctly delineated in Methods E–I, minute changes (false positive) in the background
landscape were detected and amplified. Attempts to reduce the number of false positives for these
techniques led to a significant distortion of the fire-scar boundaries and reduced the reliability of the
final change detection map. Thus, our proposed approach produced a more consistent and more
robust result as indicated by the information in Figure 12 and Table 6.
Table 6. Overall accuracy, overall error, kappa coefficient, false positive and false negative of our
proposed approach with alternative methods using scenario 4.
Proposed
approach
Method A
Method B
Method C
Method D
Method E
Method F
Method G
Method H
Method I
Overall
Accuracy (%)
Overall
Error (%)
Kappa
Coefficient
False
Positive (%)
False
Negative (%)
99.932
0.067
0.997
0.021
0.269
98.402
97.823
97.963
97.550
93.816
93.054
94.986
89.078
96.587
1.597
2.176
2.036
2.450
6.183
6.945
5.013
10.921
3.412
0.946
0.927
0.932
0.916
0.808
0.745
0.830
0.605
0.891
0.172
0.797
0.713
0.248
5.526
1.105
3.964
3.959
2.887
7.761
8.144
7.754
11.972
9.021
32.206
4.659
41.035
5.681
Remote Sens. 2016, 8, 482
Remote Sens. 2016, 8, 482
23 of 27
23 of 27
Proposed Approach
a
b
c
d
e
f
g
Figure 12. Cont.
Remote Sens. 2016, 8, 482
Remote Sens. 2016, 8, 482
h
24 of 27
24 of 27
i
Figure
Change detection
detection map
(a) (a)
proposed
approach
without
fast non-local
means filter;
Figure
12.12.Change
mapshowing:
showing:
proposed
approach
without
fast non-local
means
(b)
proposed
approach
without
2D-SWT;
(c)
proposed
approach
without
morphological
filtering;
(d)
filter; (b) proposed approach without 2D-SWT; (c) proposed approach without morphological
filtering;
proposed
approach
without
EM
algorithm;
(e)
SVM
approach;
(f)
image
denoising
using
fast
discrete
(d) proposed approach without EM algorithm; (e) SVM approach; (f) image denoising using fast
curvelet
transform
via wrapping
with EM
algorithm;
(g) FFL_ARS
approach;
(h) DT-CWT
with intradiscrete
curvelet
transform
via wrapping
with
EM algorithm;
(g) FFL_ARS
approach;
(h) DT-CWT
with
and
inter-scale
data
fusion
approach;
(i)
UDWT
with
Chan–Vese
active
contour
model
approach.
intra- and inter-scale data fusion approach; (i) UDWT with Chan–Vese active contour model approach.
4.5. Electromagnetic Interpretation of Change Signatures
4.5. Electromagnetic Interpretation of Change Signatures
After change features are detected using the aforementioned approach, the history of the
After change
are detected
usinga the
aforementioned
approach,
the history
of the
amplitude
changefeatures
can be analyzed
to attempt
geophysical
interpretation
of the observed
change.
amplitude
change
can
be
analyzed
to
attempt
a
geophysical
interpretation
of
the
observed
change.
In this section we show the kinds of analyses that can be conducted after a robust change detection
In this
section
weapplied
show the
of analyses
can be conducted after a robust change detection
approach
were
to akinds
time series
of SARthat
images.
approach
were
applied
to
a
time
series
of
SAR
images.
In the presented wildfire scenarios, we observe (from the time-series of data that was analyzed)
In the
the burn
presented
scenarios,
we observe
(from the
time-series
of data
thataffected
was analyzed)
that
event wildfire
led to a general
increase
of the average
radar
cross-section
in the
areas
that
the burn
led to of
a general
increase
oftothe
cross-section
in the This
affected
areas
(Figure
13). event
An increase
about 4 dB
relative
theaverage
pre-fire radar
situation
can be observed.
is likely
(Figure
13).
increase
of about
4 dB relative
to the
can burned
be observed.
This is likely
due to
anAn
increase
of double
bounce
scattering
afterpre-fire
the treesituation
foliage was
off, exposing
the
tree stumps
and branches
interaction
with
microwave
signals.
Figure
13exposing
also showsthe
dueremaining
to an increase
of double
bounce for
scattering
after
thethe
tree
foliage was
burned
off,
that the tree
radar
cross-section
in the affected
area slowly
decreases
starting
aboutFigure
1.5 years
aftershows
the
remaining
stumps
and branches
for interaction
with the
microwave
signals.
13 also
burn
slow return
toward
pre-fire
brightness
is likely
related
regrowth
in thethe
that
the event.
radar This
cross-section
in the
affected
areaimage
slowly
decreases
starting
aboutto1.5
years after
affected
burn
event.area.
This slow return toward pre-fire image brightness is likely related to regrowth in the
is worth mentioning that seasonal effects can be observed in the detection of the fire scar in
affectedItarea.
our
While during
the summer
seasons
the average
radar brightness
It isstudy
wortharea.
mentioning
that seasonal
effects can
be observed
in the detection
of the fireremained
scar in our
significantly
above
the
pre-burn
level
throughout
the
time
series,
it
can
be
observed
that the
average
study area. While during the summer seasons the average radar brightness remained
significantly
brightness value decrease during the winter periods, likely due to the freezing of the soils and the
above the pre-burn level throughout the time series, it can be observed that the average brightness
addition of a seasonal snow cover. After the winter periods, the average brightness value increases
value decrease during the winter periods, likely due to the freezing of the soils and the addition of
again near the radar cross-section of the previous summer. This is an interesting and significant
a seasonal snow cover. After the winter periods, the average brightness value increases again near
observation as it indicates that, for this test site and dataset, fire scar detection will be less successful
the radar cross-section of the previous summer. This is an interesting and significant observation as it
during winter.
indicates that, for this test site and dataset, fire scar detection will be less successful during winter.
To support our interpretation of the data, we plot a second time series in Figure 13 (red line) that
To support
our interpretation
of theof
data,
we plot
a second
series
in Figure
13 (redimages.
line) that
shows
the average
radar cross-section
an area
unaffected
bytime
fire in
all preand post-fire
shows
average
radar cross-section
of an
area
by fire
all preand post-fire
images. of
The
The the
seasonal
brightness
variations can
also
beunaffected
observed for
thisin
area,
supporting
the assertion
seasonal
brightness
variations
can
also
be
observed
for
this
area,
supporting
the
assertion
of
weather
weather effects as the cause of the seasonal signal.
effects as the cause of the seasonal signal.
Remote Sens. 2016, 8, 482
Remote Sens. 2016, 8, 482
25 of 27
25 of 27
Figure 13. Time series showing fire scar area plotted over time (black line) and an area not affected
by fire plotted over time (red line). The gray line represents a fire scar that cannot be seen as a result
of
of snow
snow cover.
cover. The
The circle
circle symbol
symbol on
on each
each line
line indicates
indicates an
an area
area with
with no
no fire,
fire, while
while the
the square
square symbol
symbol
indicates
a
fire
scar
area.
The
gray
shaded
box
area
indicates
winter
months,
and
the
indicates a fire scar area. The gray shaded box area indicates winter months, and the dashed
dashed line
line
denotes
denotes when
when the
the fire
fire started.
started.
5. Conclusions
Conclusions
A flexible and automatic change detection method was presented that is effective at identifying
change signatures
pairs
of SAR
The proposed
approachapproach
removes radiometric
differences
signaturesfrom
from
pairs
of images.
SAR images.
The proposed
removes radiometric
between
SAR
imagesSAR
acquired
from
different
geometries
by utilizingby
radiometric
terrain correction
differences
between
images
acquired
from
different geometries
utilizing radiometric
terrain
(RTC)
which
enables
change
detection
from
different
image
geometries
hence, improves
the
correction
(RTC)
which
enables
change
detection
from
different
imageand,
geometries
and, hence,
temporal
of surface
change
that can
be achieved
a given from
database.
Suppressing
improves sampling
the temporal
sampling
of surface
change
that canfrom
be achieved
a given
database.
background
enhancing
information
by performing
log-ratio operations,
Suppressing information
background and
information
andchange
enhancing
change information
by performing
log-ratio
our
approach
detection
performance
while preserving
change signature
details.
operations,
ourdisplayed
approach high
displayed
high detection
performance
while preserving
change signature
The
integration
of modern
non-local
filteringfiltering
and 2D-SWT
techniques
provided
robustness
against
details.
The integration
of modern
non-local
and 2D-SWT
techniques
provided
robustness
noise.
classification
performance,
increased by
integrating
EM algorithm
with
mathematical
againstThe
noise.
The classification
performance,
increased
by an
integrating
an EM
algorithm
with
morphology
preservation
of the
geometric details
the border
regions,
product
mathematicaland
morphology
and
preservation
of the in
geometric
details
in was
the shown
border when
regions,
was
rule
fusion
was
employed.
Moreover,
our approach
gave a very
high overall
accuracy.
In addition
shown
when
product
rule fusion
was employed.
Moreover,
our approach
gave
a very high
overall
to
analyzing
the performance
of our
approach
on synthetic
data, we on
used
our algorithm
toused
conduct
accuracy.
In addition
to analyzing
the
performance
of our approach
synthetic
data, we
our
change
detection
in anchange
area affected
by wildfires.
this by
change
detection
analysis,
we found
that
algorithm
to conduct
detection
in an areaFrom
affected
wildfires.
From
this change
detection
aanalysis,
fire scarwe
could
be that
detected
from
the high
available
data.from
In addition
to accurately
found
a firewith
scar high
couldaccuracy
be detected
with
accuracy
the available
data. In
detecting
the
location and
extentthe
of the
burn and
scar,extent
an analysis
the scar,
imageaninformation
the
addition to
accurately
detecting
location
of theof
burn
analysis of within
the image
information
the
detected
scar
revealed
slow changes
in image
amplitudes
time,
most
detected
scar within
revealed
slow
changes
in image
amplitudes
over time,
most likely
relatedover
to the
regrowth
likely
related
to the
the burned
regrowth
of forest within the burned area.
of
forest
within
area.
Comparison ofofour
our
approach
to selected
methods
thatapproach
(1) our performed
approach
Comparison
approach
to selected
recentrecent
methods
showedshowed
that (1) our
performed
a high
overall
accuracy
and highpreservation;
geometric preservation;
(2)any
neglecting
any in
of our
the
with
a highwith
overall
accuracy
and
high geometric
(2) neglecting
of the steps
steps in our
approach
result inchange
an inferior
change
detection capability.
approach
will
result inwill
an inferior
detection
capability.
maindrawbacks
drawbacksofof
proposed
approach
(1)assumption
the assumption
that
the isimage
is a
The main
thethe
proposed
approach
are: are:
(1) the
that the
image
a mixture
mixture
of Gaussian
distribution;
and
that the does
approach
does
take fullof
advantage
of all the
of
Gaussian
distribution;
and (2) that
the(2)approach
not take
fullnot
advantage
all the information
information
the speckle.
Future
workusing
will explore
Gammafor
distribution
for fitting
the
present
in thepresent
speckle.inFuture
work will
explore
Gammausing
distribution
fitting the EM
algorithm
EM algorithm
rather than
the assumed
Gaussian
distribution.
Non-uniform
geometric
and
rather
than the assumed
Gaussian
distribution.
Non-uniform
geometric
and radiometric
properties
radiometric properties for all the areas of change in the synthetic image will be pursued as well.
Remote Sens. 2016, 8, 482
26 of 27
for all the areas of change in the synthetic image will be pursued as well. Images with high varying
geometry will be considered and analyzed. In addition, the development of the advanced approach
for selecting the number of changed classes will be pursued.
Acknowledgments: The authors want to thank the Alaska Satellite Facility (ASF) for providing access to the
Radarsat-1 data used in this study. We furthermore thank the Geographic Information Network of Alaska (GINA)
for the provision of high resolution Digital Elevation Models (DEMs) and for providing computing support.
Thanks to Maria Tello Alonso for many fruitful discussions. The work presented here was funded through the
NASA EPSCoR program under grant #NNX11AQ27A.
Author Contributions: This research was written and revised by Olaniyi Ajadi with contributions from all
coauthors. All authors have read and approved the final manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Bruzzone, L.; Prieto, D.F. Automatic analysis of the difference image for unsupervised change detection.
IEEE Trans. Geosci. Remote Sens. 2000, 38, 1171–1182. [CrossRef]
Tello Alonso, M.; López-Martínez, C.; Mallorquí, J.J.; Salembier, P. Edge enhancement algorithm based on
the wavelet transform for automatic edge detection in SAR images. IEEE Trans. Geosci. Remote Sens. 2011, 49,
222–235. [CrossRef]
Dekker, R.J. Speckle filtering in satellite SAR change detection imagery. Int. J. Remote Sens. 1998, 19,
1133–1146. [CrossRef]
Meyer, F.J.; McAlpin, D.B.; Gong, W.; Ajadi, O.; Arko, S.; Webley, P.W.; Dehn, J. Integrating SAR and derived
products into operational volcano monitoring and decision support systems. ISPRS J. Photogramm Remote
Sens. 2015, 100, 106–117. [CrossRef]
Floyd, A.L.; Prakash, A.; Meyer, F.J.; Gens, R.; Liljedahl, A. Using synthetic aperture radar to define spring
breakup on the kuparuk river, northern alaska. Arctic 2014, 67, 462–471. [CrossRef]
Yun, S.-H.; Fielding, E.J.; Webb, F.H.; Simons, M. Damage Proxy Map from Interferometric Synthetic Aperture
Radar Coherence. U.S. Patents 20120319893 A1, 20 December 2012.
Tello, M.; Lopez-Martinez, C.; Mallorqui, J.J.; Danisi, A.; Di Martino, G.; Iodice, A.; Ruello, G.; Riccio, D.
Characterization of local regularity in SAR imagery by means of multiscale techniques: Application to
oil spill detection. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium
(IGARSS 2007), Barcolona, Spain, 23–28 July 2007; pp. 5228–5231.
D’Addabbo, A.; Refice, A.; Pasquariello, G.; Lovergine, F.P.; Capolongo, D.; Manfreda, S. A bayesian network
for flood detection combining SAR imagery and ancillary data. IEEE Trans. Geosci. Remote Sens. 2016, 54,
3612–3625. [CrossRef]
Siegert, F.; Hoffmann, A.A. The 1998 forest fires in east kalimantan (indonesia): A quantitative evaluation
using high resolution, multitemporal ERS-2 SAR images and noaa-avhrr hotspot data. Remote Sens. Environ.
2000, 72, 64–77. [CrossRef]
Loew, A.; Mauser, W. Generation of geometrically and radiometrically terrain corrected SAR image products.
Remote Sens. Environ. 2007, 106, 337–349. [CrossRef]
Bazi, Y.; Bruzzone, L.; Melgani, F. Image thresholding based on the EM algorithm and the generalized
gaussian distribution. Pattern Recognit. 2007, 40, 619–634. [CrossRef]
Celik, T. A bayesian approach to unsupervised multiscale change detection in synthetic aperture radar
images. Signal Process. 2010, 90, 1471–1485. [CrossRef]
Kasetkasem, T.; Varshney, P.K. An image change detection algorithm based on markov random field models.
IEEE Trans. Geosci. Remote Sens. 2002, 40, 1815–1823. [CrossRef]
Celik, T. Unsupervised change detection in satellite images using principal component analysis and-means
clustering. IEEE Geosci. Remote Sens. Lett. 2009, 6, 772–776. [CrossRef]
Bovolo, F.; Bruzzone, L. A detail-preserving scale-driven approach to change detection in multitemporal
SAR images. IEEE Trans. Geosci. Remote Sens. 2005, 43, 2963–2972. [CrossRef]
Celik, T. Multiscale change detection in multitemporal satellite images. IEEE Trans. Geosci. Remote Sens. 2009,
6, 820–824. [CrossRef]
Remote Sens. 2016, 8, 482
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
27 of 27
Celik, T.; Ma, K.-K. Unsupervised change detection for satellite images using dual-tree complex wavelet
transform. IEEE Trans. Geosci. Remote Sens. 2010, 48, 1199–1210. [CrossRef]
Celik, T.; Ma, K.-K. Multitemporal image change detection using undecimated discrete wavelet transform
and active contours. IEEE Trans. Geosci. Remote Sens. 2011, 49, 706–716. [CrossRef]
Schmitt, A.; Wessel, B.; Roth, A. Curvelet-based change detection on SAR images for natural disaster
mapping. Photogramm. Fernerkund. Geoinform. 2010, 2010, 463–474. [CrossRef] [PubMed]
Small, D. Flattening gamma: Radiometric terrain correction for SAR imagery. IEEE Trans. Geosci. Remote
Sens. 2011, 49, 3081–3093. [CrossRef]
Gens, R.; Logan, T. Alaska Satellite Facility Software Tools: Manual; Geophysical Institute and University of
Alaska Fairbanks: Fairbanks, AK, USA, 2003.
Darbon, J.; Cunha, A.; Chan, T.F.; Osher, S.; Jensen, G.J. Fast nonlocal filtering applied to electron
cryomicroscopy. In Proceedings of the 5th IEEE International Symposium on Biomedical Imaging: From
Nano to Macro (ISBI 2008), Paris, France, 14–17 May 2008; pp. 1331–1334.
Bazi, Y.; Bruzzone, L.; Melgani, F. An unsupervised approach based on the generalized gaussian model to
automatic change detection in multitemporal SAR images. IEEE Trans. Geosci. Remote Sens. 2005, 43, 874–887.
[CrossRef]
Coppin, P.; Jonckheere, I.; Nackaerts, K.; Muys, B.; Lambin, E. Review articledigital change detection methods
in ecosystem monitoring: A review. Int. J. Remote Sens. 2004, 25, 1565–1596. [CrossRef]
Buades, A.; Coll, B.; Morel, J.-M. A review of image denoising algorithms, with a new one. Multiscale Model.
Simul. 2005, 4, 490–530. [CrossRef]
Wang, X.; Istepanian, R.S.; Song, Y.H. Microarray image enhancement by denoising using stationary wavelet
transform. IEEE Trans. NanoBiosci. 2003, 2, 184–189. [CrossRef]
Soille, P. Morphological Image Analysis: Principles and Applications; Springer Science & Business Media: New
York, NY, USA, 2013.
Zhu, X.X.; Bamler, R. Very high resolution spaceborne SAR tomography in urban environment. IEEE Trans.
Geosci. Remote Sens. 2010, 48, 4296–4308. [CrossRef]
Pham, D.L. Spatial models for fuzzy clustering. Comput. Vis. Image Underst. 2001, 84, 285–297. [CrossRef]
Bischof, H.; Leonardis, A.; Selb, A. Mdl principle for robust vector quantisation. Pattern Anal. Appl. 1999, 2,
59–72. [CrossRef]
ENVI User’s Guide. ENVI On-Line Software User’s Manual; ITT Visual Information Solutions: Boulder, CO,
USA, 2008.
Otsu, N. A threshold selection method from gray-level histograms. Automatica 1975, 11, 23–27.
Mercier, G.; Girard-Ardhuin, F. Partially supervised oil-slick detection by SAR imagery using kernel
expansion. IEEE Trans. Geosci. Remote Sens. 2006, 44, 2839–2846. [CrossRef]
AlZubi, S.; Islam, N.; Abbod, M. Multiresolution analysis using wavelet, ridgelet, and curvelet transforms
for medical image segmentation. J. Biomed. Imaging 2011, 2011, 4. [CrossRef] [PubMed]
Wendler, G.; Conner, J.; Moore, B.; Shulski, M.; Stuefer, M. Climatology of alaskan wildfires with special
emphasis on the extreme year of 2004. Theor. Appl. Climatol. 2011, 104, 459–472. [CrossRef]
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).