Adaptive Multi-threshold Object Selection
in Remote Sensing Images
Vladimir Yu. Volkov
Radioengineering dept.
Saint-Petersburg Electrotechnical University ''LETI'';
Radioengineering dept.
Saint-Petersburg State University of Aerospace Instrumentation
Saint-Petersburg, Russia
vl_volk@mail.ru
Abstract— Algorithms for detection and selection of objects
of interest in remote sensing observations based on multithreshold processing are investigated. The studied algorithms
convert monochrome images into a set of binary layers which
are next subjected to simple morphological analysis allowing
for the selection of isolated objects in each layer. By analyzing
the location and the geometric characteristics of objects in
neighboring layers one can generalize the selection procedure
by applying objective geometric criteria to the multi-layer
scene reconstruction based on the percolation effect. This way
adaptive threshold can be selected individually for each object
of interest leading to a significant reduction in the false alarms
rate during detection especially at lower-level thresholds where
high hit rates can be achieved. The efficacy and performance of
the approach is supported using both simulated random fields
as well as television and radar remote sensing observations.
Keywords—object detection and selection, multi-threshold
processing, image segmentation, percolation effect
I.
INTRODUCTION
The problems of effective detection, selection and
localization of the objects of interest in observational images
are of immense importance for the performance of television,
infrared, laser and radar remote sensing systems [1-4]. The
keynote properties of objects in contrast to the background
are their compactness and isolation. Segmentation of an
image into individual objects is usually based on such
characteristics as homogeneity of intensity and color
matching. Regional methods are mainly based on the
assumption that neighboring pixels within the object area
have more or less similar values [3]. For a detailed overview
of object segmentation methods that are sufficiently versatile
for various image analysis applications, not limited to remote
sensing systems, but also including microscopic or
biomedical imaging, we refer to [4] and references therein.
Mikhail I. Bogachev
Radioengineering dept.
Saint-Petersburg Electrotechnical University ''LETI'';
5 Professor Popov street,
197376 Saint-Petersburg, Russia
mibogachev@etu.ru
links isolated objects in neighboring binary layers to obtain a
3D hierarchical structure for subsequent segmentation.
The percolation effect is associated with the trickle of
empty pixels in the area occupied by an isolated object with
the increase of the threshold value which ultimately leads to
its destruction and the emergence of new objects from the
separated fragments [5,6]. After 3D reconstruction, all the
objects of interest can be selected using various criteria, such
as their geometric characteristics or texture parameters [7,8].
II. SELECTION OF OBJECTS IN MULTI-THRESHOLDED IMAGE
PROCESSING
To implement object selection, one needs to know the
expected properties of the object. Typically, there is a severe
shortage of information about objects, except for their typical
sizes and some assumptions about their location, perimeter,
shape and orientation. The original idea is to select and set
the optimal threshold value based on the results of the
preliminary selection of objects for a multitude of thresholds
to achieve the best result based on a posteriori information.
This approach was originally proposed in [7] for the
allocation of small-scale objects in remote sensing images.
The object area appears very effective for the selection of
similar small-scale objects by multi-threshold processing, as
it has been shown recently for a biomedical image analysis
example [8]. It is usually possible to exclude small objects
that arise from the background or are fragments separated
from larger objects that have already destructed at this
threshold from consideration. The drawback of this approach
is the need to specify the absolute object areas in pixels thus
limiting multiscale processing that in turn requires using
some scale-invariant features of the objects of interest.
Multi-thresholding transforms the original monochrome
image into a set of binary layers. For sufficiently large
number of thresholds one can assume that this transformation
does not lead to the loss of information. At the same time,
binary image processing is simpler and faster than grayscale
image processing.
Ideally, each object of interest requires its own threshold
value, and such local thresholds can be obtained by using
local (gliding) windows, within which the background can be
assumed homogeneous [9]. Although these methods also
require a priori knowledge of the object sizes, using a
background window also results in a loss of resolution for
the nearby objects and in the suppression of one object by
neighboring objects that fall within the area of this window.
This article develops an original approach to the analysis
of monochrome images based on their multi-threshold
processing followed by scene reconstruction utilizing the
percolation effect. A specific feature of the approach is that
both image segmentation and object selection are based on
the a posteriori information obtained for a series of multiple
binary layers. The main advantage is that no prior training is
required, and the algorithm parameters are adjusted for each
image and then for each object individually. This approach
Multi-threshold processing provides with an alternative
such as setting a threshold for each category of objects of
interest, which in turn are selected according to given criteria
[10,11]. In this case various parameters to describe the
category of objects may be used, such as the object size or its
orientation. Invariant parameters such as the ratio of the
squared perimeter to the area, the elongation coefficient of
the fitting ellipse as well as other geometric or textural
characteristics are more convenient for the analysis of multi-
scale images. In each binary layer, those objects that satisfy
the specified criteria are selected, and the binarization
threshold for such objects is chosen such that the maximum
number of selected objects of this category (or their pixels) is
obtained, taking into account the required preservation of the
shape of the objects. This process can be automated,
resulting in adaptive threshold setting method and algorithm.
The use of invariant geometric metrics helps to largely
overcome the limitations of the area-based selection method
which is not suitable for objects that considerably differ in
their area and intensity. The normalized quotient of the
squared object perimeter and the object area PS = P2/4πS that
characterizes the compactness of the object is a common
example of an invariant metric [10]. The normalizing
coefficient 4π provides with a unit value for the circle which
is the most compact planar object possible. Observational
image background is commonly characterized by "fractalshaped" speckle structures characterized by PS values
significantly above one. In marked contrast, objects of
interest are typically compact indicated by lower PS values
than the background objects, which makes it possible to
distinguish them from a noisy background.
Another geometric invariant is the relative elongation of
the main axis of the fitting ellipse PL = πL2/4S normalized to
the object area such that it equals one for a simple circle [10].
In contrast to PS, the PL coefficient is rather suitable for the
selection of prolonged objects. By minimizing the geometric
invariant(s), the threshold level can be chosen adaptively for
each of the selected objects. As we show below, the above
approach leads to a significant reduction of the false alarm
rate during detection, allowing to use lower thresholds
characterized by higher hit rates for the objects of interest.
III. THE HIERARCHICAL SCENE RECONSTRUCTION
BASED ON MULTI-THRESHOLD PROCESSING RESULTS
TAKING INTO ACCOUNT THE PERCOLATION EFFECT
To select a local threshold, one must establish the
relationship between the binary layers, and decide whether
each pixel belongs to the same or to a new object formed in
the new binary layer detached from a larger object each time
the threshold level increases. For that, establishing links
between pixels with the same coordinates in different binary
layers should be supplemented by the determination of the
specific relationship between objects in different layers based
on a certain algorithm and objective criteria. The percolation
based approach suggests reconstruction of a 3D hierarchical
structure representing all binary layers and setting up
relations between isolated objects in them according to rather
universal although reasonably tunable algorithm [11].
Let a monochrome image I(x, y), where I is the intensity
and x, y are the pixel coordinates, be subjected to a fixed
global threshold T. The result is a binary layer BT: { BT = 1 if
I(x, y) ≥ T; BT = 0 if I(x, y) < T } where BT = 1 represents
the objects of interest (foreground), such as buildings,
structures, vehicles, coastlines, while BT = 0 refers to the
background represented by the landscape of the observation
area.
Let us start with zero threshold T = 0, when I(x, y) > 0 is
satisfied for the entire image, thus forming a binary layer
containing a single global isolated object with an area of S0,
that occupies the entire image. Next let the threshold T be
increased by ∆T, so that some pixels appear below the new
threshold ∆T, leading to the formation of a new binary layer
satisfying I(x, y) > ∆T. If ∆T is relatively small and only a
small fraction of pixels is excluded from the object, then the
global isolated object remains uncrippled, while reducing
slightly in its area ST < S0. When the threshold is further
increased, the fraction of pixels with an intensity below the
threshold becomes large enough that these pixels merge
together to form gaps in the image. Ultimately, this leads to
the formation of gaps in the original object, and to the
separation of isolated fragments from it. In this case, one
should decide whether among several separated fragments
there is a successor to the original object at all, or whether
the original object is destroyed, and all the fragments appear
as new objects. Usually the selection of the successor(s) is
based on the analysis of the areas of the separated fragments
relatively to the area of the original object. This kind of
phase transition is known as percolation [5,6].
For each pair of binary layers, the ratio ST+∆T / ST
characterizes the fraction of connected pixels belonging to
the isolated object. Further increase in the threshold leaves
an increasing number of pixels initially belonging to the
object below the new thresholds T+k∆T, where k is an
integer number of layers; k = 0,1, ..., K. Thus Kp = ST+∆T / ST
can be introduced as a persistence parameter of the object
that depends on its topological and textural characteristics.
As long as Kp exceeds one-half, the object in the upper layer
can be considered as an unambiguous successor of the object
in the lower layer, which turns out to be its only predecessor.
If the object in the lower layer is precisely divided in two
halves, given that some pixels contributed to the formation of
the gap, both fragments appear smaller than ST/2, and thus
two new objects appear.
The initial binary layer for the new object is formed at the
moment of percolation of its predecessor representing its
''basement''. Next the new object accumulates further binary
representations for various threshold values Tk until the
condition I(x, y) > Tk is met. Let the object arise at the
threshold value T. The base area of the object ST decreases
over K layers until one of two events occurs: 1) the object
disappears completely, i.e. ST+(K+1)∆T = 0; 2) the object
fragmented, i.e. on the (K+1) th layer the ratio ST+(K+1)∆T /
ST+K∆T is less than the specified Kp value. In the latter case,
all the fragments of the initial object appear as new objects.
The fraction of the area eliminated over the lifetime of an
object PC = ST+K·∆T /ST can be considered as its percolation
coefficient, while the threshold level TK which leads to the
disintegration of the object is known as the percolation
threshold Tc. The percolation coefficient partly characterizes
the texture of the object's surface. If an object has a flat
vertex in its 3D representation with a constant intensity value
I(x, y) = const, it disappears completely after a single
threshold increment, and its percolation coefficient PC = 1.
In this case, the intensity value itself does not affect the value
of the percolation coefficient, i.e. it turns out to be invariant
to transformations such as shifting or scaling of the image. If
the object smoothly changes its intensity, i.e. it has a small
intensity gradient, then the inheritance between adjacent
layers with an increasing threshold will be maintained as
long as ST+K·∆T ≥ Kp·ST. If the object is "long-lived", its
percolation coefficient is usually close to zero (see example
in Fig. 1).
and pure white noise, the percolation coefficient is invariant
to the noise distribution and is equal to PC ≈ 0.593.
IV.
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OBJECT SELECTION USING ADAPTIVE GLOBAL
THRESHOLD
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The simplest selection is based on the area of objects. In
some cases, there is a priori information about the typical
size or area of objects. Objects smaller than the minimum
expected area of the object Smin are eliminated this way
significantly reducing the computational of the algorithms.
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The global threshold works well when detecting and
selecting a group of similar compact (or extended) objects
from a homogeneous noisy background. Consider the case
when the image contains a number of similar objects that
need to be selected. In each binary layer, objects that satisfy
the specified properties are selected, and the selection
threshold for such objects is chosen to obtain the maximum
number of objects of this category (or their pixels), taking
into account the required preservation of the object's shape.
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Figure 2 shows simulation results for 49 square objects of
16×16 pixels each with standard Gaussian noise background
(Fig. 2a). The signal-to-noise ratio (relative expectation shift
or deflection) in each pixel is d = 1.163. The dependence of
the total number of connected objects on the threshold value
is shown in Fig. 2b. When selecting objects by area,
acceptable distortion of object boundaries is achieved at
threshold value T = 133 (Fig. 2c).
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Fig. 1. Example of two Gaussian objects (a,b) and the percolation effect:
c – reducing areas in pixels for two objects with increasing threshold; (d,e)
– binary slices at the moment of percolation at threshold T = 17
As a result of this approach, a three-dimensional
hierarchical structure is formed, containing all the selected
objects, in which each pixel no longer belongs to one binary
layer, but corresponds to several binary layers k = 0, ... , K.
Based on this reconstruction, generalization of the image
segmentation and object selection procedures can be
proposed. First restrictions on the area of the selected objects
as well as other geometric parameters that characterize their
compactness and shape are introduced. For each selected
object from its multiple representation in a series of binary
layers, the optimal Topt threshold corresponding to the layer
with the best planar representation can be selected by various
geometric or textural criteria, as indicated above.
To analyze deeper details, one can set Kp = 1, which is
the most stringent requirement when the loss of even one
pixel for the original object leads to the formation of a new
object. In this case every rising threshold gives new
collection of objects. In contrast, choosing Kp = 0.5 results in
a significant reduction in the total number of threedimensional objects spanning through multiple binary layers.
If the image contains only random noise, i.e. the intensity
is randomly distributed throughout the image, the location of
pixels that appear below a certain threshold is also random.
Theoretically, it is well known that for an infinite image size
At lower threshold values, the shape of objects is
distorted by background noise, which significantly fragments
the boundaries. At higher threshold values some objects may
be lost. A simple detector with Neumann-Pearson threshold
provides false alarm rate F = 0.01 for each pixel, as shown in
Fig. 2d, but the hit rate is only D = 0.12, so the objects are
highly fragmented and none retain their squared shape. Fig. 4
shows the corresponding detection characteristic (curve 1),
where x-axis contains signal-to-noise ratio (deflection).
Widely used Otsu detector gives too many false alarms as it
is shown in Fig. 2e.
The false alarm rate depends on the minimal area Smin of
the detected objects (x-axis). Figure 3 shows corresponding
simulation results in logarithmic scale. For a given threshold
and for each area Smin the fraction of threshold exceedances
outside the objects of interest (caused by background noise)
has been calculated and normalized to the entire image size
giving the false alarm rate (y-axis, log-scale). Curves 1 to 5
correspond to threshold levels T = 150, 155, 160, 165, 170.
The consequence of selection and removal of small
objects is the ability to reduce the threshold to levels where
useful objects are better detected while maintaining low false
alarm rate. The larger the fraction of noise objects to be
removed, the lower the detection threshold can be set for the
same false alarm rate. For Smin = 150 it leads to normalized
threshold tNP = 0.47 instead of 2.326 (see Fig. 4, 1), while
without selection the same threshold would lead to a
significantly higher false alarm rate F = 0.32 (see Fig. 4, 2).
Similar curve showing per pixel detection under object
area based preselection scenario lies in between (see Fig. 4,
3). The results are obtained by simulation so y-axis presents
the estimates of the hit rate. The threshold deflection is now
equal to 0.5 providing about 6 dB benefit in the terms of
signal-to-noise ratio. Once there is information about the
shape, the results could be further improved by averaging.
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Fig. 4. Detection characteristics for object selection by area for Smin=150.
The x-axis contains signal-to-noise ratio (deflection). 1 – Neymann-Pearson
(NP) detector with high threshold; 2 – NP detector with low threshold; 3 –
detector for low threshold with object selection
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T = 133 Object number i= 2870 LENGTH = 180
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It is worth noting that the adaptation of the threshold
level to the maximum of the selected objects makes sense in
those situations when the scene contains a sufficient number
of rather similar objects of interest. In addition, this method
gives a slightly lower value of the threshold level. To
overcome the limitations geometric invariants are used [11].
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V. OBJECT SELECTION USING ADAPTIVE LOCAL
THRESHOLD BASED ON GEOMETRIC CRITERIA
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Otsu Threshold
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Fig. 2. Detection of squared objects in background noise. The intensity
scale in Fig. 2c shows the the object area
lg10 F
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Fig. 3. Fraction of threshold exceedances by background noise (false
alarms rate) as a function of the minimum object area Smin. Curves 1 to 5
correspond to threshold levels T = 150, 155, 160, 165, 170, respectively.
Let us first consider white noise field subjected to
threshold T with Smin=10 which can substantially reduce the
number of isolated objects in the binary layer. The
dependence of the number of selected objects Nobj on
threshold value T is shown in Fig. 5a, 1 where the total
number of objects equals 500. Fig. 5a, 2 indicates the
dependence of the maximum (over all objects in the given
layer) perimeter elongation coefficient PSmax on threshold T.
Obviously this coefficient reaches large values (up to 90) for
noisy objects with fractured structure. Area based
preselection reduces the rate of the noise based exceedances
as shown in Fig. 5b, 2 compared to simple threshold based
analysis without preselection (Fig. 5b, 1), while it has
virtually no effect on the values of the perimeter elongation
coefficient PS for the remaining objects.
It is interesting to investigate the influence of limitations
on the coefficient PS. Obviously restriction of the maximum
value for PS results in additional elimination of noise objects
characterized by high elongation coefficients. It seems these
objects have fractured structure and do not represents the
objects of interest. The value PSmax is the second important
parameter for the adaptive object selection by PS > PSmax.
Figure 6 shows that limiting the elongation coefficient PS
can decrease the false alarm rate during detection, resulting
in more efficient detection of objects corresponding to the PS
although the gain substantially depends on the object shape.
As a result, the curves exhibit a decline not only at high but
also at low threshold values (see Fig. 6).
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Nobj ; Psmax
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where brightness of each object corresponds to the
individually chosen threshold values. The image contains 82
objects which are selected by the use of local adaptive
threshold for every object. Corresponding variation of
threshold values is shown in Fig. 8a where x-axis is the
isolated object number. Typical U-shaped optimization curve
is presented in Fig.8b.
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Fig. 5. Results of Gaussian noise processing: a– number of objects Nobj
and maximum perimeter elongation coefficient PSmax after area selection
with Smin = 10; b – probabilities of noise emissions for simple binarization
(1) and after preselection by area with Smin = 10 (2).
Topt
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Fig. 8. The dependence of the optimal threshold values on the object
number (a) and typical U-shaped optimization curve (b)
tNP
Fig. 6. The dependence of logarithm for rate of exceedances
(false alarm rate) upon normalizing threshold for Smin = 10 and
PSmax = 1000, 300, 100, 10, 3 (from top to the bottom)
Next let us consider an aerial radar image depicted in Fig.
9a, and a sketch based on an aerial photographic image of
the same area shown in Fig. 9b. A common problem is to
combine or match fragments obtained by different remote
sensing tools. One possible solution to this problem is to
select the same objects in different images, which are then
used to obtain reference points, this performing matching not
at pixel-level but already at object-level representation.
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Fig. 7. Object selection from a television image with Smin = 150 and
PSmax = 50. Brightness scale indicates the adaptive threshold values
VI.
PRACTICAL EXAMPLES OF PROCESSING WITH REMOTE
OBSERVATIONS
Next let us consider an aerial television image shown in
Fig. 7a. The task is to select and localize buildings in this
scene. The proposed method is applied with Smin = 150 and
PSmax = 50. The selection results are presented in Fig. 7b
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Fig. 9. Radar image (a), sketch (b) and their Otsu analysis results (c and d)
In this case, the global threshold does not work well
leading to the destruction of the majority of objects as
indicated by Figs. 9c,d showing binary layers obtained using
the Otsu threshold. In contrast, by using an adaptive local
threshold with selection of objects by area taking into
account the PS coefficient allows one to obtain several
representations for each of the selected objects, which differ
in the displayed parameter (see results in Fig. 10).
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object exhibits a characteristic contour curve following the
river bank that can be easily used for the image matching.
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VII. CONCLUSIONS
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Bright = Psmax-Vopt Psmax = 30 nobj = 200
Bright = Psmax-Vopt Psmax = 30 nobj = 151
To summarize, method and algorithm for the adaptive
selection of compact and prolonged objects in remote
sensing images are proposed. The methodology is based on
the initial multi-threshold processing of the raw image,
resulting in the creation of several binary layers. After
selecting isolated objects in each of the binary layers, the
layers containing the best object representation in terms of its
geometric criteria are used for further analysis. The key idea
of the algorithm is using the a posteriori information about
object representations in each binary layer, and finding the
best layer in terms of the object properties depending on the
requirements such as preservation of each object shape
despite the non-stationary background. Based on this
approach automated adaptive selection algorithms can be
easily implemented. In a test detection problem, the
elimination of small objects by preselection provides with at
least 6 dB benefit in terms of the signal-to-noise ratio. We
believe that this approach is particularly suitable for the
analysis of objects with characteristic edges such as detection
and monitoring of the progression of cracks in ice shields.
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ACKNOWLEDGEMENT
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We acknowledge the financial support of this work by
the Russian Science Foundation (grant No. 16-19-00172).
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REFERENCES
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[1]
e
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Fig. 10. Different views of selected objects with respect to displayed
parameter: a – object area; b – minimal coefficient Psmin; c – difference
between thresholds Tmax – Topt
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Fig. 11. Objects which are selected separately on the radar image (a) and on
the sketch (b)
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matching based on their properties in each of the original
images. To illustrate this, Fig. 11 shows the same detached
object in the radar image (a) and in the sketch (b) after the
percolation of the base object. In both images the detached
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