Change Detection & Time Series Analysis
Philosophy of Change
Change is mandatory, learning from the change is optional.
Anonymous
It is change, continuing change, inevitable change, that is the dominant
factor in society today. No sensible decision can be made any longer
without taking into account not only the world as it is, but the world as it
will be. . . . This, in turn, means that our statesmen, our businessmen, our
everyman must take on a science fictional way of thinking.
Isaac Asimov (1920–92)
Change alone is unchanging.
Heraclitus (c. 535–c. 475 B.C.)
If we want everything to remain as it is, it will be necessary for everything
to change.
Giuseppe Tomasi Di Lampedusa (1896–1957)
Every moment of one’s existence one is growing into more or retreating
into less. One is always living a little more or dying a little bit.
Norman Mailer (b. 1923)
Only man is not content to leave things as they are but must always be
changing them, and when he has done so, is seldom satisfied with the result.
Elspeth Huxley (b. 1907)
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Change Detection & Time Series Analysis
Change detection/TSA. What is it?
 Change detection refers to the difference in data between two dates pairwise image comparisons
(e.g. deforestation from one summer to the next).
 Time Series Analysis (TSA) refers to the examination of change in data
through time at more than two intervals - multiple image comparisons
(e.g. deforestation and regrowth at one year intervals over a 10-year
period).
Analysis of Change is concerned with two basic types of data:
 Quantitative - differences in degree (continuous data ) e.g. DEM
 Qualitative - differences in kind (discrete data ) - e.g. landuse
Techniques will tend to differ depending on whether
 the data is quantitative or qualitative
 pairwise (simple change) or time series comparisons are being made
Change can occur in time, space, or both:
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Change Detection & Time Series Analysis
Change Detection - Why bother?
Different reasoning tasks for developing space-time paths
within a Spatio-Temporal Data Model
Task
Prediction
Description
Given a description of the world over some period of time, and the
set of rules governing change, predict the world at some future
time
Description + rules  prediction of potential future state
Explanation
Given a description of the world over some period of time and the
rules governing the change, produce a description of the world at
some earlier time
Description + rules  description of a past state
Learning new
rules
Given a description of the world at different times, produce the
rules governing change which account for the observed regularities
in the world
Description + observed states - rules
Planning
Given a description of some desired state of the world over some
period of time and given the rules governing change, produce a
sequence of actions that would result in a world fitting that
description
Description of potential future state + rules  actions
Wachowicz, Monica, Object-Oriented Design for Temporal GIS, Taylor &
Francis, 1999.
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Change Detection & Time Series Analysis
Change Detection Analysis
General data processing elements (steps)
1. Data Acquisition and Preprocessing
 Establish suitable study area
 Evaluating the data for cloud cover and general data quality
 Purchasing the data
 Creating mosaics, taking sub-areas, masking unwanted features
2. Geometric and Radiometric Corrections
 Geometric fidelity is particularly important for change detection since
analysis is performed on a pixel-by-pixel basis (local operation)
 Spatial RMS errors should not exceed 0.5 pixel (image-to-image
registration)
 Radiometric corrections must be made to account for differences in
atmospheric effects (e.g. images might be selected that are weeks,
months, years apart) and sensor properties (e.g. gain & offset,
spectral range)
3. Data Normalization
 Select one image in the set as a reference and use radiometric
normalization techniques to normalize the remaining images to the
reference image
4. Change Detection Analysis
 Image differencing, image ratioing, image regression, PCA, CVA
(Change Vector Analysis), (SMA) Spectral Mixture Analysis
5. Accuracy Assessment
 Error / Confusion / Contingency matrix creation and analysis
 Kappa statistic
6. Final Product Generation
 Maps and reports of change
From Ross S. Lunetta, "Applications, project formulation, and analytical approach", in
Remote Sensing Change Detection, Ross S. Lunetta and Christopher D. Elvidge (ed.),
Ann Arbor Press, 1998
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Change Detection & Time Series Analysis
Overview of Change Detection Analysis techniques
4.
Change Detection Analysis
4.1. Pairwise Image Comparison (Change detection)
4.1.1. Quantitative Data
4.1.2. Qualitative Data
4.1.3. Spectral Mixture Analysis (SMA)
4.2. Multiple Image Comparisons (Time Series Analysis)
4.2.1. Image Deviation
4.2.2. Change Vector Analysis
4.2.3. Time Sequencing & Profiles
4.2.4. Principle Components Analysis
5.
Accuracy Assessment
Problems with Change Detection
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Change Detection & Time Series Analysis
4.
Change Detection Analysis
4.1.
Pairwise Image Comparison (Change detection)
4.1.1. Quantitative Data
4.1.1.1.
1.
2.
3.
4.
Image differencing
Image_C = Image_A - Image_B
Then threshold Image_C to classify "change" and "no change" pixels
Check classification accuracy with error (contingency) matrix
Repeat 2 and 3 until maximum accuracy is achieved.
Ground truth is required to create an error matrix as shown below:
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Change Detection & Time Series Analysis
4.1.1.2.
Image ratioing
Image C = Image_A / Image_B
Image differencing is for measuring differences in an absolute sense.
Image ratioing is used for measuring differences in a relative sense.
For example, if biomass level differences were measured and for one group
of pixels, the biomass levels increased from 5 to 10 and another group of
pixels, the increase was from 95 to 10, then the absolute difference between
the two sites is 5 (ie. 10 - 5 = 5 and 100 - 95 = 5). However, the former
represents a 100% increase and the latter a 5% increase.
More weight is given to values as they approach 0. Using the above
numbers:
10/5 = 2 vs. 100/95 = 1.05
Three important considerations:
1. Must use ratio scale data (i.e. must be a"true" zero)
2. Division by zero is an error. A small number must be added to the
numerator and denominator. Evaluate effects by looking at extreme
values, i.e.
 find maximum numerator and minimum denominator
 add small number to both and divide
 add double small number to both and divide
 assess whether small increment will affect your analysis
3. The resulting numeric scale is neither symmetric or linear so thresholding
is difficult. For example, 1 is twice as big as 0.5 but the difference is 0.5.
2 is twice as big as 1 but the difference is 1.0.
Solution: Take the natural logarithm of the ratio;
X
0.5
1
2
ln(X)
-0.693
0
+0.693
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Change Detection & Time Series Analysis
4.1.1.3.
Image regression
Regression coefficient provides a measure of the statistical correlation
between two images. However, regression assumes representative sample of
independent measurements. Raster imagery violate this basic assumption
due to high autocorrelation of adjacent pixels. If valid regression
coefficients, degrees of freedom, etc. are required, then the following
procedure will more accurately calculate these statistical parameters.
1.
2.
3.
4.
5.
Use AUTOCORR to calculate spatial autocorrelation
Use contract to sample the data at wider spacing
Repeat 1 and 2 for wider spacings (coarser resolutions)
Plot autocorrelation vs. sample spacing
Graph will indicate a sample spacing with sufficiently low
autocorrelation.
6. Run regression on images with sample spacing indicated in 5.
Regression can also be used for Radiometric Correction. Assume simple
difference or log transformed ratio image with value of 0 means no change.
This may not be the case! There are cases where images must be calibrated
to each other. Comparison of uncalibrated images will not be valid.
For example, gain and offset of a satellite sensor may be different for two
images taken a year apart or atmospheric conditions might be different.
Image regression computes gain and offset values to compensate for such
affects (radiometric correction).
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Change Detection & Time Series Analysis
4.1.1.4.
Change Vector Analysis
Assume pixel values for two different bands (images) change from one time
to another as shown in the following graph. It is possible to characterize the
change with the distance and direction images. The values of the pixels in
these images will help the analyst to visualize the change in multi-band
space.
D
 X 2  X 1 2  Y2  Y1 2
 Y  Y  
Angle  tan 1  2 1 
 X 2  X1 
where,
X1, X2 = pixel value of band1 at time 1 and time 2 respectively
Y1, Y2 = pixel value of band2 at time 1 and time 2 respectively
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Change Detection & Time Series Analysis
4.1.2. Qualitative Data
4.1.2.1.
Cross-classification
Cross-classification maps the logical AND of all possible combinations of
categories on two maps. This is summarized with a cross-classification
matrix as shown above.
In Idrisi, the CROSSTAB command produces a cross-classification image.
Analysis of the crosstabulation table focuses on the elements along the
diagonal as compared with the off-diagonal elements.
The per-category Kappa tabulation (discussed later) can be used to quickly
gain an appreciation of which categories are the major ones that have been
changed, and the nature of that change.
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Change Detection & Time Series Analysis
4.1.3. Spectral Mixture Analysis (SMA)
The reflected spectra measured by a sensor, such as Landsat TM, can be
modelled as the sum of the "pure" spectra within the instantaneous field of
view (IFOV) weighted by the areal proportion of each material. The "pure"
spectra are called endmembers and the process of solving for endmember
fractions is called linear Spectral Mixture Analysis.
This figure shows a schematic of a
TM Pixel containing three feature
types: soil, vegetation, and vegetation
shadow.
The middle graphs show the
reflectance spectra of the three feature
types.
The graph at the bottom of shows the
reflectance spectra of the pixel.
This figure shows the three
endmember mixture plotted on a
TM4 vs. TM3 scatter diagram
(NIR vs. Red )
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Change Detection & Time Series Analysis
The figure below shows the steps used in Multitemporal SMA.
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Change Detection & Time Series Analysis
By decomposing the image data into spectral fractions of "pure" spectra, a
decision tree can be created to classify the images based on changes in
spectral fractions. Changes in pixel spectra with time can be tabulated in
transition matrices for analysis.
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Change Detection & Time Series Analysis
4.2. Multiple Image Comparisons (Time Series Analysis)
Fewer methods exist for multiple image comparisons relative to pairwise
comparisons.
Helps examine (a) trends or, (b) anomalies from a general trend.
One of the major problems is that the time of images capture is not
synchronized with the variability in the phenomenon measured.
4.2.1. Image Deviation
Difference relative to a long term average. Difference between any image in
the series and the long term average can be analyzed. Adding all the
"difference" images would provide an image of the most "dynamic" areas on
in the image.
4.2.2. Change Vector Analysis
Computationally similar to pairwise analysis. There is often a strong
correlation between the variability in the measured phenomenon and the
distance component of the change vector.
4.2.3. Time Sequencing & Profiles
Time sequencing refers to the sequential display of images. In Idrisi, this is
achieved by using the Media Viewer to create AVI files.
Time profiles involves analysing the behaviour of a descriptive statistic (e.g.
min, mean, max, standard deviation, etc.) for selected sites (in Idrisi, up to
15 sites can be monitored) for series of images through time.
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Change Detection & Time Series Analysis
4.2.4. Principle Components Analysis
PCA for a series of images through time. First PC has areas of similarity,
the minor components highlight areas of change. The series can be
examined as a whole and change can be investigated in a progressive
manner from most significant to least significant (PC2, 3, etc.).
5.
Accuracy Assessment
Change Detection Matrix for a three-feature classification
Change
Classified
NC
T1
A
B
C
A
A
B
B
C
C
T2
A
B
C
B
C
A
C
A
B
No Change (NC)
A
B
C
A
B
C
1
3
3
3
1
3
3
3
1
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Reference
Change
A
A
B
B
B
C
A
C
5
5
5
5
5
5
5
5
5
5
5
5
2
6
6
6
6
2
6
6
6
6
2
6
6
6
6
2
6
6
6
6
6
6
6
6
C
A
5
5
5
6
6
6
6
2
6
Summary of possible combinations of change/no change represented in a
change detection error matrix
Classified
Reference
True Change
True No Change
Correct Change
Correct No Change
Incorrect Change
Incorrect No Change
No error (2)
Not Possible
Not Possible
No error (1)
Classification error(6)
False Positive(4)
False Negative (2)
Classification error(3)
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C
B
5
5
5
6
6
6
6
6
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Change Detection & Time Series Analysis
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Change Detection & Time Series Analysis
Producer and User accuracy
User accuracy:
Percentage of pixels that were predicted to be a cover
type that actually were that cover type according to the
"ground truth" (Rows)
Producer accuracy:
Percentage of pixels that were assumed to be true and
reflect errors of omission (Columns)
Example provided in the following tables
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Change Detection & Time Series Analysis
Problems with Change Detection
1. Many techniques rely on thresholding but there are no clear guidelines on
how these thresholds should be set.
2. Often there is a poor relation between the temporal resolution of the
remotely sensed data and temporal variability of the phenomena.
3. Many techniques rely on standard statistical techniques that do not take
into account autocorrelation.
4. There are few options for Change Detection Analysis given more than
two images (e.g. TSA)
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