Abstract This paper deals with the application of the MAD transformation to change detection in bi-tempotal hyperspectral data. Several processing schemes are proposed in order to facilitate both the actual change detection, the many variables involved and the spatial nature of the data. The MAD Transformation Applied to Hyperspectral Data The multivariate alteration detection (MAD) transformatio

A A Nielsen

A Müller

W Dorigo

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HYPERSPECTRAL DATA, CHANGE DETECTION AND THE MAD 
TRANSFORMATION 
Nielsen, A.A.1, Müller, A.2 and Dorigo, W.2 
1Technical University of Denmark, Informatics and Mathematical Modelling 
Richard Petersens Plads, Building 321, DK-2800 Lyngby, Denmark 
Phone +45 4525 3425, Fax +45 4588 1397 
aa@imm.dtu.dk 
2German Remote Sensing Center, Environment and Geoinformation Dept. 
Münchener Str. 20, D-82234 Wessling, Germany 
Phone +49 8153 281153, Fax +49 8153 281458 
Andreas.Mueller@dlr.de, Wouter.Dorigo@dlr.de 
Abstract 
This paper deals with the application of the MAD transformation to change 
detection in bi-tempotal hyperspectral data.  Several processing schemes are 
proposed in order to facilitate both the actual change detection, the many 
variables involved and the spatial nature of the data. 
The MAD Transformation Applied to Hyperspectral Data 
The multivariate alteration detection (MAD) transformation (Nielsen et al., 1998) 
is based on the established technique of canonical correlation analysis (CCA).  
The MAD variates are calculated as the differences between the canonical 
variates from an ordinary CCA (in reverse order).  The canonical variates are 
found by solving two coupled generalised eigenvalue problems.  The MAD 
change variables are invariant to linear (affine) transformations in the original 
variables such as 1) an additive shift in mean level (offset) or a multiplicative 
shift in calibration of a measuring device (gain), and 2) data normalisation or 
calibration schemes that are linear (affine) in the gray values of the original 
variables.  Changes of such nature are not detected which is an enormous 
advantage over most other multivariate change detection schemes published. 
The sum of the squared MAD variates standardised to unit variance ideally 
follow a χ2 distribution with as many degrees of freedom as there are terms in 
the sum.  This can be exploited to identify both change and no-change 
observations by means of percentiles in the χ2 distribution.  The no-change 
observations (the ones with very low χ2 values, say, below the 1% fractile) can 
be used in an automated procedure to normalise data between the two points in 
time, Canty et al (2004). 
The invariance of the MAD variates to linear (affine) transformations of the 
original variables can be exploited when we work with hypervariate data.  If we 
have very many variables the solutions to the coupled generalised eigenvalue 
problems involved may become unstable due to ill-conditioned variance-
covariance matrices.  A possible solution to (near) singularity problems in 
hyperspectral data transformations may be regularisation as hinted in Nielsen 
and Müller (2003).  Possible (near) singularities may also be remedied by 
means of for instance singular value decomposition, principal component 
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analysis (PCA) or maximum autocorrelation factor (MAF) analysis applied to the 
variables at the two points in time separately before doing canonical correlation 
and MAD analysis.  This approach is used here. 
Hyperspectral Data and Processing Scheme 
Two geometrically and atmospherically corrected HyMap scenes with 126 
spectral bands acquired on 30 June 2003 at 8:43 UTC and 4 August 2003 at 
10:23 UTC covering a small area near Lake Waging-Taching in Southeast 
Germany near the city of Salzburg (in Austria) are used to illustrate the method.  
The image size is 400 by 379 5 m by 5 m pixels.  The 30 June data are shown 
in Figure 1 and the 4 August data are shown in Figure 2. 
 
Figure 1: HyMap data from 30 June 2003 at 8:43 UTC 
798 nm (red), 677 nm (green), 570 nm (blue) 
The processing scheme presented here consists of four steps.  The originally 
measured 126 spectral bands at the two points in time are subjected to 1) CCA 
and MAD transformation; 2) PCA with 100 components retained at each point in 
time; and alternatively to 3) MAF analysis with 40 components retained at each 
point in time (processing step 4 follows below).  For the PCA the number of 
components retained corresponds to a span in eigenvalues of about 108.  For 
the MAF analysis the number of components retained was determined based 
on visual inspection; the cut-off occurs at an autocorrelation of 0.10-0.20.  For 
both steps 2 and 3 the retained components from the two points in time are 
used as input to the MAD transformation to detect change.  Without PCA or 
MAF pre-processing the CCA and MAD processing in step 1 gives negative 
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estimates of the lower order squared canonical correlations which are clear 
signs of singularity problems.   
 
Figure 2: HyMap data from 4 August 2003 at 10:23 UTC 
798 nm (red), 677 nm (green), 570 nm (blue) 
The change detected in steps 2 and 3 are shown in Figure 3 (left and middle 
subfigures).  Using the 40 MAF components rather than the 100 principal 
components clearly cleans up noise in the change image.  The change detected 
in the 40 retained MAF components is associated with the infrastructure such 
as built-up areas in the villages and field boundaries.  These changes, however, 
constitute artefacts and can be attributed to the following main causes: a) the 
time of acquisition for the second image is about two hours later than for the 
first acquisition; consequently, near sharp edges such as buildings and forest 
stands there is a shift in shadow which causes the large changes between the 
two images, and besides, in the villages a change in the direction of specular 
reflectance of roof tops can play a prominent role; b) small anomalies in the 
geometric correction and divergences that result from resampling procedures 
during data processing can attribute to high differences along field boundaries, 
lake shore and infrastructure.  To remedy this we 4) leave out observations with 
high change (above the 95% fractile) due to these effects from the statistics 
calculations in a second MAD transformation of the 40 retained MAF 
components.  The resulting change image is shown in Figure 3 (right subfigure). 
 4
 
Figure 3: The approximate χ2 value stretched linearly between the 1% and 99% 
fractiles of the relevant χ2 distributions for the left and middle images.  The right image 
is stretched linearly between ad hoc limits 20 and 200.  Bright regions are areas of high 
change, dark regions are areas of no change. 
More specifically Figure 3 shows the approximate χ2 values for the MAD 
transformation based on the 100 PCs (left), the 40 MAFs (middle), and the 40 
MAFs after removing observations with high change in the situation depicted in 
the middle subfigure from the statistics calculations (right).  The approach 
illustrated in the right subfigure highlights change in areas outside the high 
change areas in the middle subfigure such as the fields. 
Figure 4 shows the first three MAD variates of the first 40 MAFs after removing 
observations with high change in the situation depicted in the middle subfigure 
of Figure 3 from the statistics calculations.  Saturated colours give a more 
subtle indication of change areas as depicted in the first three change variables 
than does the right subfigure in Figure 3.  Correlations between the MAD 
variates and the originally measured spectral bands facilitate interpretation of 
the types of change indicated in Figure 4. 
Figure 5 shows the first three MAF variates of the MAD variates of the first 40 
MAFs after removing observations with high change in the situation depicted in 
the middle subfigure of Figure 3 from the statistics calculations.  Here, saturated 
colours simultaneously indicate high change areas as depicted in all change 
variables and high autocorrelation, and again correlations between the new 
variates (here the MAFs of the MADs) and the originally measured spectral 
bands facilitate interpretation of the types of change indicated.  These 
correlations are not shown here. 
Change Detected 
The change detected over the five weeks by the method in step 4 is due to 
growth of the main crop types such as maize, barley and wheat.  Furthermore, 
change can be detected that results from cutting and regrowth of meadows, i.e., 
from both decrease and increase of plant organic matter.  Meadows in the area 
are cut approximately five times during the growing season, independently from 
each other as regards the point of time.  As one would expect, on pastures, 
which are constantly being grazed, on forest stands and on the lake in the 
south, almost no change can be observed. 
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Figure 4: MAD variates 1 (red), 2 (green) and 3 (blue) of the 40 MAFs after removing 
observations with high change in the situation depicted in the middle subfigure of 
Figure 3 from the statistics calculations. 
References 
Nielsen, A.A., Conradsen, K., and Simpson, J.J., 1998, Multivariate alteration 
detection (MAD) and MAF post-processing in multispectral, bi-temporal image 
data: New approaches to change detection studies.  Remote Sensing of 
Environment 64:1-19. 
Nielsen, A.A. and Müller, A., 2003, Change detection by the MAD method in 
hyperspectral image data.  Proceedings of the 3rd EARSeL Workshop on 
Imaging Spectroscopy, pp. 115-116. 
Canty, M.J., Nielsen, A.A. and Schmidt, M., 2004, Automatic radiometric 
normalization of multitemporal satellite imagery.  Remote Sensing of 
Environment 91(3-4): 441-451. 
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Figure 5: MAF variates 1 (red), 2 (green) and 3 (blue) of the MAD variates of the 40 
MAFs after removing observations with high change in the situation depicted in the 
middle subfigure of Figure 3 from the statistics calculations. 
 


HYPERSPECTRAL DATA, CHANGE DETECTION AND THE MAD TRANSFORMATION

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HYPERSPECTRAL DATA, CHANGE DETECTION AND THE MAD TRANSFORMATION

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