de Carvalho, Luis 
  
4 WAVELET BASED CHANGE DETECTION 
To be able to digitally detect changes on images acquired by different sensors we need first to bring all images to the 
same ground resolution. This was achieved by applying a one level pyramidal wavelet algorithm to the Landsat TM 
image from 1998 using as the scaling function a cubic spline (Starck et al. 1998). The resolution decreases by a factor 
of two after each decomposition level. Hence, the pixel size for the Landsat TM images became 60x60m after the 
transformation. Landsat MSS images were already acquired with a ground resolution of 57x57m and reduced to 
60x60m by a simple nearest neighbour resampling procedure. The Landsat TM images from 1985 and from 1998 were 
also processed at the original ground resolution of 30x30m. 
Ten ground control points were visually selected at corresponding locations on both images to perform geometric 
registration. The deformation model used was a polynomial of first degree and a nearest neighbour resampling created 
the warped image. No radiometric rectification was applied to the input images and the spatial misregistration (RMS 
error < 1 pixel) ranged from one to three pixels when visually evaluated. 
All images were then individually decomposed into five levels by the ‘a trous’ algorithm (Starck et al. 1998). Again, a 
cubic spline was used as the low pass filter and the difference between the scaling function at one level and a dilated 
version of the same function became the high pass filter. Finally, subtracting corresponding wavelet images we end up 
with the equivalent of decomposing the difference image. At this point the differences between the images are separated 
into five detail levels ranging from fine to coarse and a smoothed representation of the original difference image (Figure 
4). 
  
(b) 
    
(d) (e) (f) 
Figure 4. Detail images ranging from fine to coarse (a, b, c, d and e) and smoothed version (f) of the 
difference between 1998 (TM band 3) and 1981 (MSS band 2) decomposed using the à trous algorithm. 
In order to detect deforestation and new mining areas we multiplied details at the second scale by the details at the third 
scale when comparing images of 60x60m of ground resolution, hereafter called changes of interest. The product of 
wavelet scales is analysed in Sandler and Swami (1999) as a means of enhancing important transitions in the data. For 
images of 30x30m of ground resolution we used details at third and fourth scale levels. This product acts as an 
enhancement technique to further separate meaningful information from noise. It also combines in one image size 
classes from different scale levels. Depending on the types of changes under investigation other scale levels could be 
combined or even analysed alone. 
Image processing was carried out in ENVI, The Environment for Visualising Images (ENVI, 1997) except for the 
wavelet transforms that were performed in the MR/1, Multiresolution Analysis Software (MR/1, 1999). 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 343