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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
classification methods. Our change detection approach that will 
be proposed in section Ill is a kind of post-classification 
method, so the classification is a very important step. In this 
paper. the classification methods we used are: thresholding, 
fuzzy C-means (FCM) and decision trees. 
2.1 Thresholding 
Considering a grayscale image, it is possible to do the 
classification by applying the thresholding technique using the 
map histogram. Thresholding permits the distinction of relevant 
topographic information, such as the lakes, rivers, wetlands, 
wooded areas, eskers, roads, etc., from contours and grid lines. 
The map thresholding classification technique is based on the 
fact that different textures have different mean gray values on 
the map. This technique is defined as follows. If a pixel 
represents the texture of interest, we set its value to “1” in the 
new classified image, and all the other pixels are set to “0”, 
such as 
sols | c frg sri visae, 
foy i0 for r(x,y)<g, and r(x,y)>g, 
where f(x, y)is the pixel value in the new classified image, 
and r(x, y)is the original pixel value. g, and 8; are gray 
values used as thresholds. Normally, we are interested in more 
than one regions. In this case, different values will be assigned 
to f(x, y) for different regions to distinguish them. The most 
appropriate threshold values have to be determined by the 
operator, since these values may vary according to the printing 
and scanning specifics. 
Take a look at Figure 1, in which there are two RADARSAT 
images taken in May and August 1997. These images were 
provided by the Defence Research and Development Canada 
(DRDC)-Ottawa. These images were registered by the 
automatic registration algorithm of A.U.G. Signals Ltd that is 
available through the distributed computing at 
www signallusion.com. Roughly there are two regions in these 
images: water and land. We can easily see the differences of 
water levels due to flooding of the river in May. We take out 
the regions we are interested from Figure 1 and plot them in 
Figure 2, which are the sub-images of the original ones. To 
apply the thresholding method to find the exact water and land 
regions, we have to determine the threshold first. Pick up some 
small regions with known classes (water or land) from the two 
images. The pixels in these regions are used as the training data. 
The histogram of these training data will be plotted. Since there 
are totally two regions in the images, the histogram is bimodal. 
The lowest point between the two amplitude peaks in the 
histogram can be set as the threshold. If there are N regions 
needed to be classified, the histogram should have N peaks. The 
thresholds should be set as the lowest points between every two 
consecutive amplitude peaks in the histogram. Figure 3 gives 
the classification results of these two images using this 
thresholding method. 
Furthermore, if we want to classify these images in more 
details, instead of water and land, there are three regions: deep 
water, shallow water and land. Using the above thresholding 
classification method, the results are given in Figure 4, where 
the black regions represent the deep water, grey ones are the 
shallow water, and the white regions stand for the lands. 
   
2.2 Fuzzy C-Means 
Fuzzy clustering has been proved that very well suited to deal 
with the imprecise nature of geographical information 
including remote sensing data. According to the fuzzy 
clustering framework, each cluster is a fuzzy set and each 
pixel in the image has a membership value associated to each 
cluster, ranging between 0 and 1, measuring how much the 
pixel belongs to that particular cluster [13]. There have been 
many different families of fuzzy clustering algorithms 
proposed in the last decade. The one used in this work is the 
Fuzzy C-Means algorithm (FCM), which is an iterative 
technique based on the minimization of a generalized group 
sum of squared error objective functions [14], [15]. 
€ n 
J Uv) =D ul, - v 
i=l k=} 
where the real number m is a weighting exponent on each 
fuzzy membership with] <m <=. c¢ is the total number of 
clusters and n is the total number of pixels in the image being 
^ 
  
classified. v—(w,v,,A,v,) are geometric cluster 
prototypes. U = tu,  } is a ¢ x matrix, where the element of 
U, u, satisfies 24, , € [0,1] and S e — 1 for all &. 
izl 
  
    
X 
Figure 2: sub-images of the images in Figure 1. 
Minimization of In is based on the suitable selection of U 
and v using an iterative process through the following steps. 
1. Determining values for c, M, error (e) and loop 
counter t=1. 
2. Creating a random c x 7 membership matrix U. 
3. Computing cluster centers. 
H 
(ut? m x 
ik xk 
vlad rte 
i n 
ENTE 
k=]