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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
This method classifies each group of pixels as a unit. 
This will tend to minimize misclassification for isolated 
pixels with outlier spectral characteristics. 
3-2. Region-based maximum likelihood classification 
with pdf 
The method suggested in this study can be summarized 
as a comparison of the pdf of an unknown group with 
pdfs of each of the training data sets. If two samples 
originate from the same population, the pdfs of the two 
groups should be similar to each other. Significantly, 
the distribution of radiance values that causes 
misclassification in pixel-based approaches (Swain and 
Davis, 1978), is critical information for the method 
developed in this study. 
To simplify the explanation, suppose two normally 
distributed populations have means 4; and u,, and 
standard deviation o, and o5 , respectively. 
Figure 3 represents three different cases that could 
occur. If two populations are very similar, then the 
two pdfs almost completely overlap (Figure 3a). If it 
is possible to estimate the area of the overlapped 
region, it should be close to 1, because the sum of all 
possible probabilities is equal to 1. However, if two 
populations are very different from each other, there 
should only be a very small overlap area for the two 
pdfs (Figure 3c). Thus it can be seen that the size of 
the overlapped area is proportionate to the similarity of 
the two pdfs. If the two pdfs are identical to each 
other, the overlapping area is equal to 1, if completely 
different, then 0, and the values between are an index of 
similarity (Figure 3b). The area of overlap can be 
found by integrating the relevant overlap portions of the 
two pdfs: 
Class 15} Class i Class 
a) 
Class : Class | 
c) 
Figure 3. Likelihood measured with pdf. The areas 
with diagonal lines indicate the degree of similarity 
between two classes. (a) Two almost completely 
overlapping class. | (b) Two partially overlapping 
classes. (c) Two almost completely separated classes. 
  
0j 7 ra esta Lm Ë pax, 6) 
m m 
Where: 0} likelihood index between X| and X, 
m-2for X| z.Y. 
m-Tlfor Xi X» 
When the likelihood index is extended to a multivariate 
pdf, with p variables and multiple samples, the 
equation is modified as follows: 
t M oo 1 1 
Ojj = po [7 sees PC. git m 
2x Il 
7 sts 7d T : 
Émile (Ay NE tin dp 
(5) 
Where Oj; : likelihood index between X; and X; 
i : patch id under investigation 
j : training data set id under investigation 
m= gj for X; 2X; 
J 
m= for KA; 
The decision rule in this study is extracted from the 
relationship between the likelihood and similarity as 
follows: 
Os = Ojj (6) 
Thus a patch is assigned to class c if the maximum of 
the likelihood index values is found for the pdf 
comparison of the patch and training data set C. 
With this method, a very stable similarity index is 
obtained because the variance and covariance 
information, as well as the class mean, are all directly 
used. One disadvantage of this method is that it 
requires much computing time. 
4. APPLICATION OF THE PIXEL AND REGION- 
BASED CLASSIFICATION METHODS 
The ADAR data is used to compare the new approach 
with traditional methods. The system captures images 
1,000 by 1,500 pixels in size, each pixel approximately 
1 x 1 meter. The ADAR system acquires four bands 
of data with four separate digital cameras sensitive to 
blue, green, red, and infrared wavelengths covering the 
range from 400 to 1,000 nm. 
The data were acquired at 19:42:18 GMT (2:42 pm 
local time) on March 24 1997 (early spring, prior to 
tree leaf-out) from an altitude of 2,522 meters. Leaf- 
off data provides clearer observation of ground 
features, but less spectral discrimination of forest cover. 
The analysis procedure in this study comprises three 
stages. It is assumed that patches have previously 
been identified by image segmentation using the region 
growing process incorporating thresholding and region 
growing. In the first stage, statistics for the patches 
are computed. The statistics used were the same as 
those used in the region growing stage, including the 
mean vectors and variance-covariance matrices. 
For the second stage, representative patches were 
selected to build a training data set for seven classes: 
Building, Road, Forest, Lawn, Shadowed Vegetation, 
Water, and Shadow. The patches selected as training