Oliveira, Hermeson 
where |C] is the determinant of the covariance matrix and u is the mean vector. 
In this way, it’s possible to define a Mahalanobis distance between two points x and y_ (equation 2): 
G-xYC"(y-x) Q) 
Supposing that different observations are independent from one another, then the value of the equation 2 is an 
aleatoric variable with X^ (Chi-squared) distribution (Bins et al, 1993). 
The algorithm consists of three steps. On the first step a region list is ordered in a decrescent way by its area. 
It's expected that regions with big areas are representative of a class. The threshold, given in percentage, 
defines a maximum Mahalanobis distance that regions could be far from the class center. In another way, we 
could say that this threshold define an hiperelypsoid in the attributes space that every region, whose means are 
inside it, are considered to belong to a certain class. The distance values for each percentual are defined on X? 
table. 
The second step is initial classes detection. The proceeding is: get the statistics parameters of the first region 
of the list as initial parameters of the class. On an iterative process, remove from the list every region whose 
Mahalanobis distance is lower than a threshold. New statistics parameters of the class are calculated. This 
process is repeated until is possible to remove regions from the list. The next class is recognized as the same 
way and the process goes on until the list is empty. 
In the previous step, it could happen that a region could be misclassified. In the third step, the regions are 
classified again using the new centers defined on the previous Step, to correct any distortion (Bins et al, 1993). 
es RE LM S itla sisi i 
Mii rai iuf arf iacit Ac dub 8 cR 
2.2.2 Supervised Classification. The first thing to do is training fields selection, then the Bhattacharya 
algorithm is used. The Bhattacharya classificator is a supervised method used to classify segmented images, 
that is, the object to be classified is not necessarily a pixel but a region in the image. The steps of this 
classification are the same as the pixel classification. The Bhattacharya distance is traditionally used as a 
separability measure between classes to select image attributes. 
This distance is calculated using the equation 3: 
B-lMH«m (e eol (3) 
8 2 | (cha 
  
  
where, Ca and Cb are the covariance matrix of classes A and B; MH is the Mahalanobis distance defined for 
two distinct classes using the equation 4: 
CY 1/2 
wit =~ YEE) (1,1) e 
where, p is the means of each class. 
3 EXPERIMENTAL RESULTS 
To proceed the experiments, the channels 3, 4 and 5 of the LANDSAT-TM satellite were chosen, The 
definition of the cartographic scale as 1:50.000 to express the results, considered characteristics like 
fragmentation patterns and heterogeneity. The area of study was chosen because it was heterogeneous. 
  
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 1067