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Grid Data to be Classified 
  
      
  
   
    
     
  
Search for Smallest Homo- 
genous Image Areas 
  
  
Reduction of the Homo- 
genous Image Areas to Classes 
  
  
Attaching the Grid Data to 
Spectral Classes 
Classified Grid Data 
  
  
fig. 2: Flowchart of the classification process. 
The class creation depends on the search for training 
areas with homogeneous sites in the grid data and on 
the attachment of the determined training areas to 
final classes. An area is considered as homogenous, 
ifthe grey values of each band show normal distribu- 
tion according to the z-transformation, and the bands 
are correlated with each other to a certain degree, 
depending on the choosen values of reliability. This is 
achieved, if first the previously set variance threshold 
is not violated. Second, if the pixel neighbourhood is 
considered to be at a 68%-level within the single stan- 
dard deviation. Third, the pixel neighbourhood lies at 
least with a 95%-level within the second standard 
deviation, and fourth the prove of a previously set 
correlation coefficient with a confidence level of 99% 
is achieved. The correlation test can only be applied if 
the influence of the other random variables has been 
eliminated as in the three steps before (WOLF 1968, 
p.519). The number of pixels in the neighbourhood 
can be varied by the size of the moving search wind- 
ow. Possible arrays are 3X3, 5X5, 7X7 etc.. 
The attaching of training areas to clusters and finally 
classes (up to several thousand, depending on the 
image content) is based on the  'modified 
Mahalanobis-Distance f” (SCHULZ & WENDE 1993, see 
formula 1) or Hotelling-T?-Test (BORTZ 1989). This 
deviation measure consists of a quantitative and a 
qualitative part as represented by the vectors of me- 
ans u and v, and on the other hand of the correlation 
matrixes A and B of two training sets which have to 
be compared. 
t? - (u-v)' * (A*B)" *(u-v) (1) 
The decision to combine two training areas to a clu- 
ster is oriented on the previously defined threshold of 
t?, or the smallest allowed distance of two classes to 
each other, which can not be exceeded by the com- 
puted t 2-values. 
45 
The t ?-test establishs a reduction of the discovered 
training sites by comparing each site with all the ot- 
hers, a necessary step to reduce the possibly large 
number of similar TA's. In a three channel image, 
each Channel is represented by 8-bit data, and 16.7 
million combinations possible. This computation will 
be repeated until the number of clusters can not be 
further reduced and the final classes are fixed. For 
each of the given classes results a mean vector and a 
correlation matrix clearly characterizing each class 
will be obtained. The result allows the further pixel 
attachment to the classes. A similar method has been 
described by MCCAFFREY & FRANKLIN (1993) and is 
centered around the F-test and limited to four chan- 
nels to evaluate. 
In order to get a classified result of an image it is pos- 
sible to apply a variety of methods with a given set of 
classes. In this paper only one procedure will be pre- 
sented. It is a distance measure applied to all pixel 
vectors to be compared with the class vectors in the 
lookup table from the calcclas-algorithm. A pixel vec- 
tor will be attached to one class if a previously given 
threshold of maximum deviation is not exceeded and 
the class is the nearest. The deviations will be de- 
termined by comparing the vectors of grey values with 
the mean vectors of the computed classes. Until now 
the classification scheme does not allow more then 
256 classes due to the 8-bit image-representation. 
The center scheme of this proposal is the class gene- 
rating algorithm. 
2040000 r 2040000 
   
2032500 2032500 
2025000 | 
2025000 
2017500 
  
195000 
fig.3: Band 4 image of the area under research with contou- 
red area of the tested subset. Subset size is 256 X 256 
Pixel. 
The coordinates represent the UTM-Grid for Zone 37 and 
Speroid Clarke 1880. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996