j B: i 
—À To demonstrate the consequences of direction dependant radiance behaviour for classification 
the analyzed results are displayed in the two dimensional fedture space in figure 3. 
The means are determined by second order polynomials, the plotted ellipses represent the 
À trendcorrected covariance matrices calculated for 5 scan angle ranges. These results 
qe indicate a strong variation of means for all analyzed objects and additional hue shifts for 
: N some objects (winterwheat and grass in the + 40° region). Because this radiance behaviour 
i varies from object to object, correction is not possible without knowledge of the object[1]. 
  
Consequently the direction dependant grey value changes must be considered in the 
classification stage. There are also changes in covariance matrices (ellipses in figure 3), 
which should be accounted for if there are objects with similar spectral characteristics. 
3. DIRECTION DEPENDANT CLASSIFICATION 
  
3.1 Realization in a computer program 
  
Therefore a procedure for a direction dependant maximum likelihood classification was 
developed. In the maximum likelihood classification the unknown pixel is classified to 
the class with the maximum likelihood, using the following discriminant functions L2 I: 
1 
9; (X)=log_p (w.) - log, |<] - (x-u) ! c7! (x- u) 
In this formula the grey values X of unknown pixels are known, whereas mean vectors U 
  
  
and covariance matrices C are unknown. U and C are estimated before classification for 
each class i using training areas. Normally for each class only one mean vector U. 
and one covariance matrix C are used. The statistical values determined in this way are 
not representative for the whole strip as shown above. Therefore serious misclassifications 
in some scan angle regions occur. 
  
gle. 
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