ta 
vn " di ES o A: 
  
Each hyperplane in a classification may have a different width D of its 
dead zone. Based on the size of the smallest spectral interval in the classifi- 
cation, the program DIMIC - SH defines a basic value D which may lie anywhere 
between 0.002 and 0.6. This basic value is further magnified up to a maximum 
of 12 times for any hyperplane, depending on the size of the corresponding 
spectral interval, as well as on the degree of polynomials: 
The larger the spectral interval the larger the value of D computed for a par- 
ticular hyperplane. A second order hyperplane receives a value D that is twice 
what it would be if it was first order (see Table 1). 
  
  
  
Polynomials 
Spectral Interval 1st Degree 2nd Degree 
< 20 D D x 2 
20 - 90 Dx2 D x 4 
90 - 200 Dx4 Dx 8 
> 200 Dx6 D. x. 19 
  
  
  
  
  
Table 1: Determination of width of dead zone. 
D = basic value (only for Landsat data) 
2.4.3 Data Preprocessing 
Without preprocessing, Landsat MSS data could produce wrong estimates of 
"distances" (a very important concept in digital classifications). Of special 
importance to the Separating Hyperplanes method are: 
(1) Scale differences in the feature space. A calibration or normalization 
within each spectral band is done in order to be able to differentiate 
correctly among the classes. Data normalization is a division of every 
grey value by the standard deviation of the corresponding band. The n 
standard deviations are computed using all training pixels. 
(2) Correlations in the data 
  
The "distance" represented by the decision function f(g) oder f?(g) could 
be wrong because of the correlations among the n spectral bands. These corre- 
lations are eliminated through the transformation of all normalized datato n 
new orthogonal "coordinate" axes. This is the Pincipal Component transformation 
(Mulder et al 1974, Morrison 1976, Donker et al 1976). It is the linear pixel- 
wise transformation: 
giz T bg (2.18) 
where g is the original gray values vector of a pixel. The n X n transformation 
matrix T is a matrix of eigenvectors, computed from the covariance matrix for 
all training pixels in the classification. 
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