re an in- 
ed in or- 
ergence 
may be 
(2.13) 
0e compu- 
assigned 
(2.14a) 
(2.14b) 
(2.14c) 
computer 
ting 
e Opti- 
first 
t far 
second 
to judge 
d as the 
lasses. 
1yper- 
lasses 
data. 
larger 
ne of 
Tr EE OS E USE 
  
— P» Band 2 
$e 
Pd 
  
  
  
—>Band 1 
Fig, 3: Second degree polynomial 5 2 (9) 
(1 = class ot, 2 = class O ) 
S 2 2 
fu.B (g) = C194 + C59» + C491 + C495 4 C59197 + Co (2.15) 
or 
S 1 1 1 1 1 
LB (9) = C19] + C,99 + C293 + C494 + C595 + C6 (2.16) 
In this way, the two grey values of a pixel (eqn. 2.2) are expanded to five "new 
grey values". A comparison of eqns. (2.15) and (2.16) shows that 
2. à 2 4 
94 * 94595595. 94:7:94» 94 z 955.95 = 9405 
The number of coefficients in a second order polynomial is found as follows: 
: n * 1)! 
ni | = ACI) (2.17) 
where n' is the number of the "new spectral bands". For Landsat data (with 
n = 4 spectral bands) one obtains n' = 14. 
2.4.2 Choice of width of dead zone 
  
During the iterations procedure the algorithm changes the position of the 
hyperplane continuously in order to have the dead zone cleared of all training 
pixels. A hyperplane is fast to compute if the dead zone is small, and fastest 
if there is absolutely no dead zone. But such a hyperplane is poor, considering 
the unpredictable locations in the feature space of the numerous unknown pixels. 
Fig. 4 shows the hyperplane fi (9) between the classes ol and 02 without 
dead zone. This classification is "'' 100 % successful as far as the training 
pixels are concerned. It can however be seen that many of the other (unknown) 
pixels are wrongly classified. Therefore, from the point of view of the un- 
known pixels, a dead zone is important, since, according to Fig. 5 the algo- 
rithm must rotate the hyperplane in order to clear the dead zone of all train- 
ing pixels, and thereby saving several unknown pixels from wrong classification. 
61 
NEUE