polyno- 
ater and 
(2.2) 
S sets 
fered to 
an un- 
e three 
classes 
six sepa- 
r k clas- 
(2.3) 
jn. 
(2.4) 
table as 
(2.5) 
jmented 
higher 
ne" whose 
fact, 
rations 
ning 
one set 
G = (2.6) 
which for n = 2 and for two training pixels per class is as follows: 
933-09921,:4! 
942 9» 1! 
"Ma 93 7l 
7044/57924 4 
In this example, the total number N of pixels for the computation of the coef- 
ficients C is 4. The mathematical model is 
eG): eas eu) (2.7) 
In this iterative procedure, the "i" refers to the i-th iteration. y(i) is the 
corrections vector; e is a multiplier. The initial values of the coefficients 
are set to zero. 
Each of the N training pixels is tested for "classifiability". A pixel is 
accepted as classifiable if 
Dol s gg (2.8) 
Only the unclassifiable pixels are used for the computation of the corrections: 
J 
i 1 
Vl ados miri ideis. (2.9) 
J-1 
where J is the number of the unclassifiable pixels. The multiplier is evaluated 
as follows: 
e Ee x d (2.10) 
EV] 
where ¢ is an input, qonstant ("correction factor") and || y) |] oiscthe Eucli- 
dean distance of Vli). 
Iterations are cut off automatically when J reduces to zero. That is, ite- 
rations continue so long as the algorithm converges. Convergence exists if 
g( iti rig oo, (2.11) 
where r(1) is the sum of errors in the i-th iteration: 
J 
i 1 1 D i 
pli) = X "Ty (5 - c(i) ° gj) (2.12) 
jme 
59