' where Q (1) is the Euclidean distance of the vektor cli),
If there is divergence, then iterations are cut off, but not before an in-
put number of iterations has been carried out. This condition is allowed in or-
der to avoid a premature cut-off, because for certain data types, convergence
begins only after a few iterations.
2.3 Classifying the Pixels
The decision function for the separation of the classes 0! and 07 may be
written as follows
fj, (9) 6g 3 (5.15;
For the pixel g about to be classified, the decision value (2.13) may be compu-
ted for each of the 1 (see eqn. (2.3)) hyperplanes. This pixel is then assigned
to class Ol if the decision values
F1,2(9)s ooo F, (9) are > 0. (2.14a)
9
It is however assigned to class q if the decision values
Fas(q+1)(9) » aus Fa,k(9) are > 0 (2.14b)
and also
|
fa» cu Frq-1) 499) are < 0. (2.14c)
2.4 Computer Program Optimization In th
nth:
The foregoing describes the core of the algorithm as found in the computer grey '
program DIMIC - SH (DIgital Multispectral Image Classification - Separating
Hyperplanes). (See Ekenobi 1981). For best classification results, three opti- |
mization measures are incorporated:
The ni
(1) Choice of degree of polynomials,
(2) Choice of width of dead zone, and
(3) Data preprocessing.
where
2.4.1 Choice of Degree of Polynomials n = 4
Fig. 3 shows that not all data are classifiable by polynomials of first 24:2
degree. It shows also that the spectral means of the two classes are not far
from each other, and this is the criterion on which the decision to use second |
order polynomials is based. The concept of "spectral interval" is used to judge hyper|
nearness of means of any two classes, where this interval may be defined as the pixel:
difference between the Euclidean Norms of the mean vectors of the two classes. if the
the ui
The program DIMIC - SH adopts the second order polynomials for all hyper-
planes in the classification if the spectral interval between any two classes |
is smaller than 20. This limiting value has been found good for Landsat data. dead :
The decision to use second order polynomials means a decision to use a larger
number of coefficients and also a transformation of all data. Hh
known
A second order polynomial may be developed out of the first order one of un
eqn. (2.2) as follows: ina 5
gp
60
