It has been demonstrated in an investigation with Landsat MSS data 
(Ekenobi 1982) that an adjustment of variance levels whereby classes of high 
variance levels lose weight while those of low variance levels gain weight, im- 
proves considerably the classification accuracy. A complete elimination of the 
problem was however not possible. 
A new classifier, the Separating Hyperplanes Classifier has been developed, 
which assumes absolutely no conditions of the classification data. This classi- 
fier, that is, the operation and the mathematics of it, is fully described in 
this paper. 
1.1 Maximum Likelihood versus Separating Hyperplanes: Manners of Operation 
Every picture element, or pixel, may be represented by 
g = (915 99 +++... > 9h) (1.1) 
Band 2 grey values /4 y 
where the multispectral scanner generates data in n spectral bands. In Fig. 1 
measurements are represented, which were made in only two bands for several 
pixels, which include those of vegetation, water and bare ground. The figure 
is refered to as a two-dimensional feature space, in which every pixel may be 
viewed as a point in the coordinate system. The encircled pixels represent the 
"ground truth" and are used for the computation of the "discriminators" which 
are required for assigning the rest of the pixels (called "unknowns") to the 
classes they should belong. 
In the Maximum Likelihood classifier, each of the three discriminators 
fu(g). fu(g) and fg (g) 
Fig. 1 
(where V, W and B refer to vegetation, water and bare ground respectively) is a 
normal density function computed using the mean values vector and the covariance 
matrix of the training data of the corresponding class (Swain et al 1978). 
In the Separating Hyperplanes classifier on the other hand, each of the 
three discriminators (Fig. 2) 
fy w(9); fu, B C9? and fg, v (9) 
is a linear hyperplane which runs between two classes and is computed using a 
combination of the training data sets on both sides of it. Whereas the Maximum 
Likelihood algorithm assigns a pixel to the class whose middle point (mean va- 
lues vector) in the feature space the pixel lies closest to, the Separating 
Hyperplanes algorithm breaks the whole feature space up into "boxes" defined 
by linear hyperplanes. 
Band 2 arev values 
2. SEPARATING HYPERPLANES METHOD 
The mathematical function of a hyperplane is the "locus" of all points 
(pixels) which satisfy the equation 
f(g) = C191 + €292 * 0000000000 C = 0 (2.1) 
n*n n+l 
where Fig. 2: 
C1» Co» 44000 Cn» Cn+1 âre coefficients and g1» 92 +<<<<> 9, are the grey 
values of an arbitrary pixel g. 
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