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31 PAR Algorithm 
This is a widely used decision rule based on simple Boolean 
"and/or" logic. Training data in n spectral bands are used in 
performing the classification. Brightness values from each 
pixel of the multispectral image are used to produce an n- 
Hits ea 
H =) with 4 , being the mean value of the training data 
dimensional mean vector, Mc =( U 4, U ,, ..., 
obtained for class c in band k out of m possible classes. S, is 
the standard deviation of the training data class c of band k out 
of m possible classes. Using a one-standard deviation threshold, 
a parallelepiped algorithm decides BV, is in class c if, and 
only if, 
Ha Sa s BV, * Ha + Ser (1) 
where c 2 1, 2, .., m is number of classes; k 2 1, 2, .., n is 
number of bands. Therefore, if the low and high decision 
boundaries are defined as 
La = Het = Sa (2) 
and 
Ha = Ha + Sa (3) 
the parallelepiped algorithm becomes 
L.S BV ei, (4) 
lhese decision boundaries form an n-dimensional 
parallelepiped in feature space. If the pixel value lies above the 
lower threshold and below the high threshold for all n bands 
evaluated, it is assigned to that class. When an unknown pixel 
does not satisfy any of the Boolean logic criteria, it is assigned 
to an unclassified category. 
3.2 MID Algorithm 
For two bands, k and / , the Euclidean distance is 
  
Dist = (av, -n4) *(BV,-u,) (5) 
where ,, and ,,, represent the mean vectors for class c 
measured in bands k and /. 
It should be obvious that any unknown pixel will definitely be 
assigned to one of the training classes using this algorithm. 
There will be no unclassified pixels. 
When more than two bands are evaluated in a classification, it 
is possible to extend the logic of computing the distance 
between just two points in m space using the equation 
(Schalkoff, 1992) 
(6) 
2 A 
Das = n/a - b) 
3.3 MAL Algorithm 
The maximum likelihood decision rule assigns each pixel 
having pattern measurements or features X to the class c whose 
units are most probable or likely to have given rise to feature 
vector X (Foody et al., 1992). It assumes that the training data 
statistics for each class in each band are normally distributed, 
that is, Gaussian (Blaisdell, 1993). In other words, training 
data with bi- or trimodal histograms in a single band are not 
ideal. 
The decision rule applied to the unknown measurement vector 
X is (Schalkoff, 1992): 
Decide X is in class c if, and only if, 
D- => Pi (7) 
where i =1, 2, 3, ..., m possible classes, and 
P.=- T flos, [det(V, ) * (x - M.y v^(x - M, ) (8) 
and det(V ) is the determinant of the covariance matrix V. 
Therefore, to classify the measurement vector X of an unknown 
pixel into a class, the maximum likelihood decision rule 
computes the value p for each class. Then it assigns the pixel 
to the class that has the largest (or maximum) value. 
This assumes that each class has an equal probability of 
occurring in the terrain. However, in most remote sensing 
applications, there is a high probability of encountering some 
classes more often than others. Thus, we would expect more 
pixels to be classified as some class simply because it is more 
prevalent in the terrain. It is possible to include this valuable a 
priori (prior knowledge) information in the classification 
decision. We can do this by weighting each class c by its 
appropriate a priori probability, a. The equation then 
becomes: 
Decide X is in class c if, and only if, 
p.(a.)= pa) (9) 
where i 2 1, 2, 3, ..., m possible classes, and 
P. (a.) - log, (a.) - 
DS 
{log [det(V, )] + (x — M.) v^(x = M.)} 
(10) 
This Bayes’s decision rule is identical to the maximum 
likelihood decision rule except that it does not assume that 
each class has equal probabilities. 
3.4 MAD Algorithm 
The Mahalanobis Distance classification is a direction 
sensitive distance classification algorithm that uses statistics 
for each class (Research Systems, Inc., 1996). It is similar to 
the maximum likelihood classification algorithm but assumes 
all class covariances are equal and therefore is a faster method. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 401