313 
where To is the time required to extract pixel data out of 
the MSS data. T1 is the time required to link a cell with 
the cell followed by the pointer in it, fki is the frequancy 
of the data stored in i-th linked cell with the key of value 
k. nk is the number of pixels which have a key of value k. 
N is the number of the whole pixcels in the MSS imagery. It 
is important to get the mean access time T as small as 
possible because the table is accessed N times. To make 
the mean access time T minimize as possible, 
1) to minimize To and T1, 
2) to minimize the averaged nk by unifying distribution 
in the index table and 
3) to satisfy the condition that fi > fj for i < j 
are desired and necessary. 
The third constrain can not be satisfied when the table is 
generated, but it can be satisfied when the table is 
searchedfor the classification. 
CLUSTER ANALYSIS 
Background theory 
Most likelvhood strategy. Now, for convenience of 
ex pi an ation,assume that there are only two clusters in one 
dimensional space and that the intrinsic conditional 
probability distribution of a cluster i is p(x!wi) and one 
of a cluster j is p(x|wj). They are drawn by the thin solid 
lines in Fig.2. It is noticable that we can know nothing 
about these two distributions. The dotted line shows the 
probability function of x po(x), that is,the sum of these 
two distributions multiplied by probability of the class i 
p(wi) and probability of the class j p(wj), respectively. 
We can know only about the histogram h(x) in place of the 
intrinsic probability function po(x). 
On the other hand,when a pixel included in the class m is 
classified into the class l.then assume that the loss L(llm) 
is given by 
for 1=m 
(5) 
otherwise 
It is well known that the pixel x is decided to belong to 
the class 1 by Bays' strategy as the following equ.(6 ) holds 
p(xIwl)*p(wl) >= p(xIwm)*p(wm) 
(6) 
m=1 ,2,3 
N 
where N is the number of the total classes. 
From eq.(6 ) , the boundary between the class i and the class j 
is governed by the following eq.(7), 
B(x)=p(x|wi)*p(wi)-p(x|wj)*p(wj)=0 
(7 ) 
Approximation. Probability distribution function Po(x) 
can be approximated by the multi- dimensional histogram h(x) 
as followings