classes in a two dimensional band space using the extracted 
class statistics. If a sample point satisfying Eq.(7), we 
can expect that a sample point belongs to a class number i, 
with 10Ox(1 - a ) % confidence. 
D 2 (i) < X 2 ( 2a ) (7). 
In our study a = 0.05 is used. When the overlap domains 
appears as are shown in Figure 13, they are sequentially 
numbered as 1001,1002,.. and so on. Such numbers are called 
index number. The linked list structure is useful to 
determine which classes are involved in the overlap domain. 
We use two tables here, i.e., a index table INDEX and a link 
list LINK shown in Figure 14. Column 1 in of INDEX contains 
nonnegative integers, called pointers, the value of which is 
the row of the array LINK. LINK has the class numbers in 
column 1 and the pointers in column 2. When the value of 
the pointer in column 2 of the array LINK becomes zero, it 
indicates the end of the list. For example, we can find the 
classes with class number 210 and 110 by which the overlap 
domain 1001 is made from the tables in Figure 14. 
The confidence regions for pattern classes in a two 
dimensional band space are tabulated and stored in a look-up 
table LUT. More specifically, row number m and column number 
n of the table LUT corresponds to the integer part of 100x 
albedo value in band I and in band J, respectively. We have 
that 0 ¿ml 100, and 0 £n 1100: m,n are positive integer. 
Values of I and J could be chosen from 4,5,6 and 7 , but I ^ 
J. In a discrete two dimensional I-J space a point (m,n) 
fallen in the confidence region of a certain pattern class 
is assigned to have a correcponding class number and each 
element of LUT(m,n) is, thus, determined to have a 
corresponding class number. When a point (m,n) can not 
belong to any confidence region, then class number 0 is 
assigned. The sample array of a look-up table LUT is shown 
in Figure 15. 
Consultation of the LUT is done in the table look-up 
step. If an unknown albedo pattern having p = ( 15,10) in a 
I-J space, the LUT assigns immediately to a class with class 
number 440 for such a pattern in the case of Figure 15. 
Suppose an assigned class number k > 1000, then a pattern 
falls in an overlap domain. In this case tables of INDEX and 
LINK are referred to identify classes involved in the 
overlap. Then, the Mahalanobis distances from a pattern to 
each class center of involved are computed and 2 a pattern is 
assigned to a class which gives the minimum D(i). We can 
obtain a classification result by applying the foregoing 
table look-up approach to every point in a new albedo data 
set. As for computer times, the time required to classify 
256 x 256 pixels into 11 classes by our table lool-up 
approach was about 50 seconds of IBM 4341 CPU time, whereas 
8 minutes were needed to do the same classification by a 
conventional method based on a maximum likelihood dicision 
rule. 
DISCUSSIONS