The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B3b. Beijing 2008 
determinate the number of clusters for a clustering. Another 
issue is how to calculate the fuzzy c-partition matrix. In this 
paper the number of cluster is determined by user a prior. The 
second issue is solved by calculating colour similarity 
measurement as follows. 
For a given vector set V = {v ls ... , v„), the fuzzy c-partition 
matrix can be calculated as follows. 
YjP(u k ,Vj) m -' 
k=1 
simplest is called mutation. Just as mutation in living things 
changes one gene to another, so mutation in a genetic algorithm 
causes small alterations at single points in an individual's code. 
The second method is called crossover, and entails choosing 
two individuals to swap segments of their code, producing 
artificial offspring that are combinations of their parents. This 
process is intended to simulate the analogous process of 
recombination that occurs to chromosomes during sexual 
reproduction. Common forms of crossover include single-point 
crossover, in which a point of exchange is set at a random 
location in the two individuals' genomes, and one individual 
contributes all its code from before that point and the other 
contributes all its code from after that point to produce an 
offspring. 
where m e (1, go) is the weighting exponent on each fuzzy 
membership. The larger m is the fuzzier the partition is, «,• is 
central vector for cluster /, and p{u h vj) is a similarity measure 
between vectors «, and Vj and can be calculated by 
M(u n v ] ) = exp(-^£/ («,., Vj)) cos(£ 2 #(ii,. , v y )) (4) 
where k\ and k 2 are parameters and d{w„ vj) and 6{u n vj) are the 
distance and the angle between u, and Vj as follows, 
( L 
d(u n v.) = 
V 
(5) 
2.3 Colour Histogram 
Colour histogram is an important technique in colour image 
analysis, because of its efficiency, effectiveness and triviality in 
computation (Pratt, 1991). Generally speaking, a colour 
histogram represents the statistical distribution of the colours in 
a colour image on all colours in a colour space. 
Given a colour space divided into / colour bins, the colour 
histogram of the colour image with n pixels is represented as a 
vector H = [h 0 , ..., hi.i], in which each entry hj indicates the 
statistical figures of the colours in the colour image which 
belong to the ;th bin, i.e., 
( 
#(«,., v.) = arccos 
v 
Yj U » V J> 
1=1 
(6). 
h.=-i = 0,l,,I-l (7) 
n 
where is the number of pixels with colours in the ith colour 
bin. 
2.2 Genetic Algorithm 
Genetic Algorithms (GA) are computer procedures that employ 
the mechanics of natural selection and natural genetics to 
evolve solutions to problems (Goldberg, 1989). Given a specific 
problem to solve, the input to the GA is a set of potential 
solutions to that problem encoded in some fashion, and a metric 
called a fitness function that allows each candidate to be 
quantitatively evaluated. These candidates may be solutions 
already known to work, with the aim of the GA being to 
improve them, but more often they are generated at random. In 
a pool of randomly generated candidates, these promising 
candidates are kept and allowed to reproduce by evaluating 
each candidate according to the fitness function using a series 
of genetic operations: selection, crossover and mutation. 
There are many different techniques by which a genetic 
algorithm can be used to select the individuals to be copied over 
into the next generation. Roulette-wheel selection is one of the 
most common methods. It is a form of fitness proportionate 
selection in which the chance of an individual's being selected 
is proportional to the amount by which its fitness is greater or 
less than its competitors' fitness. Conceptually, this can be 
represented as a game of roulette, each individual gets a slice of 
the wheel, but more fit ones get larger slices than less fit ones. 
The wheel is then spun, and whichever individual owns the 
section on which it lands each time is chosen. Once selection 
has chosen fit individuals, they must be randomly altered in 
hopes of improving their fitness for the next generation. There 
are two basic strategies to accomplish this. The first and 
Let RGB colour space be discretized along the R, G, and B axes 
by the numbers N R , N G , and N B , respectively. Then the total N 
(= N r x Nq x Nj) bins are available. These bins are coded in 
such a sequence from R to G and then from G to B. According 
to the specified discretizing and coding scheme the index of 
each bin can be represented as 
i - R + N g xG + N B 2 x B (8) 
where R = 0, 1, ... ,N R -1, G = 0, 1, ...,N G -1, and 5 = 0, 1,..., 
N B -1. 
Then the pixel (r p , g p , b p ) will be in the bin with the index i p , 
r N 
r p 1 v R 
+ N g x 
S p N g 
+ N B x 
b p N t 
[ 256 J 
[_ 256 
256 _ 
J is an integral operator. 
3. DESCRIPTION OF PROPOSED APPROACH 
3.1 Fuzzy Segmentation 
Based on the concept of the fuzzy c-partition above mentioned, 
the colour segmentation approach is designed. The approach 
consists of three steps: (1) Pre-clustering. This process includes 
finding an initial centre vector set U 0 and indicating the ranges 
in which the centre vectors are chosen in the following optimal 
procedure. This procedure is finished by using a histogram-