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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vo l. XXXVII. Pari B 3b. Beijing 2008 
based technique, (2) Searching the best fuzzy c-partition. It is 
realized by genetic algorithm to find a optimal fuzzy c-partition 
matrix, (3) Defuzzifing procedure. It converts the fuzzy 
partition matrix to the crisp c-partition matrix. 
3.1.1 Pre-clustering: For the given colour image C, the 
colour histogram H(C) can be obtained by method described in 
2.3 Section. It is obvious that if an image is composed of 
distinct objects with different colours, its colour histogram 
usually shows peaks. Each peak corresponds to one object and 
adjacent peaks are likely to be separated by a valley. The height 
of a peak implies the number of the pixels falling in the bin 
corresponding to the location of the peak. 
After the number of the clusters in the fuzzy c-partition c is 
chosen by user, the c highest peaks in the colour histogram can 
be detected and the bins corresponding to the detected peaks 
determine the ranges in which the centre vectors are 
investigated for the purpose of the optimization. The initial 
centre vectors are randomly selected in each of c bins. 
3.1.2 Optimizing: To search the optimal resolution of the 
fuzzy c-partition, a genetic algorithm is utilized and designed as 
follows. 
Chromosome Representation 
For a given m-dimensional vector set, the chromosome in a 
population is represented by a string consisting of c m- 
dimensional real vectors which encode the center vectors 
corresponding to c clusters in a c-partition. Figure 1 gives an 
example of such string where U donates the centre vector set 
corresponding to a string with c centre vectors. 
crossover is applied to selected two strings to generate two 
offspring. The crossover operation is applied stochastically with 
probability p c . After crossover, the offspring is considered for 
mutation. In this algorithm, the mutation is carried out by 
replacing strings in current generation to new strings selected 
from the same bins in which the original strings are. The 
mutation is performed with a fixed probability p m . 
Stopping Criterion 
There are two stopping criterion for the GA. Firstly, after some 
number of generations without improvement in the solution 
pool, the algorithm terminates. Secondly, setting a maximum 
iteration, after the iteration the algorithm terminates. 
3.1.3 Defuzzifing 
In order to obtain the segmented image, it is necessary to 
transform the fuzzy c-partition matrix to the crisp partition 
matrix. In this study, the following defuzzification scheme is 
used. 
Let P - [p,y] i = 1, ..., c and j = 1, ..., n be the fuzzy c-partition 
matrix, it is well known that p,, presents the membership grade 
for pixel j belonging to cluster i. A percent partition matrix, P p , 
is defined as 
«1 
«2 
Ui 
U. 
Figure 1 String consisting of c vectors 
Population Initialization 
In the initial population, the string vectors are the colour vectors 
randomly selecting from each bin of c bins mentioned in 2.3 
Section The number of strings in the population N is given by 
users. 
Fitness Computation 
In order to use the genetic algorithm, it is necessary to define an 
objective function. In this paper, the aggregation similarity for a 
set of centre vectors to all vectors in the considered vector set is 
used to be the function 
\±±p, 
c i-l j=\ 
(10) 
The fitness of each chromosome in the population is evaluated 
with the objection function. For each chromosome, the center 
vectors encoded in it are first evaluated, and then the fuzzy c- 
partition matrix corresponding to the chromosome is calculated 
by using the Equation (3). 
Genetic Operations 
Three kinds of genetic operators are used in this genetic 
algorithm, selection, crossover and Mutation. The conventional 
roulette wheel method is used for selection. Then one-point 
Pa 
Po 
j=i 
(11) 
In terms of the percent partition, the crisp partition matrix, P c 
\p ci j\, is defined as 
Pc = 
I !» Ppu =™x(P P ij) 
0, otherwise 
(12) 
It is clear that in the crisp-partition matrix each pixel belongs to 
a certain cluster. 
3.2 Object Extractions 
Once the segmented images are obtained by the above 
segmentation algorithm, the binary object image can be 
extracted by selecting the pseudo-colour corresponding to the 
object regions. In general, the objects in the binary image are 
corrupted by noise objects, which have the similar colour to 
objects. In order to make the object regions clear, it is necessary 
to filter the corrupted object image. To this end, binary 
morphological operations are used. For example, depending on 
the shapes of noise objects, the appropriate combinations of 
binary dilation, erosion, opening, and closing should be chosen. 
3.3 Delineation of Vehicle Outline 
To extract the building regions according to the colour features 
of the buildings and uses an edge extraction algorithm to detect 
the skeletons of the detected buildings. To this end, a boundary 
extractor is designed and described in this section. 
Following the definition of 8-neighborhood shown in Figure 2, 
the boundary pixel for building is determined if it is a contour