Zhaobao Zheng
Figure 1. The structure of five-order MRF
In this section, we will discuss how to apply genetic algorithm in solving above 24 parameters. It includes following
aspects.
2.2.1 Encoding Scheme of Chromosome. Now we define a set of individuals in a population generated during t
generation cycles. P(t)={l; k=1,2,...,m}, where m is the number of individuals or the population size. The size affects
both the ultimate performance and the effic iency of GA. Each individual is generated by some encoded form known as
a chromosome.
For a five-order MRF, the error equation is:
-n (x) = hr + bag + b,8 +.b4 D + bsl, + be f + bay
+ bou + how, + bas + byh+bat+bpt +hby h
+ bis 5, + DiewW+ bu, + bia V1 + bio f) t bul tb; p, (3)
Tbostbug| tb, T-—-x
Total 24 parameters(b ; -b»,) are encoded as a chromosome. Each parameter is represented by a 16- bit binary string. Fig.
2 illustrates the chromosome structures .
| b4 | b» | ee | bo |
»» 16bis Chi 23 lk 16bits
Figure 2. A five-order MRF chromosome structure
The rang of MRF parameters is defined in [-6.0,6.0]. For a 16-bit binary string corresponding to a parameter , the
decoding equation is :
b, -604 —— 1 -—— ha 24 4)
Where Bi; is a bit value (0 or 1) of parameter b;.
2.2.2 Fitness Function. Based on Eq.3, the fitness function is defined as:
N N
f = vix.)
Y. 2 ij (5)
i=l j=1
Where M is the width of the image, N is the height of the image. v(x;) is the value of the error function at pixel Xj.
2.2.3 Crossover operator. The crossover is an important operator in GA. It is first begun by selecting two
chromosomes of parents (P; and P5) randomly in a population. The selection is randomly determined by the Roulette
Wheel slot whosesize is proportional to the fitness . Also, the crossover of P, and P» is determined by a probability of
the crossover rate Pg. - Here ,the MRF parameters in a parent need to do crossover operation with the same
parameter from the other parent . As a result, 24 crossover points will be generated. Each crossover point is selected by
1050 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
