7A-5-4 
(a) (b) 
Figure 5: (a) Original imager(b) through a red filter 
ongmal mage yalownest 
(a) (b) 
Figure 6: (a) Original imager (b) through a yellow 
filter 
(a) (b) 
Figure 7: (a) Original imager(b) through a red filter 
based on structural information is used to segment 
the color image. A Bayesian method is introduced in 
the following: 
Markov Random Field (MRF) technologies are fre 
quently used in image segmentationrtexture classifica 
tion and image restoration since they provide a general 
and elegant method for vision problem [7]. 
The segmentation field is modeled as a Markov 
Random Fieldra discrete random field Z(x). The field 
Z assumes discrete values from the label set T = [Oil]. 
Let z be a realization of Z with z(x) = 1 meaning the 
site x belongs to region lTand z(x) = 0 meaning that 
site belongs to region 0. Because the colorness image 
is similar to a gray level imageTthe label set T can be 
assumed as a binary set [011]. 
The redness computed by equation (1) can be mod 
eled as the true red plus a zero-meanT white Gaus 
sian noise. The colorness segmentation problem can 
be stated as finding the labeling filed z to maximize 
the posterior probability distribution function P(z\r). 
P{z\r) = P(r\z)P(z)/P(r) 
Here P{r) = 1. P(z) is the a priori probability distri 
bution function (a Gibbs distribution) defined by 
1 U(z) 
P(z) = -ex p—1-, 
where the partition function 
Q = ^exp-^ 
z£.Z 
serves as a normalized constant. In itTT is a constant 
called the temperature which controls the sharpness 
of the distributionTand 
U(z) = J2 v c(z) 
c 
is a sum of clique potentials V c (z) over all possible 
cliques C that are defined on a neighborhood systemr 
e.g. a 4-neighborhood system or an 8-neighborhood 
system. For examplerin a 4-neighborhood systemT 
U{z) = Vi((*(*)>*))+ v *( z ( x )> x ) 
x6C i x€C 2 
= a (*(*).*) + S II - z{Xj) || 2 
xec 1 x€C 2 
Here cq z ( x ) >x ) is a function of z(x) and the site xTCi is 
a set of single-pixel cliquesrand C2 is a set of pair-pixel 
cliques.