7A-5-5 
As we knowr P(z) imposes a spatial connectivity 
constraint and contextual constraints. For exampler 
traffic signs often occur on both sides of a traffic scene. 
The single-pixel clique potential V\ (z(x),x) with small 
value a( z ( x ) ?x ) can be pre-defined on those sites which 
means the likelihood of those regions which contain 
potential traffic signs is higher. 
The conditional probability function P(r\z) is de 
fined by 
P{r\z) 
1 
n V 2 * 
exp 
Vc(z{xi),Xi) 
D 
Ar(xi,Xj) 
X Vi{z(xi),Xi) 
XiECi 
+ X V 2( Z (Xi),Xi) 
XiECi 
X a (x(xi),Xi) 
+ X D ii z ( Xi ) “ ii 2 
exp(—/3 || Ar{xi,Xj) || 2 ) 
r(xj) - r(xi) 
Here the redness image r is modeled as a mean in 
tensity function u plus a zero-meanT white Gaussian 
noise n(0, <7 2 )r> = u + n. Thus the colorness image 
segmentation is solved by maximizing the posteriori 
distribution function 
Here (3 is a factor. Because V2 is a smoothness 
constraint if two pixels in a pair-site clique C2 
have very different valuesrthen the region class 
of the two pixels is not possibly the sameTthen D 
nears zerorwhich does not affect V2. 
P(z\r) = -pr exp u ( z ) ^ exp u ( z \ r ) 
Q 
■irai 
where 
U{z\r) = X ¿2 K®) - w U(x),x)] 2 - 
X x 
This yields 
arg minX^rW - u {z{x)>x) ] 2 
X x 
T } ^ a (z(x),x) + XI II Z ( X i) ~ z i x j) II 
xECi XÇ.C2 
The complete algorithm (given here using a redness 
image) is as follow: 
1. Given initial parameters 0 = {redhaT redhcT 
redsaFredscTredlarredlbrredlcjra, degree of red 
ness r is computed using equation (2). 
2. To solve the optimization problemTan ICM (iter 
ated condition method) method [9] is usedTvisit 
each site xTfind z{x) by maximizing: 
P(z(xi)\r(xi),z(xj),all Xj e N Xi ) 
Vc (z(Xi),Xi) 
= exp ' c 
Here 
3. Once all sites visitedTre-estimate 0 by minimiz 
ing : 
0* = arg nun X II u (*(*),x) “ 
*(*)=! 
r(x,h(x),s(x),l(x),Q) || 2 
4. Exit if the segmentation is satisfied (e.g. class 
assignment no longer changes)Totherwise repeat 
steps 2-3. 
4.4 Size filter by blob analysis 
In most casesT unwanted regions appear in a color- 
component image due to noise. UsuallyTsuch regions 
are small. After a binarized image is obtainedTblob 
analysis is used to find those isolated regions whose 
size are below a threshold To and remove them. Re 
sults of extracted signs are given in Figure 8. 
5 Shape analysis by NFD 
Traffic signs have special shapes (octagonT trian 
gler circleT semi-circleT pennantT diamondr rectangleT 
trapezoidr and pentagon) with traffic meanings de 
pending on shape. Similar shapes of traffic signs have 
similar traffic meaning which usually are grouped to 
gether. These shape information can be directly ex 
tracted from boundaries of color regions.