7A-5-3 
0’ 
Figure 3: HSL color space 
Figure 4: Fuzzy membership functions for the color 
red: (a) huer(b) saturationFand (c) intensity 
Ureds 
U re dl 
1 
1 + exp(—redsa ■ (x — redsc)) 
1 
1 4. ((. x ~ redl c) 2 \redlb 
' redla 2 > 
4.2 Color fuzzification 
The HSL color space used hereHs depicted in Figure 
3. The expressions (1) are used to convert a RGB 
image to a HSL image. 
H' = cos -1 2 r-g-b 
2y/[(R-G)*+(R-B)(G-B)] 
_ max(R,G,B) + min(R,G,B) 
_ 
3 * min(R,G,B) (1) 
(R + G + B) 
2tt -H\ if B > G 
Hotherwise 
To define a certain color in a color spacer one 
may use experimental thresholds. For exampleTthe 
(SOW*) color space [3] shows that Stop signs are con 
tained in the subregion spanned by S > 15r3° < 0 < 
56°YW* < 84. In [5]Ta look-up table is trained off 
line. Then a color pixel (rTgrb) is labeled with a color 
(redT blueT yellowTwhiter blackTetc. 1} by consulting 
the look-up table. 
To model color perceptionTwe use a fuzzy concept 
to define each color. For examplera degree of rednessT 
that isrthe property for a pixel to have the color “red” 
can be define as follows: 
T — Uredhijl) ' Ureds^s) • Uredli,0 (2) 
where 
(h — redhc 
Uredh = exp 2 rcdha* 
Here UredhTUredsTand U re di are membership functions 
containing parameters redhaT redhcT redsaT redscY 
redlaYredlbY and redlc. Their profiles are plotted in 
Figure 4. 
Fuzzy characterizations of the colors yellowForanger 
greenTbluerblackrand white can be similarly defined. 
For blackr gray and whiter the RGB components 
are essentially all equal: R ~ G ~ B. In this caseT 
there is a hue singularity due to the denominator of 
the hue expression in equation (1) being close to zero. 
Thus color fuzzification near white or black should be 
carefully considered. For exampleTwhiteness may be 
given by 
whiteness = 17gray(R, G, B) ■ U wh itei(l) 
with 
Ugray{R,G,B) = exp {-^\\m^(R,G,B)-min(R,G,B)\\) 
Here a is an adjustable factor. When R ~ G ~ BY 
UgrayiR, G, B) ~ 1 means that the pixel (RFGFB) will 
be a monochromatic pixel (black-gray-white). Figures 
5-7 shows two images and their related colorness im 
ages. 
4.3 Thresholding a colorness image 
Once a colorness image is obtainedrclassical thresh 
olding technologies can be applied to segment the col 
orness image. Because traffic signs are smalirthresh- 
olding methods which treat local windows are recom 
mended. In [10]r an optimal thresholding algorithm