A rough fuzzy neural network approach for robust face detection and tracking - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 241

2. Let C = ( Γ , m , M ) and C ′ = ( Γ ′, m ′, M ′) two rough fuzzy sets related, respectively, to partitions
Γ = ( T 1 , …, T s ) and Γ ′ = ( T 1 ′, …, T s ′) with m ( m ′) and M ( M ′) indicating the measures expressed
in Equation (1) . The product between two C -sets C and C ′, denoted by⊗, is defined as a new
rough fuzzy set C ′′ = C ⊗ C ′ = ( Γ ′′, m ′′, M ′′) where Γ ′′ is a new partition whose elements are
T ″ i , j = T i ∩ T ′ j and m ′′ and M ′′ are obtained by:
As shown in Ref. [ 29 ] , this computation scheme generalizes the concept of fuzzy set to rough
fuzzy set. It has been also demonstrated in Ref. [ 30 , 31 ] that recursive application of the pre-
vious operation provides a refinement of the original sets, realizing a powerful tool for meas-
urement and a basic signal-processing technique.
3 Face-detection method
The RGB color space is considered native to computer graphics (the encoding of files, CRT
monitors, CCD cameras and scanners, and the rasterization of graphics cards usually use this
model), and is therefore the most widespread. It is an additive model, in which the colors are
produced by adding, the primary colors red, green, and blue, with white having all the colors
present and black representing the absence of any color. RGB is a good space for computer
graphics but not so for image processing and analysis. RGB's major defects are the high cor-
relation between the three channels (varying the intensities, all three components change) and
the fact that it is not perceptually uniform. However, this color space can be used to gener-
ate other alternative color formats, including YC b C r , HSI, and CIE Lab . CIE Lab is the most com-
plete color space specified by the International Commission on Illumination (CIE). This color
space is based on the opponent-colors theory of color vision, which says that a single values
can be used to describe the red/green and the yellow/blue atributes as two colors cannot be
both green and red at the same time, nor blue and yellow at the same time. When a color is ex-
pressed in CIE Lab , L defines lightness ( L = 0 denotes black and L = 100 indicates diffuse white),
the chromaticity coordinates ( a , b ), which can take both positive and negative values, denote,
respectively, the red (+ a )/green (− a ) value and the yellow (+ b )/blue (− b ) value. The CIE Lab
color space covers the entire spectrum visible to the human eye and represents it in a uniform
way. It thus enables description of the set of visible colors independent of any graphics tech-
nology. This color space has two advantages:
1. It was designed to be perceptually uniform, i.e., perceptually similar images have the same
chromaticity components.
2. The chromaticity coordinates ( a , b ) are distinct and independent of the lightness L .
The smooth shape and curve of a face, in some cases, may be varied considerably the in-
tensity of the light reflected from it. The chromaticity components, instead, remain relatively
unchanged and it can be used to detect skin regions. For this reason, to separate the skin from
the non-skin regions, we analyze only the chromaticity distribution of an image, in particular,
those relating to the chromaticity component a regardless of the lightness component. After