A rough fuzzy neural network approach for robust face detection and tracking - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 242

detection of the skin regions, the luminance component of the colors is used to capture the de-
tails of the face (eyes, nose, lips, eyebrows, beard, etc.). The overall algorithm for face detection
is given as a flow chart in Figure 1 , where the input to the algorithm is an RGB image.
FIGURE 1 Overall face-detection method.
The luminance component L and the chrominance components a are used to create the skin
map at each pixel ( x , y ) as follows:
where SM L ( x , y ) and SM a ( x , y ) are obtained as the output of a specialized NN incurred from
the integration of the rough-fuzzy-set-based scale space transform and neural clustering, and
separately applied to the L component image, and a component image, as depicted in Figure
1 . Finally, the skin map SM is fed as input to an algorithm for the detection of elliptical objects,
as an extension of the technique reported in Ref. [ 32 ] .
In Figure 2 , we have presented the results obtained by applying this method to some images
of CalTech database. It can be observed from the figures that the a component identifies the
skin region, while the L component is used mainly to obtain the details of the face (eyes, nose,
lips, eyebrows, beard, etc.).
FIGURE 2 L component, a component, and skin map (SM).
3.1 The Proposed Multiscale Method
Let us consider an image as a set X of picture elements, i.e., a Cartesian product
[0, …, N − 1] × [0, …, M − 1]. X / is a discretization grid in classes of pixels, such that [ x ]
denotes the class of pixels containing x and μ is the luminance function of each pixel. Given a
subset T of the image not necessarily included or equal to any [ x ] , various approximations
( RS − ( T ) and RS − ( T )) of this subset can be obtained. As instance, this subset defines the contour
or uniform regions in the image. On the contrary, regions appear rather like fuzzy sets of gray
levels and their comparison or combination generates more or less uniform partitions of the
image. Rough fuzzy sets, and in particular C -sets, seem to capture these aspects together, try-
ing to extract different kinds of knowledge in data. In particular, let us consider four different
partitions Υ i , i = 1, 2, 3, 4, of the set-image X , such that each element of Υ i is a sub-image of di-
mension w × w and Υ 2 , Υ 3 , Υ 4 are taken as shifted versions of Υ 1 in the directions of 0 °, − 45 °,