A rough fuzzy neural network approach for robust face detection and tracking - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 244

If c i , j 1 and c i , j 2 satisfy a specific constraint, the region under consideration is seen as RC
( R egion to be C ategorize) and the values are retained as elementary features of such a region.
Otherwise, the region is divided in four sub-regions each of dimension equal to w /2. The pre-
processing subnetwork is applied again to the newly defined regions. The fuzzy intersections
computed by the preprocessing subnetwork are fed to a clustering subnetwork which is fed
scribed in the following.
3.2 Clustering Subnetwork
Each node in the clustering sub network receives, as shown in Figure 4 , two input values from
each corresponding neuron at the previous layer. In particular, at each iteration, a learning
step is applied to the clustering subnetwork according to the minimization of a Fuzzines Index
(FI), applying, and somewhere extending, the learning mechanism proposed in Ref. [ 35 ] .
FIGURE 4 The preprocessing networks.
The output of a node j is then obtained as:
where and , where w j , i q indicates the connection weight
between the j ith node of the output layer and the i ith node of the previous layer in the q ith cell-
plane, q = 1, 2. Each sum is intended over all nodes i in the neighborhood of the j th node at
the upper hidden layer. f (the membership function ) can be sigmoidal, hyperbolic, Gaussian, Ga-
borian, etc. with the accordance that if o j takes the value 0.5, a small quantity (usually 0.001)
is added; this reflects into dropping out instability conditions. g is a similarity function, e.g.
correlation, Minkowsky distance, etc. To retain the value of each output node o j in [0, 1], we
apply the following mapping to each input image pixel g :