A rough fuzzy neural network approach for robust face detection and tracking - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 245

where g min and g max are the lowest and highest gray levels in the image.
The subnetwork has to self-organize by minimizing the fuzziness of the output layer. Since
the membership function is chosen to be sigmoidal, minimizing the fuzziness is equivalent to
minimizing the distances between corresponding pixel values in both cell-planes at the up-
per hidden layer. Since random initialization acts as noise, all the weights are initially set
to unity. The adjustment of weights is done using the gradient descent search, i.e., the in-
cremental change Δ w j , i l , l = 1, 2, is taken as proportional to the sum of the negative gradient
− η (∂ E /∂ o i ) f ′( I i ) o j . The adjustment rule is then the following:
Specifically, we adopted the Linear Index of Fuzziness (LIF), whose updating rules look as
follows, where E indicates the energy-fuzziness of our method and n = M × N . LIF learning:
where η LIF = η × 2/ n .
The previous rules hold also for the determination of an exact threshold value, θ , adopted
for dividing the image into skin regions and nonskin regions, when convergence is reached.
According to the properties of fuzziness, the initial threshold is set to be 0.5; this value allows
to determine an hard decision from an unstable condition to a stable one. As said before, the