Image Processing Reference
Throughout most of this work the classical multi-layer feed-forward network, as described
in (Henry and Peters, 1996), is utilized. The most commonly used learning algorithm is
back-propagation. The signals flow from neurons in the input to those in the output layer,
passing through hidden neurons, organized by means of one or more hidden layers.
By a sigmoidal excitation function for a neuron we will understand a mapping of the
1 + e − βx
f (x) =
where x represents weighted sum of inputs to a given neuron and β is the coe cient called
gain, which determines the slope of the function.
Let Icn i , Ocn j and w ij be input to neuron i, output from neuron j, and the weight of
connection between i and j, respectively. We put:
w ij Ocn j
Ocn i = f (Icn i )
Statistically, texture is a unity of local variabilities and spatial correlations. Gray level
co-occurrence matrix (GLCM) is one of the most known texture analysis methods that
estimates image properties related to second-order statistics. Each entry (i, j) in GLCM
corresponds to the number of occurrences of the pair of gray levels i and j which are a
distance d apart in original image. In order to estimate the similarity between different
gray level co-occurrence matrices, Haralick (Haralick, 1979) proposed 14 statistical features
extracted from them. To reduce the computational complexity, only some of these features
were selected. In this paper we use energy, entropy, contrast and inverse difference moment.
For further reading see,e.g, (Aboul Ella, 2007).
Rough Hybrid Approach
In this section, an application of breast cancer imaging has been chosen and hybridiza-
tion scheme that combines the advantages of fuzzy sets, rough sets and neural networks in
conjunction with statistical feature extraction techniques, have been applied to test their
ability and accuracy in detecting and classifying breast cancer images into two outcomes:
cancer or non-cancer.
The architecture of the proposed rough hybrid approaches is illustrated in Figure 1. It is
comprised of four fundamental building phases: In the first phase of the investigation, a pre-
processing algorithm based on fuzzy image processing is presented. It is adopted to improve
the quality of the images and to make the segmentation and feature extraction phase more
reliable. It contains several sub-processes. In the second phase, a modified version of the
standard fuzzy c-mean clustering algorithm is proposed to initialize the segmentation, then
the set of features relevant to region of interest is extracted, normalized and represented in a
database as vector values. The third phase is rough set analysis. It is done by computing the
minimal number of necessary attributes, their significance and by generating a sets of rules.
Finally, a rough neural network is designed to discriminate different regions of interest in