Image Processing Reference

In-Depth Information

For this strategy we can also introduce the concept of weighted input pat-

terns presented already in Section 6.3.1. The weight would be interpreted

as degree of belief to the usefulness of each data pair from training data set.

Suppose that for every input-output pattern we can assign a weight ω then

we have:

SD(R
j
) = [µ(x
(1)

)(v = C)·. . .·µ(x
(n)

j

)(v = C)]·µ(x
j
)(v = C)ω

(6.36)

j

This strategy gives good results even when a small number of training sam-

ples is available.

FIGURE 6.6: Example of two clusters and the corresponding rule bank in two-dimensional

space

After the minimisation of fuzzy rules we create a rule bank which later will be used for

classification. The form of the rule bank for a 2-dimensional feature space with 2 clusters

is shown in Fig. 6.6. The boxes of the bank are filled with fuzzy rules originating either

from the numerical data or from linguistic rules given by the expert. For conjunction AND

defined between two features only one box of the rule bank is filled. For OR relations all

the boxes are filled that are in the rows or columns corresponding to the regions of the

antecedent IF part.

To determine the mapping (Eq. 6.1) in fuzzy systems, a deffuzification method needs

to be adopted. The deffuzification problem defines the strategy of using the fuzzy result

given by degree values Eq. 6.4 and Eq.6.5 to guide us in the selection of one representative

element (class) of the setC.

6.4

Applications

To demonstrate the applicability of the ideas described in this chapter we present a few ap-

plications of fuzzy If-Then rule-based systems in medical image understanding. We present

computer-aided diagnosis systems for breast cancer diagnosis (Section 6.4.1) and thermog-

raphy (Section 6.4.2) where the idea of weighted fuzzy classifier with integrated learning

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