Design a fuzzy, rule-based system for reducing the effects of impulse noise on a noisy ima...

Design a fuzzy, rule-based system for reducing the effects of impulse noise on a noisy image with intensity values in the interval [0, L − 1]. As in Section 3.8.5, use only the differences d2, d4, d6, and d8 in a 3 × 3 neighborhood in order to simplify the problem. Let z5 denote the intensity at the center of the neighborhood, anywhere in the image. The corresponding output intensity values should be , where v is the output of your fuzzy system. That is, the output of your fuzzy system is a correction factor used to reduce the effect of a noise spike that may be present at the center of the 3 × 3 neighborhood. Assume that the noise spikes occur sufficiently apart so that you need not be concerned with multiple noise spikes being present in the same neighborhood.The spikes can be dark or light. Use triangular membership functions throughout.

(a) Give a fuzzy statement for this problem.

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(b) Specify the IF-THEN and ELSE rules.

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(c) Specify the membership functions graphically, as in Fig. 3.57.

FIGURE 3.57 (a) Membership function of the fuzzy set zero. (b) Membership functions of the fuzzy sets black and white.

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(d) Show a graphical representation of the rule set, as in Fig. 3.58.

FIGURE 3.58 Fuzzy rules for Boundary detection.

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(e) Give a summary diagram of your fuzzy system similar to the one in

FIGURE 3.52 Example illustrating the five basic steps used typically to implement a fuzzy, rule-based system: (1) fuzzification, (2) logical operations (only OR was used in this example), (3) implication, (4) aggregation, and (5) defuzzification.