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Weighted Fuzzy Mean(WFM) filter

Weighted Fuzzy Mean(WFM) filter. For executing the filtering task, the WFM filter adopts a 3×3 sample window. Knowledge base supported image noise removal process-Dynamic. The image transmission process when applying the WFM filter with a dynamic knowledge base. (source). Hist( ． ).

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Weighted Fuzzy Mean(WFM) filter

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  1. Weighted Fuzzy Mean(WFM) filter • For executing the filtering task, the WFM filter adopts a 3×3 sample window.

  2. Knowledge base supported image noise removal process-Dynamic • The image transmission process when applying the WFM filter with a dynamic knowledge base. (source) Hist(．) Dynamic Knowledge Base Sender:S Channel WFM(．) Y Receiver: X (noise) (filtered) (13’sa parameters)

  3. Knowledge base supported image noise removal process-Static • The image transmission process when applying the WFM filter with a static knowledge base. Sender:S Static Knowledge Base Channel Y Receiver: X WFM(．)

  4. Knowledge base supported image noise removal process-Definition • Definition - The WFM adopts LR fuzzy sets which can be characterized by the following equation Let LR(y)=L(y)=R(y) for each y in real, F(x) can be represented by bounded differences(the symbol▽) .

  5. Knowledge base supported image noise removal process-Example • Example of membership functions for the fuzzy sets DK, MD, and BR. membership grade BR DK MD 1 0 0 160 255 gray level

  6. Construction algorithm of fuzzy sets-Graph example Number of pixels MDbegin MDend

  7. Fuzzy inference rules of WFM filter • Rule 1:if • Rule 2:if • Rule 3:if

  8. 2 Definition- Fuzzy interval • A fuzzy interval I is of LR-type if there exists two shape functions L and R and four parameter α, and β to constitute the membership function of I ml mr α β • The fuzzy interval is then denoted by

  9. Definition- Fuzzy estimator If I is the fuzzy interval stored in the knowledge base, then a fuzzy estimator can be produced by the following formula where is a n1×n2 sample matrix centered at the input pixel x(i,j) ．

  10. Fuzzy inference result where each weight wr is 1 if the 2-norm of associatedintermediate inference result and the fuzzy estimator is minimum; otherwise it is zero.

  11. Experimental results • The experimental results of test image”Lenna”.

  12. Fig.19.(a) Noise image ”Lenna” with p=0.9, (b) result of WFM filter, (c) result or median filter, (d) Noise image ”Boat” with p=0.9, (e) result of WFM filter, (f) result of median filter.

  13. Experimental results • The experimental results of test image.

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