Weighted Fuzzy MeanWFM filter

1
Weighted Fuzzy Mean(WFM) filter

• For executing the filtering task, the WFM filter
  adopts a 33 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
SenderS
Channel
WFM(.)
Y
Receiver X
(noise)
(filtered)
(13sa parameters)
3
Knowledge base supported image noise removal
process-Static

• The image transmission process when applying the
  WFM filter with a static knowledge base.

SenderS
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
255
160
gray level
6
Construction algorithm of fuzzy sets-Graph example
Number of pixels
MDbegin
MDend
7
Fuzzy inference rules of WFM filter

• Rule 1if

• Rule 2if

• Rule 3if

8
Definition- Fuzzy interval

• A fuzzy interval I is of LR-type if there exists
  two shape functions L and R and four parameter
• a, and ß to constitute the membership
  function of I

ml
mr
a
ß

• 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 n1n2 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 imageLenna.

12

• Fig.19.(a) Noise image Lenna with p0.9, (b)
  result of WFM filter, (c) result or median
  filter, (d) Noise image Boat with p0.9, (e)
  result of WFM filter, (f) result of median filter.

13
Experimental results

• The experimental results of test image.

14
(No Transcript)