1 Competitive fuzzy edge detection Source: Forensic Science International 155 (2005) 35–50 Authors: Che-Yen Wen*, Jing-Yue Yao Reporter : 黃 宇 睿 Teacher : 陳榮昌 老師

2 Outline 1. Introduction 2. Methodology 3. The algorithm 4. Experimental results 5. Conclusions

3 1. Introduction  Edge pixels form curved or straight boundaries.  There are many different methods for edge detection has common problems of these methods are a large volume of computation, sensitivity to noise, anisotropy and thick lines.  Neural networks and radial basis functional link nets  A fuzzy classifier is a system that accepts inputs that are either:  (i) feature vectors; or  (ii) vectors of fuzzy truths for the features to belong to various fuzzy set membership functions (FSMFs).

4 1. Introduction  An earlier fuzzy classifier [11,21] created extended ellipsoidal Epanechnikov functions as the fuzzy set membership functions centered on the class prototypes.  The class assigned to an input feature vector is the one with the maximum fuzzy truth given by the FSMFs.  non-competitive fuzzy classifier does not implement an edge thinner and has five classes.  Competitive Fuzzy Edge Detector (CFED) Cont.

5 2. Methodology  The feature vector for a pixel P5 P3 P6 P9P8P7 P4 P1P2 d1 = |p1 − p5| + |p9 − p5| (Direction 1) (1a) d2 = |p2 − p5| + |p8 − p5| (Direction 2) (1b) d3 = |p3 − p5| + |p7 − p5| (Direction 3) (2a) d4 = |p4 − p5| + |p6 − p5| (Direction 4) (2b) Direction 1Direction 2Direction 3 Direction 4 feature vector x = (d1, d2, d3, d4)

6 2. Methodology  Pixel edge classes  four edge classes  a background class  Speckle edge class (a speckle is a noisy pixel).

7 2. Methodology  Pixel edge classes  Other neighborhoods

8 2. Methodology  The fuzzy classifier architecture

9 2. Methodology  Extended Epanechnikov functions fuzzy truth values: μ(x) width parameter ω

10 2. Methodology  Extended Epanechnikov functions (cont.) the quality of the edge detection, as measured by the fuzzy truth of its memberships in the fuzzy classes, depends on the parameters lo, hi, and w (and on the image contrast and the purpose of the edges). We can use a value of, say, 200–256 for ω.

11 2. Methodology  Extended Epanechnikov functions (cont.) Fig. 5. A three-dimensional view of the FSMFs.

12 2. Methodology  The competitive rules IF x is Class 1 (edge) THEN compete d3 with neighbor pixels in Direction 3 IF it wins THEN change it to black (edge) ELSE change to white. IF x is Class 2 (edge) THEN compete d4 with neighbor pixels in Direction 4 IF it wins THEN change it to black (edge) ELSE change to white. IF x is Class 3 (edge) THEN compete d1 with neighbor pixels in Direction 1 IF it wins THEN change it to black (edge) ELSE change to white. IF x is Class 4 (edge) THEN compete d2 with neighbor pixels in Direction 2 IF it wins THEN change it to black (edge) ELSE change to white.

13 2. Methodology  The competitive rules IF x is Class 0 (background) THEN change pixel to white. IF x is Class 5 (speckle edge) THEN change pixel to black (edge).

14 3. The algorithm step 1 Step 2 step 3 Fuzzy classificationDespeckling Step 1: Set lo, hi, w Select smooth or not Step 2: construct x Compute Fuzzy truth Edge strength competition Edge class background class→ ■ Speckle edge class→ □ Isolated sigle Double speckle Direction 4

15 4. Experimental results  Output Image = edge(Input Image, ‘canny’, T, σ)  ‘upper threshold’ T (upper edge sensitivity) and ‘sigma’ σ (the Gaussian parameter). Fig. 6. The original building image.

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28 4. Experimental results  4.2. Speed Sun Sparc 64 bit processor running at 266MHz  Building image (240 × 320)  CFED ： 0.49 s  Matlab Canny ： 2.3 s  peppers image(512×512)  CFED ： 4 s  Matlab Canny ： 8.5 s

29 5. Conclusions  The benefits of using our CFED model in edge detection are:  yields moderately thin black lines  fast with only six simple fuzzy set membership functions  the method works well even when the intuitive parameters are adjusted somewhat coarsely  the process is isotropic in that lines of all directions are detected equally well.

30 Comment  CFED 方法提供了另一個邊緣處理的方法，他的 計算量不大，與先前不錯的邊緣偵測方法 （ SOBEL ）比較來說， Sobel 的計算量需要水平 與垂直各一次。  邊緣偵測可以利用該種方法增加速度，也可以免 去如類神經的學習偵測邊緣，並且可以得到適當 粗係的邊緣線。  缺點：對於有漸層到背景的邊緣還是非常破碎， 無法完整的將物件輪廓完整的標示出來。