1. Wavelet Edge Detection and Applications Rapporteur: Chen Hung-Yi Advisor: Prof. Ding Jian-Jiun November 26,2015

2. Outline  Background Introduction  Traditional Edge Detection (Canny edge detection 1986 )  Wavelet Multi-scale Edge Detection  Wavelet Multi-scale Edge Detection Using Adaptive threshold  Wavelet Edge Detection using LH,HL,HH parts  Edge Detection’s Application on data compression  Conclusion  Reference

3. Part 1

4. Edge Detection ( 檢測邊緣 )  要找出 Pixel value 有劇烈變化的邊界 Strong Edge Weak Edge

5. Edge Detection ( 檢測邊緣 )

6. SNR ( 信噪比 )

7. Salt & Pepper Noise

8. The Continuous Wavelet transform x(t) is the input, is the mother wavelet, a is the location, b is the scaling

9. Wavelet Transform on Image Fig.: Image decomposition based on the wavelet transform ApproximateHorizontal edge Vertical edge Corner Points

10. Wavelet Transform on Image Approximate Horizontal edge Vertical edge Corner Points

12. Part 2 Traditional Edge Detection (Canny edge detection 1986 )

13. Canny edge detection algorithm - 1986 Traditional Method  1. Gaussian filter to smooth and remove the noise  2. Find the intensity gradients of the image  3. Non-maximum suppression to reduce spurious response  4. Double threshold to determine potential edges  5. Suppressing all the other edges that are weak and not connected to strong edges.

14. Part 3 Multi-scale Edge Detection

15. Multi-scale Edge Detection with Dyadic Wavelet Transform  Let θ(x) be the impulse response of L.P.F  mother wavelet :

16. Multi-scale 2-D Edge Detection with Dyadic Wavelet Transform  mother wavelet:  s-dilation of mother wavelet:  wavelet transform:  Modulus value

17. 2-D smoothing function Modulus Image

18. Part 4 Multi-scale Edge Detection Using Adaptive Thresholding Method

19. The Decision Method of Threshold - Adaptive Thresholding Method  S. Wenchang “Wavelet Multi-scale Edge Detection Using Adaptive threshold”  Scan the probable edge image P(x) with 24*24 window

20. The Decision Method of Threshold - Adaptive Thresholding Method Iterative Way to Synthesize Multi-Scale Edges

21. The Decision Method of Threshold - Results

22. The Decision Method of Threshold - Results on P & S noise reduction

23. Part 5 Wavelet Edge Detection using LH,HL,HH parts

24. Wavelet Edge Detection using LH,HL,HH  Jian-jia. Pan, “Edge detection combining wavelet transform and Canny operator based on fusion rules,”  Step 1: The Denoising Algorithm  Step 2: Using Wavelet LH,HL,HH parts for edge detection

25. Wavelet Edge Detection using LH,HL,HH  Combining 3 edge images:  Edge Images:  Wavelet coefficients of G:  + + = 1 : corresponding weights J.J.Pan’s Method

26. Wavelet Edge Detection using LH,HL,HH on Noise condition

27. Part 6 Edge Detection’s Application - computer simulation on data compression

28. Edge Detection Application

29. Mean Color

30. Receiver

31. Edge Detection Application Statistics  原先一張圖的資訊量 : 256*256*2 8 *3 = 50.33MB (bmp 格式 )  透過利用 Edges 的 Contour Compression + Residue 壓縮 = 11.518kB + 1.2MB = 1.201MB  Compression Ratio = 39.9 ( 倍 )  壓縮總時間 : 16.7sec

32. Edge Detection Application Statistics 照片不壓縮 壓縮照片後 (JPEG) 原圖 = 50.33MB 本方法壓縮後 = 1.2MB ( 不失真 ) 32GB 記憶卡 = 635 張相片 32GB 記憶卡 = 26667 張相片 ============= 1000 張相片 網速 900Mbps ================== 需要 55.92 秒 需要 1.3 秒

33. Conclusion – Edge Detection

34. Conclusion – Wavelet Transform

35. Reference  [1] S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelet,” IEEE Tran. Inform. Theory, Vol. 38, No. 2, March, 1992.  [2] Jun Li, “A wavelet approach to edge detection,” Sam Houston State University, August, 2003.  [3] S. Wenchang, S. Jianshe, Z. Lin, “Wavelet Multi-scale Edge Detection Using Adaptive threshold,” IEEE, 2009.  [4] J. Pan, “Edge detection combining wavelet transform and Canny operator based on fusion rules,” IEEE Proceedings of the 2009 international conference on wavelet analysis and pattern recognition, July, 2009.  [5] L. Zhang, P. Bao, “Edge detection by scale multiplication in wavelet domain,” Elsevier Science B.V. Pattern Recognition letters 23, pp. 1771-1784, 2002.  [6] Prof. 傅楸善教授 CV CH7 ppt  [7] Li-Ang Chen, Jian-Jiun Ding, and Hung-Yi Chen, “ A DCT-based Contour Compression Algorithm Using Weighted Curvature and Adaptive Arithmetic Coding, ” National Computer Symposium 2015 (NCS2015), pp.40

36. Wavelet Transform on Edge Detection  θ(x) ： impulse response of L.P.F  mother wavelet :

37. The End of the Oral Presentation