1. © 2002-2003 by Yu Hen Hu 1 ECE533 Digital Image Processing Image Segmentation

2. © 2002-2003 by Yu Hen Hu 2 ECE533 Digital Image Processing What is Image Segmentation? l Segmentation: »Split or separate an image into regions »To facilitate recognition, understanding, and region of interests (ROI) processing l Ill-defined problem »The definition of a region is context- dependent

3. © 2002-2003 by Yu Hen Hu 3 ECE533 Digital Image Processing Outline l Discontinuity Detection »Point, edge, line l Edge Linking and boundary detection l Thresholding l Region based segmentation l Segmentation by morphological watersheds l Motion segmentation

4. © 2002-2003 by Yu Hen Hu 4 ECE533 Digital Image Processing Point Detection Apply detection mask, followed by threshold detection

5. © 2002-2003 by Yu Hen Hu 5 ECE533 Digital Image Processing Line Detection Useful for detecting lines with width = 1.

6. © 2002-2003 by Yu Hen Hu 6 ECE533 Digital Image Processing Edge Detection l Points and lines are special cases of edges. l Edge detection is difficult since it is not clear what amounts to an edge!

7. © 2002-2003 by Yu Hen Hu 7 ECE533 Digital Image Processing Edge Detection

8. © 2002-2003 by Yu Hen Hu 8 ECE533 Digital Image Processing Impact of Noise

9. © 2002-2003 by Yu Hen Hu 9 ECE533 Digital Image Processing First & Second Derivatives of Edges

10. © 2002-2003 by Yu Hen Hu 10 ECE533 Digital Image Processing Edge Detection Operators Figure 10.8, 10.9

11. © 2002-2003 by Yu Hen Hu 11 ECE533 Digital Image Processing Approximate Gradient with L1 Norm

12. © 2002-2003 by Yu Hen Hu 12 ECE533 Digital Image Processing Effects of Smoothing

13. © 2002-2003 by Yu Hen Hu 13 ECE533 Digital Image Processing Emphasizing Diagonal Edges Use diagonal Sobel operator shown in figure 10.9(d)

14. © 2002-2003 by Yu Hen Hu 14 ECE533 Digital Image Processing Laplacian and Mexican Hat LoG operator

15. © 2002-2003 by Yu Hen Hu 15 ECE533 Digital Image Processing Comparison of Edge Detection originalSobelLoG Threshold LoG Zero-crossing Gaussian smooth operator Laplacian operator Gradient method: suitable for abrupt gray level transition, sensitive to noise 2 nd order derivative: good for smooth edges

16. © 2002-2003 by Yu Hen Hu 16 ECE533 Digital Image Processing Boundary Extraction l Edge detection classifies individual pixels to be on an edge or not. l Isolated edge pixels is more likely to be noise rather than a true edge. l Adjacent or connected edge pixels should be linked together to form boundary of regions that segment the image. l Edge linking methods: »Local processing »Hough transform »Graphic theoretic method »Dynamic programming

17. © 2002-2003 by Yu Hen Hu 17 ECE533 Digital Image Processing Local Processing Edge Linking An edge pixel will be linked to another edge pixel within its own neighborhood if they meet two criteria:

18. © 2002-2003 by Yu Hen Hu 18 ECE533 Digital Image Processing Global Processing Edge Linking: Hough Transform Find a subset of n points on an image that lie on the same straight line. Write each line formed by a pair of these points as y i = ax i + b Then plot them on the parameter space (a, b): b = x i a + y i All points (x i, y i ) on the same line will pass the same parameter space point (a, b). Quantize the parameter space and tally # of times each points fall into the same accumulator cell. The cell count = # of points in the same line.

19. © 2002-2003 by Yu Hen Hu 19 ECE533 Digital Image Processing Hough Transform in (  ) plane To avoid infinity slope, use polar coordinate to represent a line. Q points on the same straight line gives Q sinusoidal curves in (   ) plane intersecting at the same (  i  i ) cell.

20. © 2002-2003 by Yu Hen Hu 20 ECE533 Digital Image Processing Example

21. © 2002-2003 by Yu Hen Hu 21 ECE533 Digital Image Processing Example

22. © 2002-2003 by Yu Hen Hu 22 ECE533 Digital Image Processing Threshold Segmentation

23. © 2002-2003 by Yu Hen Hu 23 ECE533 Digital Image Processing Effect of Illumination on Thresholding

24. © 2002-2003 by Yu Hen Hu 24 ECE533 Digital Image Processing Threshold Example

25. © 2002-2003 by Yu Hen Hu 25 ECE533 Digital Image Processing Needs of Adaptive Threshold

26. © 2002-2003 by Yu Hen Hu 26 ECE533 Digital Image Processing Needs of Local Threshold Properly and improperly segmented subimages from Fig. 10.30. Further division of the sub-image, and result of adaptive thresholding

27. © 2002-2003 by Yu Hen Hu 27 ECE533 Digital Image Processing Threshold: Hypothesis Testing l Question: »Does this pixel with intensity z belong to a region (edge) or not? l Hypothesis »H 0 : Null. It does not »H 1 : Alt. It does l Likelihood »p(z|z  H 0 ) = p 1 (z) »p(z| z  H 1 ) = p 2 (z) l Prior »P 1 = p(z  H 0 ), »P 2 = p(z  H 1 ) l Maximum likelihood: »Pixel z belongs to a region if p(z|H 1 ) > p(z|H 0 ) l Bayesian: P 2 p(z|H 1 ) > P 1 p(z|H 0 ) l Sufficient statistic: z > T

28. © 2002-2003 by Yu Hen Hu 28 ECE533 Digital Image Processing Uni-model Gaussian Example l Given Set P 1 p 1 (T) = P 2 p 2 (T) and solve for T. l Take log on both sides and simplify to AT 2 + BT + C = 0

29. © 2002-2003 by Yu Hen Hu 29 ECE533 Digital Image Processing Clustering Problem Statement l Given a set of vectors {x k ; 1  k  K}, find a set of M clustering centers {w(i); 1  i  c} such that each x k is assigned to a cluster, say, w(i*), according to a distance (distortion, similarity) measure d(x k, w(i)) such that the average distortion is minimized. l I(x k,i) = 1 if x is assigned to cluster i with cluster center w(I); and = 0 otherwise -- indicator function.

30. © 2002-2003 by Yu Hen Hu 30 ECE533 Digital Image Processing k-means Clustering Algorithm Initialization: Initial cluster center w(i); 1  i  c, D(–1)= 0, I(x k,i) = 0, 1  i  c, 1  k  K; Repeat (A) Assign cluster membership (Expectation step) Evaluate d(x k, w(i)); 1  i  c, 1  k  K I(x k,i) = 1 if d(x k, w(i)) < d(x k, w(j)), j  i; = 0; otherwise. 1  k  K (B) Evaluate distortion D: (C) Update code words according to new assignment (Maximization) (D) Check for convergence if 1–D(Iter–1)/D(Iter) < , then convergent = TRUE,

31. © 2002-2003 by Yu Hen Hu 31 ECE533 Digital Image Processing A Numerical Example x = {  1,  2,0,2,3,4}, W={2.1, 2.3} Assign membership 2.1: {  1,  2, 0, 2} 2.3: {3, 4} Distortion D = (  1  2.1) 2 + (  2  2.1) 2 + (0  2.1) 2 + (2  2.1) 2 + (3  2.3) 2 + (4  2.3) 2 3. Update W to minimize distortion W 1 = (  1  2+0+2)/4 = .25 W 2 = (3+4)/2 = 3.5 4. Reassign membership .25: {  1,  2, 0} 3.5: {2, 3, 4} 5. Update W: w 1 = (  1  2+0)/3 =  1 w 2 = (2+3+4)/3 = 3. Converged.

32. © 2002-2003 by Yu Hen Hu 32 ECE533 Digital Image Processing Thresholding Example Threshdemo.m