Chapter 10

1. Chapter 10 Image Segmentation

2. Preview • Segmentation subdivides an image into its constituent regions or objects. • Level of division depends on the problem being solved. • Image segmentation algorithms generally are based on one of two basic properties of intensity values: discontinuity (e.g. edges) and similarity (e.g., thresholding, region growing, region splitting and merging)

3. Chapter Outline • Detection of discontinuities • Edge linking and boundary detection • Thresholding • Region-based segmentation • Morphological watersheds • Motion in segmentation

4. Detection of Discontinuities • Define the response of the mask: • Point detection:

5. Point Detection Example

6. Line Detection • Masks that extract lines of different directions.

7. Illustration

8. Edge Detection • An ideal edge has the properties of the model shown to the right: • A set of connected pixels, each of which is located at an orthogonal step transition ingray level. • Edge: local concept • Region Boundary: global idea

9. Ramp Digital Edge • In practice, optics, sampling and other image acquisition imperfections yield edges that area blurred. • Slope of the ramp determined by the degree of blurring.

10. Zero-Crossings of 2nd Derivative

11. Noisy Edges: Illustration

12. Edge Point • We define a point in an image as being an edge point if its 2-D 1st order derivative is greater than a specified threshold. • A set of such points that are connected according to a predefined criterion of connectedness is by definition an edge.

13. Gradient Operators • Gradient: • Magnitude: • Direction:

14. Gradient Masks

15. Diagonal Edge Masks

16. Illustration

17. Illustration (cont’d)

18. Illustration (cont’d)

19. The Laplacian • Definition: • Generally not used in its original form due to sensitivity to noise. • Role of Laplacian in segmentation: • Zero-crossings • Tell whether a pixel is on the dark or light side of an edge.

20. Laplacian of Gaussian • Definition:

21. Illustration

22. Edge Linking: Local Processing • Link edges points with similar gradient magnitude and direction.

23. Global Processing: Hough Transform • Representation of lines in parametric space: Cartesian coordinate

24. Hough Transform • Representation in parametric space: polar coordinate

25. Illustration

26. Illustration (cont’d)

27. Graphic-Theoretic Techniques • Minimal-cost path

28. Illustration

29. Example

30. Thresholding • Foundation: background point vs. object point • The role of illumination: f(x,y)=i(x,y)*r(x,y) • Basic global thresholding • Adaptive thresholding • Optimal global and adaptive thresholding • Use of boundary characteristics for histogram improvement and local thresholding • Thresholds based on several variables

31. Foundation

32. The Role of Illumination

33. Basic Global Thresholding

34. Another Example

35. Basic Adaptive Thresholding

36. Basic Adaptive Thresholding (cont’d)

37. Optimal Global and Adaptive Thresholding • Refer to Chapter 2 of the “Pattern Classification” textbook by Duda, Hart and Stork.

38. Thresholds Based on Several Variables

39. Region-Based Segmentation • Let R represent the entire image region. We may view segmentation as a process that partitions R into n sub-regions R1, R2, …, Rn such that: • (a) • (b) Ri is a connected region • (c) • (d) P(Ri)= TRUE for i=1,2,…n • (e) P(Ri U Rj)= FALSE for i != j

40. Region Growing

41. Region-Splitting and Merging

42. Morphological Watersheds (I)

43. Morphological Watersheds (II)

44. Motion-based Segmentation (I)

45. Motion-based Segmentation (II)