Image Segmentation – Edge Detection

1. Image Segmentation – Edge Detection Dr. Jiajun Wang School of Electronics & Information Engineering Soochow University

2. Image Segmentation - 1 Contents • Edge detection • Gradient operators • Edge linking • Hough transform

3. Image Segmentation - 1 Revisit - Goals of image processing • Image improvement – low level IP • Improvement of pictorial information for human interpretation (Improving the visual appearance of images to a human viewer ) • Image analysis – high level IP • Processing of scene data for autonomous machine perception (Preparing images for measurement of the features and structures present )

4. Image Segmentation - 1 Image analysis – HLIP • Extracting information form an image • Step 1: segment the image ->objects or regions • Step 2 : describe and represent the segmented regions in a form suitable for computer processing • Step 3 : image recognition and interpretation

5. Image Segmentation - 1 Image analysis – HLIP (cont’)

6. Image Segmentation - 1 Image segmentation • Definition • Subdivide an image into its constituent regions or objects • Based on two properties of gray-level image values • Discontinuity • point / line / edge / corner detection • Similarity • thresholding • region growing / splitting / merging

7. Image Segmentation - 2 Image Segmentation (cont’)

8. Image Segmentation - 1 What Should Good Image segmentation be? • Region interiors • Simple • Without many small holes • Adjacent regions • Should have significantly different values • Boundaries • Simple • Not ragged • Spatially accurate Achieving all these desired properties is difficult. There is no theory of image segmentation. Image segmentation techniques are basically ad hoc.

9. Image Segmentation - 1 Point detection

10. Image Segmentation - 1 Line detection

11. Image Segmentation - 1 Line detection (cont’)

12. Image Segmentation - 1 Edge detection • Definition • An edge is a set of connected pixels that lie on the boundary between two regions • The difference between edge and boundary, pp.68 • Edge detection steps • Compute the local derivative • Magnitude of the 1st derivative can be used to detect the presence of an edge • The sign of the 2nd derivative can be used to determine whether an edge pixel lies on the dark or light side of an image • Zero crossing of the 2nd derivative is at the midpoint of a transition in gray level, which provides a powerful approach for locating the edge.

13. Image Segmentation - 1 Edge detection (cont’)

14. Image Segmentation - 1 Edge detection (cont’)

15. Image Segmentation - 1 Edge detection (cont’) The derivatives are sensitive to noise

16. Image Segmentation - 1 Gradient operators • Use gradient for image differentiation • The gradient of an image f(x,y) at point (x,y) is defined as • Some properties about this gradient vector • It points in the direction of maximum rate of change of image at (x,y) • Magnitude • angle

17. Image Segmentation - 1 Edge operator

18. Image Segmentation - 1 Sobel edge operator • Advantages : providing both differencing and a smooth effect and slightly superior noise reduction characteristics.

19. Image Segmentation - 1 Edge detection example

20. Image Segmentation - 1 Edge detection example (cont’)

21. Image Segmentation - 1 Edge detection example (cont’)

22. Image Segmentation - 1 Laplacian edge operator • A second order derivative • Problems • Very sensitive to noise • Detect double edges • Can’t detect edge direction • Usage • Find the location of edge using zero-crossing property

23. Image Segmentation - 1 Marr and hildreth’s approach • Smooth the image to reduce noise • Then calculate the 2nd derivative • Finally, find the zero-crossing • LoG (Laplacian of Gaussian, Mexican hat function)

24. Image Segmentation - 1 LoG function

25. Image Segmentation - 1 discussion • Edge detection by gradient operations tends to work well when • Images have sharp intensity transitions • Relative low noise • Zero-crossing approach work well when • Edges are blurry • High noise content • Provide reliable edge detection

26. Image Segmentation - 1 Gradient operators – examples Zero-Crossing: Advantages: noise reduction capability; edges are thinner. Drawbacks: edges form numerous closed loops (spaghetti effect); computation complex.

27. Image Segmentation - 1 Edge linking • How to deal with gaps in edges? • How to deal with noise in edges? • Linking points by determining whether they lie on a curve of a specific shape

28. Image Segmentation - 1 Edge linking – Local Processing • Analyze the characteristics of the edge pixels in a small neighborhood • Its magnitude • Its direction

29. Image Segmentation - 1 Edge linking - Hough transform • Can tolerate noise and gaps in edge image • Look for solutions in a parameter space • Classical Hough transform • Detect simple shape • Line detection • Circle detection • Generalized Hough Transform • Detect complicated shapes

30. Image Segmentation - 1 Edge linking - Hough transform

31. Image Segmentation - 1 Edge linking - Hough transform

32. Image Segmentation - 1 Edge linking - Hough transform

33. Image Segmentation - 1 Edge linking - Hough transform

34. Image Segmentation - 1 Edge linking - Hough transform

35. Image Segmentation - 2 Dr. Jiajun Wang School of Electronics & Information Engineering Soochow University

36. Foundation of thresholding • Idea: object and background pixels have gray levels grouped into two dominant modes Original image histogram

37. Foundation of thresholding • Input f(x,y), given threshold T

38. Thresholding as a multi-variable function: g(x,y) = T[ f(x,y), x, y, p(x,y) ] Adaptive: Depend on position Local: local property func. Issues of thresholding • Selection of threshold T ? • Complex environment – illumination • Multiple thresholds – more than one object • Global threshold • Local threshold

39. m1 m2 1. Automatic selection of T G2 G1 1. Select an initial T • Average gray level • Mean of max. and min. gray level 2. Segment the image using T T 3. Calculate mean of G1 and G2 T2 4. New threshold: T2 = 0.5(m1 + m2) 5. Repeat steps 2~4 until difference in successive T is small

40. Example: automatically select T Initial: gray level mean 3 iterations T = 125.4 fingerprint

41. 2. Effects of illumination • Recall: f(x,y)=i(x,y) r(x,y) illumination: reflectance: Illumination source scene reflection

42. Example: illumination x Original image Illumination source histogram histogram

43. Example: bad histogram * The gray levels of the object is mixed with background

44. 4. Motivation for adaptive thresholding A single Global threshold histogram

45. Adaptive local thresholding Subdivide image into blocks Q: Improperly segmented subimages !

46. subdivision Iterative subdivision histogram

47. Image Segmentation - 2 Region based segmentation • R: the entire image • Segmentation: partition R into n subregions R1,…Rn • Ri is a connected region • P(Ri) = true • P( ) = false

48. Image Segmentation - 2 Region growing • Groups pixels or subregions into larger regions based on predefined criteria (gray tone or texture). • Step 1: Assume we find a good threshold, and use it to partition the regions into pure black and white. • Step 2: Use different labels to identify different objects • Use region growing to connect parts that should have belong to the same region • This is called “Connected component analysis” • The region with the same label generate one segment

49. Image Segmentation - 2 Region growing - example

50. Image Segmentation - 2 Region Splitting and Merging QuadTree Decomposition