1. Segmentation and Perceptual Grouping The problem Gestalt Edge extraction: grouping and completion Image segmentation

3. Camouflage

10. Kanizsa Triangle

17. The image of this cube contradicts the optical image

23. Perceptual Organization Atomism, reductionism:  Perception is a process of decomposing an image into its parts.  The whole is equal to the sum of its parts. Gestalt (Wertheimer, Köhler, Koffka 1912)  The whole is larger than the sum of its parts.

24. Mona Lisa

26. Gestalt Principles Proximity

27. Gestalt Principles Proximity Similarity

28. Gestalt Principles Proximity Similarity Continuity

29. Gestalt Principles Closure Proximity Similarity Continuity

30. Gestalt Principles Proximity Similarity Continuity Closure Common Fate

31. Gestalt Principles Proximity Similarity Continuity Closure Common Fate Simplicity

32. Smooth Completion Isotropic Smoothness Minimal curvature Extensibility

33. Elastica Elastica is not scale invariant

34. Elastica Scale invariant measure Approximation

36. Finding lines from points

37. Parametric methods: RANSAC

38. RANSAC RANdom SAmple Concensus Complexity:  Need to go over all pairs: O(n 2 )  For each pair check how many more points are consistent: O(n)  Total complexity: O(n 3 )

39. RANSAC Another application of RANSAC: Find transformation between images Example: compute homography  Compute homography for every 4 pairs of corresponding points  Choose the homography that best explains the image  m 4 n 4 sets should be tested Another example: compute epipolar lines  How many correspondences are needed?

40. Hough Transform

41. Linear in the number of points Describe lines as Or better Prepare a 2D table θ c

42. Hough Transform θ c +1

43. Hough Transform θ c 13 16 What if we want to find circles?

44. Curve Salience

45. Saliency Network Encourage Length Low curvature Closure

46. Saliency Network

47. Tensor Voting Every edge element votes to all its circular edge completions Vote attenuates with distance: e -αd Vote attenuates with curvature: e -βk Determine salience at every point using principal moments

48. Tensor Voting

49. Stochastic Completion Field Random walk: In addition, a particle may die with probability:

50. Stochastic Completion Fields

51. Most probable path: with Can be implemented as a convolution

52. Stochastic Completion Fields

54. Snakes Given a curve Г(s)=(x(s),y(s)), define: with

55. Extremum: Calculus of Variation Given a functional A condition for a local extrimum is obtained using the Euler-Lagrange equation Curve evolution is defined Solution obtained when

56. Curve evolution

57. Level Set Methods Curve defined implicitly by

58. Curve Evolution

60. Shortest Path

61. Image Segmentation: Thresholding

62. Histogram

63. Thresholding

64. 125 156 99

65. S-T Min-Cut/Max Flow

66. S t

67. Normalized Cuts Given a graph G=(V,E), define  W = {w ij } weights  D = diag{d i },  L = D - W Laplacian Let, we seek to solve

68. Normalized Cuts This can be show to be equivalent to with With these constrains the problem is NP-hard. Without the constraint the solution is obtained through the generalized eigenvalue problem

69. Normalized Cuts Dividing into two segments:  Partition determined by the eigenvector with the second smallest eigenvalue  We need to pick a threshold Dividing into more than two segments:  Pick several thresholds.  Divide each segment recursively.  Pick the best few eigenvectors and then perform k-means.

70. Texture Examples

71. Filter Bank

72. Textons imagetextons texton assignment

73. Normalized Cuts

74. Mean Shift Segmentation

75. Given an image, convert it to a function that is inversely related to edgeness Perform mean shift from every pixel Cluster pixels that lead to the same peak

76. Mean Shift Segmentation

77. Summary Local processing is often insufficient to separate objects We reviewed several approaches for  curve extraction, completion  region segmentation

78. Preattentive: Parallel

80. Attention: Serial