1. Lecture(s) 3-4. Morphological Image Processing

2. 3/13/20162 Introduction ► ► Morphology: a branch of biology that deals with the form and structure of animals and plants ► ► Morphological image processing is used to extract image components for representation and description of region shape, such as boundaries, skeletons, and the convex hull

3. 3/13/20163 Introduction

4. 4 Preliminaries (1) ► ► Reflection ► ► Translation

5. 3/13/20165 Example: Reflection and Translation

6. 3/13/20166 Preliminaries (2) ► ► Structure elements (SE) Small sets or sub-images used to probe thăm dò an image under study for properties of interest

7. 3/13/20167 Logic operations involving binary images

8. 3/13/20168

9. 9 Examples: Structuring Elements (1) origin

10. 3/13/201610 Examples: Structuring Elements (2) Accommodate the entire structuring elements when its origin is on the border of the original set A Origin of B visits every element of A At each location of the origin of B, if B is completely contained in A, then the location is a member of the new set, otherwise it is not a member of the new set.

11. 3/13/201611 Erosion

12. 3/13/201612 Example of Erosion (1)

13. 3/13/201613 Example of Erosion (2)

14. 3/13/201614 Dilation

15. 3/13/201615 Examples of Dilation (1)

16. 3/13/201616 Examples of Dilation (2)

17. 3/13/201617 Duality ► ► Erosion and dilation are duals of each other with respect to set complementation and reflection

18. 3/13/201618 Duality ► ► Erosion and dilation are duals of each other with respect to set complementation and reflection

19. 3/13/201619 Duality ► ► Erosion and dilation are duals of each other with respect to set complementation and reflection

20. 3/13/201620 Opening and Closing ► ► Opening generally smoothes the contour of an object, breaks narrow isthmuses eo, and eliminates thin protrusions lồi lõm ► ► Closing tends to smooth sections of contours but it generates fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour

21. 3/13/201621 Opening and Closing

22. 3/13/201622 Opening

23. 3/13/201623 Example: Opening

24. 3/13/201624 Example: Opening

25. 3/13/201625 Example: Closing

26. 3/13/201626

27. 3/13/201627 Duality of Opening and Closing ► ► Opening and closing are duals of each other with respect to set complementation and reflection

28. 3/13/201628 The Properties of Opening and Closing ► ► Properties of Opening ► ► Properties of Closing

29. 3/13/201629

30. 3/13/201630

31. 3/13/201631

32. 3/13/201632

33. 3/13/201633 The Hit-or-Miss Transformation

34. 3/13/201634 Some Basic Morphological Algorithms (1) ► ► Boundary Extraction The boundary of a set A, can be obtained by first eroding A by B and then performing the set difference between A and its erosion.

35. 3/13/201635 Example 1

36. 3/13/201636 Example 2

37. 3/13/201637 Some Basic Morphological Algorithms (2) ► ► Hole Filling A hole may be defined as a background region surrounded by a connected border of foreground pixels. Let A denote a set whose elements are 8-connected boundaries, each boundary enclosing a background region (i.e., a hole). Given a point in each hole, the objective is to fill all the holes with 1s.

38. 3/13/201638 Some Basic Morphological Algorithms (2) ► ► Hole Filling 1. Forming an array X 0 of 0s (the same size as the array containing A), except the locations in X 0 corresponding to the given point in each hole, which we set to 1. 2. X k = (X k-1 + B) A c k=1,2,3,… Stop the iteration if X k = X k-1

39. 3/13/201639 Example

40. 3/13/201640

41. 3/13/201641 Some Basic Morphological Algorithms (3) ► ► Extraction of Connected Components Central to many automated image analysis applications. Let A be a set containing one or more connected components, and form an array X 0 (of the same size as the array containing A) whose elements are 0s, except at each location known to correspond to a point in each connected component in A, which is set to 1.

42. 3/13/201642 Some Basic Morphological Algorithms (3) ► ► Extraction of Connected Components Central to many automated image analysis applications.

43. 3/13/201643

44. 3/13/201644

45. 3/13/201645 Some Basic Morphological Algorithms (4) ► ► Convex Hull A set A is said to be convex if the straight line segment joining any two points in A lies entirely within A. The convex hull H or of an arbitrary set S is the smallest convex set containing S.

46. 3/13/201646 Some Basic Morphological Algorithms (4) ► ► Convex Hull

47. 3/13/201647

48. 3/13/201648

49. 3/13/201649 Some Basic Morphological Algorithms (5) ► ► Thinning The thinning of a set A by a structuring element B, defined

50. 3/13/201650 Some Basic Morphological Algorithms (5) ► ► A more useful expression for thinning A symmetrically is based on a sequence of structuring elements:

51. 3/13/201651

52. 3/13/201652 Some Basic Morphological Algorithms (6) ► ► Thickening:

53. 3/13/201653 Some Basic Morphological Algorithms (6)

54. 3/13/201654 Some Basic Morphological Algorithms (7) ► ► Skeletons

55. 3/13/201655 Some Basic Morphological Algorithms (7)

56. 3/13/201656 Some Basic Morphological Algorithms (7)

57. 3/13/201657

58. 3/13/201658

59. 3/13/201659 Some Basic Morphological Algorithms (7)

60. 3/13/201660

61. 3/13/201661 Some Basic Morphological Algorithms (8) ► ► Pruning

62. 3/13/201662 Pruning: Example

63. 3/13/201663 Pruning: Example

64. 3/13/201664 Pruning: Example

65. 3/13/201665 Pruning: Example

66. 3/13/201666 Pruning: Example

67. 3/13/201667 Some Basic Morphological Algorithms (9) ► ► Morphological Reconstruction

68. 3/13/201668 Morphological Reconstruction: Geodesic Dilation

69. 3/13/201669

70. 3/13/201670 Morphological Reconstruction: Geodesic Erosion

71. 3/13/201671

72. 3/13/201672 Morphological Reconstruction by Dilation

73. 3/13/201673

74. 3/13/201674 Morphological Reconstruction by Erosion

75. 3/13/201675 Opening by Reconstruction

76. 3/13/201676

77. 3/13/201677 Filling Holes

78. 3/13/201678

79. 3/13/201679

80. 3/13/201680 Border Clearing

81. 3/13/201681

82. 3/13/201682 Summary (1)

83. 3/13/201683 Summary (2)

84. 3/13/201684

85. 3/13/201685

86. 3/13/201686 Gray-Scale Morphology

87. 3/13/201687 Gray-Scale Morphology: Erosion and Dilation by Flat Structuring

88. 3/13/201688

89. 3/13/201689 Gray-Scale Morphology: Erosion and Dilation by Nonflat Structuring

90. 3/13/201690 Duality: Erosion and Dilation

91. 3/13/201691 Opening and Closing

92. 3/13/201692

93. 3/13/201693 Properties of Gray-scale Opening

94. 3/13/201694 Properties of Gray-scale Closing

95. 3/13/201695

96. 3/13/201696 Morphological Smoothing ► ► Opening suppresses bright details smaller than the specified SE, and closing suppresses dark details. ► ► Opening and closing are used often in combination as morphological filters for image smoothing and noise removal.

97. 3/13/201697 Morphological Smoothing

98. 3/13/201698 Morphological Gradient ► ► Dilation and erosion can be used in combination with image subtraction to obtain the morphological gradient of an image, denoted by g, ► ► The edges are enhanced and the contribution of the homogeneous areas are suppressed, thus producing a “derivative-like” (gradient) effect.

99. 3/13/201699 Morphological Gradient

100. 3/13/2016100 Top-hat and Bottom-hat Transformations ► ► The top-hat transformation of a grayscale image f is defined as f minus its opening: ► ► The bottom-hat transformation of a grayscale image f is defined as its closing minus f:

101. 3/13/2016101 Top-hat and Bottom-hat Transformations ► ► One of the principal applications of these transformations is in removing objects from an image by using structuring element in the opening or closing operation

102. 3/13/2016102 Example of Using Top-hat Transformation in Segmentation

103. 3/13/2016103 Granulometry ► ► Granulometry deals with determining the size of distribution of particles in an image ► ► Opening operations of a particular size should have the most effect on regions of the input image that contain particles of similar size ► ► For each opening, the sum (surface area) of the pixel values in the opening is computed

104. 3/13/2016104 Example

105. 3/13/2016105

106. 3/13/2016106 Textual Segmentation ► ► Segmentation: the process of subdividing an image into regions.

107. 3/13/2016107 Textual Segmentation

108. 3/13/2016108 Gray-Scale Morphological Reconstruction (1) ► ► Let f and g denote the marker and mask image with the same size, respectively and f ≤ g. The geodesic dilation of size 1 of f with respect to g is defined as The geodesic dilation of size n of f with respect to g is defined as

109. 3/13/2016109 Gray-Scale Morphological Reconstruction (2) ► ► The geodesic erosion of size 1 of f with respect to g is defined as The geodesic erosion of size n of f with respect to g is defined as

110. 3/13/2016110 Gray-Scale Morphological Reconstruction (3) ► ► The morphological reconstruction by dilation of a gray- scale mask image g by a gray-scale marker image f, is defined as the geodesic dilation of f with respect to g, iterated until stability is reached, that is, The morphological reconstruction by erosion of g by f is defined as

111. 3/13/2016111 Gray-Scale Morphological Reconstruction (4) ► ► The opening by reconstruction of size n of an image f is defined as the reconstruction by dilation of f from the erosion of size n of f; that is, The closing by reconstruction of size n of an image f is defined as the reconstruction by erosion of f from the dilation of size n of f; that is,

112. 3/13/2016112

113. 3/13/2016113 Steps in the Example 1. 1. Opening by reconstruction of the original image using a horizontal line of size 1x71 pixels in the erosion operation 2. 2. Subtract the opening by reconstruction from original image 3. 3. Opening by reconstruction of the f’ using a vertical line of size 11x1 pixels 4. 4. Dilate f1 with a line SE of size 1x21, get f2.

114. 3/13/2016114 Steps in the Example 5. 5. Calculate the minimum between the dilated image f2 and and f’, get f3. 6. 6. By using f3 as a marker and the dilated image f2 as the mask,