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Image segmentation 3 morphology

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• 1. Morphological Image Operation
• 3. Mathematical Morphology Mathematical morphology is a powerful methodology which was initiated in the late 1960s by G.Matheron and J.Serra at the Fontainebleau School of Mines in France. nowadays it offers many theoretic and algorithmic tools inspiring the development of research in the fields of signal processing, image processing, machine vision, and pattern recognition. 3
• 4. Morphological Operations -1The four most basic operations in mathematicalmorphology are dilation, erosion, opening and Closing: 4
• 5. Morphological Image Processing Boolean algebra Dilation and erosion Opening and closing Hit-or-miss Basic algorithms Extension to gray-scale 5
• 6. Examples of Boolean Algebra Switching algebra  S = {0, 1} Finite Boolean algebras  Example: S = {(0, 0), (0, 1), (1, 0), (1, 1)}  (a1, a2)’ = (a’1, a’2)  (0, 1) (1, 0) = (0, 0) Set unions/intersections  Union is like  Intersection is like  Empty set is like 0  There is no 1 (universal set) 6
• 7. Review: Boolean Algebra A Boolean algebra is a set with at least two elements, three operations (and , or , not ‘) and two special elements (0, 1) that have the following properties.  A B is an element of the set. This function is defined for all elements A and B in the set. It is symmetric (A B = B A)  A B has the same properties  A’ is defined for all elements in the set.  A A’=0, A A’=1  The operations and + are distributive.  A (B C)=(A B) (A C)  A (B C)=(A B) (A C)  0 and 1 are identities, in the following sense  0 A=A  1 A=A 7
• 8. Some Basic Definitions  Let A and B be sets with components a=(a1,a2) and b=(b1,b2), respectively.  The translation of A by x=(x1,x2) is A + x = {c | c = a + x, for a A}  The reflection of A is Ar = {x | x = -a for a A}  The complement of A is Ac = {x | x A}  The union of A and B is A B = {x | x A or x B }  The intersection of A and B is A B = {x | x A and x B } 8
• 9. Some Basic Definitions  The difference of A and B is. A – B = A Bc = {x | x A and x B}  A and B are said to be disjoint or mutually exclusive if they have no common elements.  If every element of a set A is also an element of another set B, then A is said to be a subset of B. 9
• 10. Additional Operations Elements of set: points  Points are integers (1-D discrete space)  Points are 2-D vectors with integer components (2-D discrete space) Operations  Addition (vector addition)  Reflection (multiply by -1)  Integer multiplication A set of points can be translated or reflected  S+x = x+S (new set consists of all points of S, translated by x)  S^ is the set reflected through the origin 10
• 11. Boolean Algebra 11
• 12. Continuous and Discrete Morphology There are morphology theories of continuous and discrete spaces Example of continuous space  Real line Example of discrete space  Integers We will talk about the morphology of discrete spaces 12
• 13. Morphology A binary image containing two object sets A and B  B = {(0,0), (0,1), (1,0)}  A = {(5,0), (3,1), (4,1), (5,1), (3,2), (4,2), (5,2)} 13
• 14. Basic Morphological Operations Dilation  A+B = {x| x = y+z, y in A, z in B}  Equivalent definition  {x, (x+B^) A is not empty} Erosion  A-B = {x| x+B is a subset of A} 14
• 15. Some Basic Definitions (Dilation)  Dilation A B = {x | (B + x) A }  Dilation expands a region. 15
• 16. Example (1) 16
• 17. More Examples (2) 17
• 18. Some Basic Definitions (Erosion)  Erosion A B = {x | (B + x) A}  Erosion shrinks a region. 18
• 19. More Examples (3) 19
• 20. Some Basic Definitions (opening)  Opening is erosion followed by dilation: A B = (A B) B  Opening smoothes regions, removes spurs, breaks narrow lines. 20
• 21. Morphological Opening A oB @(A B) B A opened by B 21
• 22. Some Basic Definitions (closing)  Closing is dilation followed by erosion: A B = (A B) B  Closing fills narrow gaps and holes in a region. 22
• 23. Morphological Closing A • B @(A B) B A closed by B 23
• 24. Example 24
• 25. Combination of Opening and Closing 25
• 26. Hit-or-Miss Given: points on plane Template: Set of one points (foreground) and set of zero points (background) Example foreground: B1=D, B2=D Find: Points x for which B1+x are 1, B2+x are 0 Solution: 26
• 27. Exp: 27
• 28. Boundary Extraction (A) A (A B) 28
• 29. Region Filling Xk (Xk 1 B) A•Start with point in region A.Keep expanding bydilation, using points in region Aonly. 29
• 30. Extraction of Connected Component Xk (Xk 1 B) A Start with point on object. Keep adding points 30
• 31. Skeleton Morphological skeleton Start with structuring element, B Generate a sequence of elements Bk=kB, B0=0 n A k 0 Sk Bk Construction Sk (A Bk ) ((A Bk ) B) Connected skeleton 31
• 32. Morphological Skeleton 32
• 33. Connected Skeleton 33
• 34. Some Morphological Algorithms 34
• 35. Some Morphological Algorithms  Boundary of a set, A, can be found by A - (A B) B 35
• 36. Some Morphological Algorithms A region can be filled iteratively by Xk+1 = (Xk B) Ac , where k = 0,1,… and X0 is a point inside the region. 36
• 37. Some Morphological Algorithms 37
• 38. Morphological OperationsBWMORPH Perform morphological operations on binary image. BW2 = BWMORPH(BW1,OPERATION) applies a specific morphological operation to the binary image BW1. BW2 = BWMORPH(BW1,OPERATION,N) applies the operation N times. N can be Inf, in which case the operation is repeated until the image no longer changes.OPERATION is a string that can have one of these values: skel With N = Inf, remove pixels on the boundaries of objects without allowing objects to break apart spur Remove end points of lines without removing small objects completely. fill Fill isolated interior pixels (0s surrounded by 1s) ... 38
• 39. Morphological Operations BW1 = imread(circbw.tif); BW2 = bwmorph(BW1,skel,Inf); imshow(BW1); figure, imshow(BW2); 39
• 40. Morphological Operations BW1 = imread(circbw.tif); BW2 = bwperim(BW1); imshow(BW1); figure, imshow(BW2) 40
• 41. Morphological OperationsPixel ConnectivityConnectivity defines which pixels are connected to other pixels. A set ofpixels in a binary image that form a connected group is called an objector a connected component. 4-connected 8-connected 41
• 42. Morphological OperationsBW = [0 0 0 0 0 0 0 0; 0 1 1 0 0 1 1 1; 0 1 1 0 0 0 1 1; X = bwlabel(BW,4); 0 1 1 0 0 0 0 0; RGB = label2rgb(X, @jet, k); 0 0 0 1 1 0 0 0; imshow(RGB,notruesize) 0 0 0 1 1 0 0 0; 0 0 0 1 1 0 0 0; 0 0 0 0 0 0 0 0];X = bwlabel(BW,4)X = 0 0 0 0 0 0 0 0 0 1 1 0 0 3 3 3 0 1 1 0 0 0 3 3 0 1 1 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 42
• 43. Some Morphological Algorithms Application example: Using connected components to detect foreign objects in packaged food. There are four objects with significant size! 43
• 44. Some Morphological Algorithms  Thinning: Thin regions iteratively; retain connections and endpoints.  Skeletons: Reduces regions to lines of one pixel thick; preserves shape.  Convex hull: Follows outline of a region except for concavities.  Pruning: Removes small branches. 44
• 45. Summary 45
• 46. Summary 46
• 47. Summary 47
• 48. Summary 48
• 49. Extensions to Gray-Scale Images Dilation 49
• 50. Extensions to Gray-Scale Images Dilation Take the maximum within the window. 50
• 51. Extensions to Gray-Scale Images Erosion 51
• 52. Extensions to Gray-Scale Images  Dilation:  Makes image brighter  Reduces or eliminates dark details  Erosion:  Makes image darker  Reduces or eliminates bright details 52
• 53. Extensions to Gray-Scale Images 53
• 54. Extensions to Gray-Scale Images Opening: Narrow bright areas are reduced. Closing: Narrow dark areas are reduced. 54
• 55. Extensions to Gray-Scale Images 56
• 56. Application Example 57
• 57. Application Example-Segmentation 58
• 58. Application Example-Granulometry 59
• 59. Morphological Reconstruction (exp.algo)  Algorithm for binary reconstruction: 1. M = V o K , where K is any SE. 2. T = M, 3. M= M Ki , where i=4 or i=8, 4. M = M∩ V, [Take only those pixels from M that are also in V .] 5. if M T then go to 2, 6. else stop; Original (V) Opened (M) Reconstructed (T) 60
• 60. Application in 2D Image Processing Character Extraction-1 Character Extraction From Cover Image (Source) 61
• 61. Application in 2D Image Processing Character Extraction-2 Character Extraction From Cover Image (Results) 62
• 62. Application in 2D Image Processing Character Extraction-3 Morning Noon Afternoon Evening 63
• 63. Application in 2D Image Processing Character Extraction-4 Morning Noon Afternoon Evening 64
• 64. Application in 3D Image Processing Organs Extraction-1 slice20 slice25 slice30 slice25 slice30 65 slice20
• 65. Application in 3D Image Processing Organs Extraction-2 Top View Back View 66
• 66. Application in 3D Image Processing Organs Extraction-3 67
• 67. Application in 3D Image Processing Organs Extraction-4 Segmented heart beating cycle 68
• 68. Application in 3D Image Processing Organs Extraction-5 Kidney with Bones Kidney with Vessels 69
• 69. Brain View snapshot-3 --Registration tool kit Features: 1. Cut plane in 3D 2. Work in 2 data sets 3. 2D and 3D view 4. Registration methods: • LandMark • ThinPlateSpline • GridTransform • MutualInformation 70
• 70. Brain View snapshot-4 --Segmenation tool kit Features: 1. Cut plane in 3D 2. Work in 2 data sets 3. 2D and 3D view 4. Segmenation methods: • Morphology • Snake • Level Set • Watershed 71
• 71. Research Plan-1  Medical Image Analysis --- Segmentation and Registration  More efforts address on Ultrasound Image (2D, 3D) Segmented baby face from US 2D Segmentation using GDM 72 Real time US, MR integration for IGS
• 72. 73
• 73. Image Comparison Techniques• Image Subtraction the simplest and most direct approach to PCB inspection problem. The PCB is compared to an image of an ideal part. The subtraction can be done by logical XOR operation between the two images .• Feature Matching an improved form of image subtraction, in which the extracted features from the object and those defined by the model are compared.• Phase Only Method 74
• 74. Example PCB and Mask 75
• 75. Result short spur dirt open mousebite pinhole 76
• 76. Question 77