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Foundations of Computer Vision

Foundations of Computer Vision. Lecture 15 Morphological Processing Dr. Roger S. Gaborski. Agenda. Binary morphological processing Erosion and dilation Opening and closing Gray-scale morphological processing Erosion and dilation Morphological gradients. Roger S. Gaborski. 2.

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Foundations of Computer Vision

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  1. Foundations of Computer Vision Lecture 15 Morphological Processing Dr. Roger S. Gaborski

  2. Agenda • Binary morphological processing • Erosion and dilation • Opening and closing • Gray-scale morphological processing • Erosion and dilation • Morphological gradients Roger S. Gaborski 2

  3. Introduction • Morphology: a branch of biology dealing with the form and structure of creatures • Mathematical morphology: • Extract image components based on shape e.g. boundaries, skeletons, convex hull, etc • Image denoise e.g. reduce noise after edge detection Roger S. Gaborski 3

  4. Binary Morphological Processing Non-linear image processing technique Order of sequence of operations is important Linear: (3+2)*3 = (5)*3=15 3*3+2*3=9+6=15 Non-linear: (3+2)2 = (5)2 =25 [sum, then square] (3)2 + (2)2 =9+4=13 [square, then sum] Based on geometric structure Used for edge detection, noise removal and feature extraction Used to ‘understand’ the shape/form of a binary image Roger S. Gaborski 4

  5. Image – Set of Pixels Basic idea is to treat an object within an image as a set of pixels (or coordinates of pixels) In binary images Background pixels are set to 0 and appear black Foreground pixels (objects) are 1 and appear white Roger S. Gaborski 5

  6. Chapter 9 Morphological Image Processing A-B = A- (A∩B) From: Digital Image Processing, Gonzalez,Woods And Eddins Roger S. Gaborski 6

  7. DILATION A A1= A B B B a a Object B is one point located at (a,0) A1: Object A is translated by object B Since dilation is the union of all the translations, A B = U Atwhere the set union U is for all the b’s in B, the dilation of rectangle A in the positive x direction by a results in rectangle A1 (same size as A, just translated to the right) Roger S. Gaborski 7

  8. DILATION – B has 2 Elements A A2 A1 (part of A1 is under A2) -a a -a a Object B is 2 points, (a,0), (-a,0) There are two translations of A as result of two elements in B Dilation is defined as the UNION of the objects A1 and A2. NOT THE INTERSECTION Roger S. Gaborski 8

  9. DILATION Image (A) SE (B) Round Structuring Element (SE) can be interpreted as rolling the SE around the contour of the object. New object has rounded corners and is larger by ½ width of the SE Dilation Roger S. Gaborski 9

  10. DILATION Countless translation Vectors Another approach Rounded corners Image (A) SE (B) Dilation Roger S. Gaborski 10

  11. DILATION Square corners Image (A) SE (B) Square Structuring Element (SE) can be interpreted as moving the SE around the contour of the object. New object has square corners and is larger by ½ width of the SE Dilation Roger S. Gaborski 11

  12. DILATION Countless translation vectors Another approach Square corners Image (A) SE (B) Dilation Roger S. Gaborski 12

  13. DILATION The shape of B determines the final shape of the dilated object. B acts as a geometric filter that changes the geometric structure of A Roger S. Gaborski 13

  14. Chapter 9 Morphological Image Processing From: Digital Image Processing, Gonzalez,Woods And Eddins Roger S. Gaborski 14

  15. Chapter 9 Morphological Image Processing Image A Image B ~ A A U B A ∩B A-B = A ∩(~B) From: Digital Image Processing, Gonzalez,Woods And Eddins Roger S. Gaborski 15

  16. SE Original Image Translation Process Dilated Image From: Digital Image Processing, Gonzalez,Woods And Eddins Roger S. Gaborski 16

  17. imdilate • IM2 = IMDILATE(IM,NHOOD) dilates the image IM, where NHOOD is a • matrix of 0s and 1s that specifies the structuring element • neighborhood. This is equivalent to the syntax IIMDILATE(IM, • STREL(NHOOD)). IMDILATE determines the center element of the • neighborhood by FLOOR((SIZE(NHOOD) + 1)/2). • >> se = imrotate(eye(3),90) • se = • 0 0 1 • 0 1 0 • 1 0 0 • >> ctr=floor(size(se)+1)/2 • ctr = • 2 2 1 2 3 1 2 3 Roger S. Gaborski 17

  18. MATLAB Dilation Example Im (original image) Im2 (dialated image) >> Im = zeros([13 19]); >> Im(6,6:8)=1; >> Im2 = imdilate(Im,se); 1 2 3 Roger S. Gaborski 18 1 2 3

  19. MATLAB Dilation Example INPUT IMAGE DILATED IMAGE >> I = zeros([13 19]); >> I(6, 6:12)=1; >> SE = imrotate(eye(5),90); >> I2=imdilate(I,SE); >> figure, imagesc(I) >> figure, imagesc(SE) >> figure, imagesc(I2) 1 2 3 4 5 SE 1 2 3 4 5 Roger S. Gaborski 19

  20. MATLAB Dilation Example INPUT IMAGE DILATED IMAGE I I2 1 2 3 4 5 >> I(6:9,6:13)=1; >> figure, imagesc(I) >> I2=imdilate(I,SE); >> figure, imagesc(I2) SE 1 2 3 4 5 Roger S. Gaborski 20

  21. MATLAB Dilation Example DILATED IMAGE INPUT IMAGE I I2 SE = 1 1 1 1 1 1 1 1 1 Roger S. Gaborski 21

  22. Dilation and Erosion DILATION: Adds pixels to the boundary of an object EROSIN: Removes pixels from the boundary of an object Number of pixels added or removed depends on size and shape of structuring element Roger S. Gaborski 22

  23. SE Original Image Translation Process Eroded Image From: Digital Image Processing, Gonzalez,Woods And Eddins Roger S. Gaborski 23

  24. MATLAB Erosion Example ERODED IMAGE 2 pixel wide INPUT IMAGE >> I=zeros(13, 19); I(6:9,6:13)=1; >> figure, imagesc(I) >> I2=imerode(I,SE); >> figure, imagesc(I2) 1 2 3 1 2 3 24 Roger S. Gaborski SE = 3x1

  25. Chapter 9 Morphological Image Processing Original Image Erosion with a disk of radius 10 From: Digital Image Processing, Gonzalez,Woods And Eddins Erosion with a disk of radius 5 Erosion with a disk of radius 20 25 Roger S. Gaborski

  26. Combinations In most morphological applications dilation and erosion are used in combination May use same or different structuring elements Roger S. Gaborski 26

  27. Morphological Opening and Closing Opening of A by B A o B = (AO B)  B; imopen(A, B) Erosion of A by B, followed by the dilation of the result by B Closing of A by B  A B = (A  B) O B; imclose(A, B) Dilation of A by B, followed by the erosion of the result by B Roger S. Gaborski 27

  28. MATLAB Function strel strel constructs structuring elements with various shapes and sizes Syntax: se = strel(shape, parameters) Example: se = strel(‘octagon’, R); R is the dimension – see help function Roger S. Gaborski 28

  29. Opening of A by B  A B • Erosion of A by B, followed by the dilation of the result by B Erosion- if any element of structuring element overlaps with background output is 0 f (original image) fe (eroded image) FIRST - EROSION >> se = strel('square', 20); fe = imerode(f,se); figure, imagesc(fe),title('fe') Roger S. Gaborski 29

  30. Dilation of Previous Result Outputs 1 at center of SE when at least one element of SE overlaps object fe (eroded image) fd (dilated image) SECOND - DILATION >> se = strel('square', 20); fd = imdilate(fe,se); figure, imagesc(fd),title('fd') Roger S. Gaborski 30

  31. FO = imopen(f,se); figure, imagesc(FO),title('FO') FO (opened image) fd (dilated image in previous slide) Roger S. Gaborski 31

  32. What if we increased size of SE for DILATION operation?? se = 25 se = 30 se = strel('square', 30); fd = imdilate(fe,se); figure, imagesc(fd),title('fd') se = strel('square', 25); fd = imdilate(fe,se); figure, imagesc(fd),title('fd') Roger S. Gaborski 32

  33. Closing of A by B  A B Dilation of A by B Outputs 1 at center of SE when at least one element of SE overlaps object se = strel('square', 20); fd = imdilate(f,se); figure, imagesc(fd),title('fd') Roger S. Gaborski 33

  34. Erosion of the result by B Erosion- if any element of structuring element overlaps with background output is 0 Roger S. Gaborski 34

  35. ORIGINAL OPENING CLOSING Roger S. Gaborski 35

  36. Chapter 9 Morphological Image Processing original image opening opening + closing From: Digital Image Processing, Gonzalez,Woods And Eddins Roger S. Gaborski 36

  37. Hit or Miss Transformation Usage: to identify specified configuration of pixels, e.g. isolated foreground pixels pixels at end of lines (end points) Definition A B = (A B1) ∩(AcΘB2) A eroded by B1, intersects A complement eroded by B2 (two different structuring elements: B1 , B2) Roger S. Gaborski 37

  38. Hit or Miss Example Find cross shape pixel configuration: MATLAB Function: C = bwhitmiss(A, B1, B2) Roger S. Gaborski 38

  39. Original Image A and B1 A eroded by B1 Complement of Original Image and B2 Erosion of A complement And B2 Intersection of eroded images Roger S. Gaborski 39 From: Digital Image Processing, Gonzalez,Woods And Eddins

  40. Original Image A and B1 A eroded by B1 Complement of Original Image and B2 Erosion of A complement And B2 Intersection of eroded images Roger S. Gaborski 40 From: Digital Image Processing, Gonzalez,Woods And Eddins

  41. Original Image A and B1 A eroded by B1 Complement of Original Image and B2 Erosion of A complement And B2 Intersection of eroded images Roger S. Gaborski 41 From: Digital Image Processing, Gonzalez,Woods And Eddins

  42. Original Image A and B1 A eroded by B1 Complement of Original Image and B2 Erosion of A complement And B2 Intersection of eroded images Roger S. Gaborski 42 From: Digital Image Processing, Gonzalez,Woods And Eddins

  43. Original Image A and B1 A eroded by B1 Complement of Original Image and B2 Erosion of A complement And B2 Intersection of eroded images Roger S. Gaborski 43 From: Digital Image Processing, Gonzalez,Woods And Eddins

  44. Original Image A and B1 A eroded by B1 Complement of Original Image and B2 Erosion of A complement And B2 Intersection of eroded images Roger S. Gaborski 44 From: Digital Image Processing, Gonzalez,Woods And Eddins

  45. Hit or Miss Have all the pixels in B1 (hits all pixels in B1), but none of the pixels in B2 (misses all pixels in B2) More precisely, hit-and-miss operation Roger S. Gaborski 45

  46. Hit or Miss Example #2 Locate upper left hand corner pixels of objects in an image Pixels that have east and south neighbors (Hits) and no NE, N, NW, W, SW Pixels (Misses) B1 = B2 = Don’t Care about SE Roger S. Gaborski 46

  47. Chapter 9 Morphological Image Processing G = bwhitmiss(f, B1, B2); Figure, imshow(g) From: Digital Image Processing, Gonzalez,Woods And Eddins Roger S. Gaborski 47

  48. bwmorph(f, operation, n) Implements various morphological operations based on combinations of dilations, erosions and look up table operations. f: input binary image operation: a string specifying the desired operation n: a positive integer specifying iteration times (default: 1) Roger S. Gaborski 48

  49. Example 1: thinning • To reduce binary objects or shapes in an image to strokes whose width is 1 pixel • Matlab implementation >> f = imread(‘fingerprint_cleaned.tif’); >> g = bwmorph(f, ‘thin’, 1); >> g2 = bwmorph(f, ‘thin’, 2); >> g3 = bwmorph(f, ‘thin’, Inf); Roger S. Gaborski 49

  50. Input Thinned once Thinned twice Thinned until stability Roger S. Gaborski 50 From: Digital Image Processing, Gonzalez,Woods And Eddins

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