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### Ip

1. 1. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Representation and Description – Representing regions in 2 ways: • Based on their external characteristics (its boundary): – Shape characteristics • Based on their internal characteristics (its region): – Regional properties: color, texture, and … • Both 1 1E. Fatemizadeh, Sharif University of Technology, 2011
2. 2. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Representation and Description – Describes the region based on a selected  representation: • Representation  boundary or textural features • Description  length, orientation, the number of  concavities in the boundary, statistical measures of  region. 2 2E. Fatemizadeh, Sharif University of Technology, 2011
3. 3. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Invariant Description: – Size (Scaling) – Translation – Rotation 3 3E. Fatemizadeh, Sharif University of Technology, 2011
4. 4. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Boundary (Border) Following: – We need the boundary as a ordered sequence of points. 4 4E. Fatemizadeh, Sharif University of Technology, 2011
5. 5. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Moore Boundary Tracking Algorithm: 1. Let the starting point, b0 , be the uppermost, leftmost point in the  image that is labeled 1. Denote by c0 the west neighbor of b0 . Clearly  c0 always will be a background point. Then, examine the 8 neighbors  of b0 , starting at c0 and proceeding in clockwise direction. Let b1 denote the first pixel encountered whose value is 1, and let c1 be the  points immediately preceding b1 in the sequence. Store the location  of b0 and b1. 2. Let b=b1 and c=c1. 3. Let the 8 neighbors of b , starting at c and proceeding in a clockwise direction be denoted by n1,n2,... , nk . Find the first nk whose value is  1. 4. Let b=nk and c=nk-1. 5. Repeat steps 3 and 4 until b=b0 and the next boundary point found  is b1. 5 5E. Fatemizadeh, Sharif University of Technology, 2011
6. 6. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 6 6E. Fatemizadeh, Sharif University of Technology, 2011
7. 7. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Freeman Chain Code: – Code the 4 or 8 connectivity 7 7E. Fatemizadeh, Sharif University of Technology, 2011
8. 8. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Chain Code Problems: – Long Code – Low noise Robustness • Solution: Resampling – Starting Point: • Solution: Rotary/Circular shift until forms a minimum integer – 10103322 01033221 – Angle normalization: • First difference (Counterclockwise) – 10103322  3133030  or 33133030 (transition between last and first) • Useful for integer multiple of used chain code (45° or 90°) 8 8E. Fatemizadeh, Sharif University of Technology, 2011
9. 9. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: – Resampling – 4 and 8 chain codes 9 9E. Fatemizadeh, Sharif University of Technology, 2011
10. 10. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 10 10E. Fatemizadeh, Sharif University of Technology, 2011
11. 11. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Polygon Approximation: – Minimum‐Perimeter Polygons • Read Pages 801‐807. 11 11E. Fatemizadeh, Sharif University of Technology, 2011
12. 12. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example (Cont.): 12 12E. Fatemizadeh, Sharif University of Technology, 2011
13. 13. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 13 13E. Fatemizadeh, Sharif University of Technology, 2011
14. 14. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Polygon Approximation: – Merging: • Start from a seed point • Continue on a line based on local average error (e.g. linear  regression) • Stop if error exceeds a threshold • Continue from the last point • .... – No guarantee for corner detection 14 14E. Fatemizadeh, Sharif University of Technology, 2011
15. 15. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Polygon Approximation: – Splitting: • Segments to two parts based on a criteria (e.g. maximum internal  distance) • Check each segment for splitting based on another criteria (e.g.  linearity error) • …. 15 15E. Fatemizadeh, Sharif University of Technology, 2011
16. 16. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Signatures: – A 1‐D functional representation of a boundary • Distance vs. Angle (in the polar representation): – Invariant to translation – Non‐Invariant to rotation (may be achieved by start point selection) » Farthest point from centroid » The point on eigen axis » Use chain code solution for the start point • Line tangent angle • Histogram of tangent angle 16 16E. Fatemizadeh, Sharif University of Technology, 2011
17. 17. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 17 17E. Fatemizadeh, Sharif University of Technology, 2011
18. 18. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 18 18E. Fatemizadeh, Sharif University of Technology, 2011
19. 19. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Boundary Segments: – Convex Hull: Smallest convex set containing the S – Convex Deficiency: The set difference D=H‐S – Problem of noise: • Smoothing (K‐neighbour average) • Polygon approximation – Convex Hull of Polygon  19 19E. Fatemizadeh, Sharif University of Technology, 2011
20. 20. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Boundary Segments: • Skeletonization / Thinning: – Medial Axis Transform (MAT) • Point p is belong to medial (Region R and Border B): – Has more than one closest neighbor in B – Chapter 9 and Page 813 20 20E. Fatemizadeh, Sharif University of Technology, 2011
21. 21. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example of Thinning: 21 21E. Fatemizadeh, Sharif University of Technology, 2011
22. 22. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Boundary Descriptor: – Simple one: • Diameter:  – Lead to Major axis and minor axis (Perpendicular to major) – Basic Rectangle • Curvature 22 22E. Fatemizadeh, Sharif University of Technology, 2011
23. 23. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Shape Number – Smallest integers of first difference circular chain code. 23 23E. Fatemizadeh, Sharif University of Technology, 2011
24. 24. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 24 24E. Fatemizadeh, Sharif University of Technology, 2011
25. 25. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Fourier Descriptors: 25 25E. Fatemizadeh, Sharif University of Technology, 2011
26. 26. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 26 26E. Fatemizadeh, Sharif University of Technology, 2011
27. 27. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Problem of invariance: – Rotation – Normalization will solve! 27 27E. Fatemizadeh, Sharif University of Technology, 2011
28. 28. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Problem of invariance: – Translation – Translation to centroid will solve! 28 28E. Fatemizadeh, Sharif University of Technology, 2011
29. 29. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Problem of invariance: – Scaling – Normalization will solve 29 29E. Fatemizadeh, Sharif University of Technology, 2011
30. 30. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Problem of invariance: – Starting  Point – Normalization will solve 30 30E. Fatemizadeh, Sharif University of Technology, 2011
31. 31. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Properties in a single table: 31 31E. Fatemizadeh, Sharif University of Technology, 2011
32. 32. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Statistical Moments: – Boundary Representation 32 32E. Fatemizadeh, Sharif University of Technology, 2011
33. 33. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Regional Descriptor: – The simple one: • Area (Number of pixels) • Perimeter (Length of boundary) • Compactness  (Perimeter2/Area) • Circularity: Ratio of the area to the area of a circle with same  perimeter • Mean, median, max, min, ratio pixels above/below … from  intensity data. 33 33E. Fatemizadeh, Sharif University of Technology, 2011
34. 34. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: – Normalized area: • Ratio of light pixels to total light pixels 34 34E. Fatemizadeh, Sharif University of Technology, 2011
35. 35. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Topology Descriptor: – Number of holes (H): • Invariants to several operators. 35 35E. Fatemizadeh, Sharif University of Technology, 2011
36. 36. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Topology Descriptor: – Number of connected components (C) : • Invariants to several operators. 36 36E. Fatemizadeh, Sharif University of Technology, 2011
37. 37. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Topology Descriptor: – Euler number (E=C‐H) : • Invariants to several operators. 0 ‐1 37 37E. Fatemizadeh, Sharif University of Technology, 2011
38. 38. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Topology Descriptor: – Polygonal net: • V: # of vertices (7) • Q: # of edges (11) • F: # of faces (2) • E=C‐H=V‐Q+F – C=1 , H=3 – E=‐2 38 38E. Fatemizadeh, Sharif University of Technology, 2011
39. 39. Digital Image Processing ee.sharif.edu/~dip Representation and Description Original Threshold • Example: Largest Connected Region Skeleton 39 39E. Fatemizadeh, Sharif University of Technology, 2011
40. 40. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Texture: – No formal definition Smooth               Coarse                 Regular 40 40E. Fatemizadeh, Sharif University of Technology, 2011
41. 41. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Statistical Approaches – 1st order grey level statistics • From normalised histogram – One pixel gray level repeat n times – 2nd order grey level statistics • From GLCM (Grey Level Co‐ocurrence Matrix) – Repeatation of two pixels in a pre‐defined neighbourhood • Needs: – A Positioning Operator, P. – GLCM(i,j): # of times that points with gray level Zi occure relative to  points with gray level Zj 41 41E. Fatemizadeh, Sharif University of Technology, 2011
42. 42. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Texture feature from 1st order statistics: 42 42E. Fatemizadeh, Sharif University of Technology, 2011
43. 43. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: Smooth               Coarse                 Regular 43 43E. Fatemizadeh, Sharif University of Technology, 2011
44. 44. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Problem with 1st order histogram – Lack of spatial information 44 44E. Fatemizadeh, Sharif University of Technology, 2011
45. 45. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Gray Level Co‐Occurence Matrix (GLCM): 45 45E. Fatemizadeh, Sharif University of Technology, 2011
46. 46. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Gray Level Co‐Occurence Matrix (GLCM): 46 46E. Fatemizadeh, Sharif University of Technology, 2011
47. 47. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Gray Level Co‐Occurence Matrix (GLCM): 47 47E. Fatemizadeh, Sharif University of Technology, 2011
48. 48. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Texture feature from GLCM 48 48E. Fatemizadeh, Sharif University of Technology, 2011
49. 49. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: – One pixel immediately to he right 49 49E. Fatemizadeh, Sharif University of Technology, 2011
50. 50. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 50 50E. Fatemizadeh, Sharif University of Technology, 2011
51. 51. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Effect of Horizontal offset: – Correlation index – Horizontal distance between neighbors Noisy               Sin              Circuit board 51 51E. Fatemizadeh, Sharif University of Technology, 2011
52. 52. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Spectral approaches: – Peaks and Frequencies related to periodicity: – S(r,θ), Sr(θ),Sθ(r): 52 52E. Fatemizadeh, Sharif University of Technology, 2011
53. 53. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Spectral approaches: 53 53E. Fatemizadeh, Sharif University of Technology, 2011
54. 54. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Spectral approach: 54 54E. Fatemizadeh, Sharif University of Technology, 2011
55. 55. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Moments of Image as a 2D pdf: 55 55E. Fatemizadeh, Sharif University of Technology, 2011
56. 56. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Digital Data: 56 56E. Fatemizadeh, Sharif University of Technology, 2011
57. 57. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Moments: • A set of invariant moments (7 by Hu) 57 57E. Fatemizadeh, Sharif University of Technology, 2011
58. 58. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Hu Moments: 58 58E. Fatemizadeh, Sharif University of Technology, 2011
59. 59. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 59 59E. Fatemizadeh, Sharif University of Technology, 2011
60. 60. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Results of invariant moments: 60 60E. Fatemizadeh, Sharif University of Technology, 2011
61. 61. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Complex Zernike Moments: • Where Vmn are Zernike polynomials: 61 61E. Fatemizadeh, Sharif University of Technology, 2011
62. 62. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Some Zernike Polynomials: 62 62E. Fatemizadeh, Sharif University of Technology, 2011
63. 63. Digital Image Processing ee.sharif.edu/~dip Representation and Description • How to Compute Zernike Polynomials: – Scale and Translation invariance transform: • Shift to center of gravity (m10 = m01= 0) • Fix m00 at a predetermined value (= ): – Map Image to the unit disc using polar coordinates. – The center of the image is the origin of the unit disc – Those pixels falling outside the unit disc are not used in  the computation. 63 63E. Fatemizadeh, Sharif University of Technology, 2011
64. 64. Digital Image Processing ee.sharif.edu/~dip Representation and Description • How to Compute Zernike Polynomials: 64 64E. Fatemizadeh, Sharif University of Technology, 2011
65. 65. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Legendre Moments: 65 65E. Fatemizadeh, Sharif University of Technology, 2011
66. 66. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Fourier‐Mellin Moments: – Fourier‐Mellin Transform: – Fourier‐Mellin Moments: 66 66E. Fatemizadeh, Sharif University of Technology, 2011
67. 67. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Principal Component Analysis: – Consider a multi (value/Channel/Spectral) images: 67 67E. Fatemizadeh, Sharif University of Technology, 2011
68. 68. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Karhunen–Loève or Hotelling Transform: – Analysis: – Complete Synthesis: – Optimal Synthesis: 68 68E. Fatemizadeh, Sharif University of Technology, 2011
69. 69. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: 69 69E. Fatemizadeh, Sharif University of Technology, 2011
70. 70. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Data Preparation: 70 70E. Fatemizadeh, Sharif University of Technology, 2011
71. 71. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Eigenvalues Analysis: 71 71E. Fatemizadeh, Sharif University of Technology, 2011
72. 72. Digital Image Processing ee.sharif.edu/~dip Representation and Description • PCA Analysis: – Eigneimages 72 72E. Fatemizadeh, Sharif University of Technology, 2011
73. 73. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: – Using 2 components 73 73E. Fatemizadeh, Sharif University of Technology, 2011
74. 74. Digital Image Processing ee.sharif.edu/~dip Representation and Description • Example: – Difference 74 74E. Fatemizadeh, Sharif University of Technology, 2011
75. 75. Digital Image Processing ee.sharif.edu/~dip Representation and Description • PCA in Boundary description: 75 75E. Fatemizadeh, Sharif University of Technology, 2011
76. 76. Digital Image Processing ee.sharif.edu/~dip Representation and Description • PCA in Boundary description: 76 76E. Fatemizadeh, Sharif University of Technology, 2011