Fuzzy Logic Based Edge Detection

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This Algorithm is better than canny by 0.7% but lacks the speed and optimization capability which can be changed by including Neural Network and PSO searching to the same.

This used dual FIS Optimization technique to find the high frequency or the edges in the images and neglect the lower frequencies.

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Fuzzy Logic Based Edge Detection

  1. 1. Digital Image Processing Edge Detection using Dual FIS Optimization Ishaan Gupta 03914802810 7E123 – E2 Electronics and Communications MAIT Mentored By: Prof. Nitin Sharma Assistant Professor Electronics and Communications Dept MAIT
  2. 2. What is D.I.P. ? • Processing of digital images by means of a digital computer. • Output can be image and/or values. • Deals with spatial coordinates, amplitude of ‘f’ at any pair coordinates (x,y) called gray levels or intensity values which are finite and discrete.
  3. 3. Steps in DIP Image acquisition Image filtering and enhancement Image restoration Color Image Processing. Wavelets and multi-resolution Processing. Compression Morphological Processing. Segmentation Representation & Description. Object Recognition
  4. 4. Image acquisition • Done via: • Camera – Visible spectrum • Image matrix (Draw Functions / Convert intensity values -> Image) • Techniques : • Xray • Gamma • Ultrasound • IR • Satellite (Multi-resolution)
  5. 5. Image filters & enhancement • Filters – LPF, HPF, BPF, Gaussian Filters, etc. • Depth – Field view, panorama, IR based, Laser Based • Enhancement – Brightness, Contrast, Smoothening, Equalization, Saturation [RGB Master, R master, G Master, B Master] , etc.
  6. 6. Detection • Edge • Color • Intensity / gray level - Binary and grayscale Images • Objects and Object description.
  7. 7. Edge detection algos • Gaussian - Canny’s Algo, Shen-Castan, etc • LoG (Laplacian of Gaussian) – Marr-Hildreth – Second Derivative • Zero Crossing – LoG based • Classical - Prewitt • Classical - Sobel
  8. 8. Comparisons Operator Advantages Disadvantages Classical (Sobel, prewitt, Kirsch,…) Simplicity, Detection of edges and their orientations Sensitivity to noise, Inaccurate Zero Crossing(Laplacian, Second directional derivative) Detection of edges and their orientations. Having fixed characteristics in all directions Responding to some of the existing edges, Sensitivity to noise Laplacian of Gaussian(LoG) (Marr-Hildreth) Finding the correct places of edges, Testing wider area around the pixel Malfunctioning at the corners, curves and where the gray level intensity function varies. Not finding the orientation of edge because of using the Laplacian filter Gaussian(Canny, Shen-Castan) Using probability for finding error rate, Localization and response. Improving signal to noise ratio, Better detection specially in noise conditions Complex Computations, False zero crossing, Time consuming
  9. 9. Edge Detection 9
  10. 10. • Convert a 2D image into a set of curves • Extracts salient features of the scene • More compact than pixels 10
  11. 11. Origin of Edges • Edges are caused by a variety of factors depth discontinuity surface color discontinuity illumination discontinuity surface normal discontinuity 11
  12. 12. Profiles of image intensity edges 12
  13. 13. Edge detection 1. Detection of short linear edge segments (edgels) 2. Aggregation of edgels into extended edges • (maybe parametric description) 13
  14. 14. Edgel detection •Difference operators •Parametric-model matchers 14
  15. 15. Edge is Where Change Occurs • Change is measured by derivative in 1D • Biggest change, derivative has maximum magnitude • Or 2nd derivative is zero. 15
  16. 16. Image gradient • The gradient of an image: • The gradient points in the direction of most rapid change in intensity The gradient direction is given by: • how does this relate to the direction of the edge? The edge strength is given by the gradient magnitude 16
  17. 17. The discrete gradient • How can we differentiate a digital image f[x,y]? • Option 1: reconstruct a continuous image, then take gradient • Option 2: take discrete derivative (finite difference) 17
  18. 18. The Sobel operator • Better approximations of the derivatives exist • The Sobel operators below are very commonly used -1 0 1 -2 0 2 -1 0 1 1 2 1 0 0 0 -1 -2 -1 • The standard defn. of the Sobel operator omits the 1/8 term – doesn’t make a difference for edge detection – the 1/8 term is needed to get the right gradient value, however 18
  19. 19. Gradient operators (a): Roberts’ cross operator (b): 3x3 Prewitt operator (c): Sobel operator (d) 4x4 Prewitt operator 19
  20. 20. Effects of noise • Consider a single row or column of the image • Plotting intensity as a function of position gives a signal 20
  21. 21. Solution: Smooth first 21
  22. 22. Derivative theorem of convolution • This saves us one operation: 22
  23. 23. Laplacian of Gaussian • Consider Laplacian of Gaussian operator 23
  24. 24. 2D edge detection filters • is the Laplacian operator: Laplacian of Gaussian Gaussian derivative of Gaussian 24
  25. 25. Optimal Edge Detection: Canny • Assume: • Linear filtering • Additive iid Gaussian noise • Edge detector should have: • Good Detection. Filter responds to edge, not noise. • Good Localization: detected edge near true edge. • Single Response: one per edge. 25
  26. 26. Optimal Edge Detection: Canny (continued) • Optimal Detector is approximately Derivative of Gaussian. • Detection/Localization trade-off • More smoothing improves detection • And hurts localization. 26
  27. 27. The Canny edge detector • original image (Lena) 27
  28. 28. The Canny edge detector norm of the gradient 28
  29. 29. The Canny edge detector thresholding 29
  30. 30. The Canny edge detector thinning (non-maximum suppression) 30
  31. 31. Non-maximum suppression • Check if pixel is local maximum along gradient direction • requires checking interpolated pixels p and r 31
  32. 32. Predicting the next edge point Assume the marked point is an edge point. Then we construct the tangent to the edge curve (which is normal to the gradient at that point) and use this to predict the next points (here either r or s). (Forsyth & Ponce) 32
  33. 33. Hysteresis • Check that maximum value of gradient value is sufficiently large • drop-outs? use hysteresis • use a high threshold to start edge curves and a low threshold to continue them. 33
  34. 34. Effect of (Gaussian kernel size) Canny with Canny withoriginal The choice of depends on desired behavior • large detects large scale edges • small detects fine features 34
  35. 35. Scale • Smoothing • Eliminates noise edges. • Makes edges smoother. • Removes fine detail. 35
  36. 36. 36
  37. 37. fine scale high threshold 37
  38. 38. coarse scale, high threshold 38
  39. 39. coarse scale low threshold 39
  40. 40. Scale space • Properties of scale space (w/ Gaussian smoothing) • edge position may shift with increasing scale ( ) • two edges may merge with increasing scale • an edge may not split into two with increasing scale larger Gaussian filtered signal first derivative peaks 40
  41. 41. Edge detection by subtraction original 41
  42. 42. Edge detection by subtraction smoothed (5x5 Gaussian) 42
  43. 43. Edge detection by subtraction smoothed – original (scaled by 4, offset +128) Why does this work? filter demo 43
  44. 44. Gaussian - image filter Laplacian of Gaussian Gaussian delta function 44
  45. 45. An edge is not a line... 45
  46. 46. Finding lines in an image • Option 1: • Search for the line at every possible position/orientation • What is the cost of this operation? • Option 2: • Use a voting scheme: Hough transform 46
  47. 47. Finding lines in an image • Connection between image (x,y) and Hough (m,b) spaces • A line in the image corresponds to a point in Hough space • To go from image space to Hough space: • given a set of points (x,y), find all (m,b) such that y = mx + b x y m b m0 b0 image space Hough space 47
  48. 48. Finding lines in an image • Connection between image (x,y) and Hough (m,b) spaces • A line in the image corresponds to a point in Hough space • To go from image space to Hough space: • given a set of points (x,y), find all (m,b) such that y = mx + b • What does a point (x0, y0) in the image space map to? x y m b image space Hough space – A: the solutions of b = -x0m + y0 – this is a line in Hough space x0 y0 48
  49. 49. Corners contain more edges than lines. • A point on a line is hard to match. Corner detection 49
  50. 50. Corners contain more edges than lines. • A corner is easier 50
  51. 51. Edge Detectors Tend to Fail at Corners 51
  52. 52. Finding Corners Intuition: • Right at corner, gradient is ill defined. • Near corner, gradient has two different values. 52
  53. 53. Fuzzy Logic & Fuzzy Inference System (FIS)
  54. 54. Introduction to Fuzzy Sets • Introduced by A. L. Zadeh (1965) • Fuzzy sets provide the mechanism for dealing with imprecise information • Based and related closely to usage of probability in crisp information. • Provides margin for error and its correction possibilities in both input and output values. • Takes into account full or partial membership and relationship between one value to another.
  55. 55. Fuzzy Inference System (FIS) FIS Types Mamdani Sugeno Components Membership Functions IF-THEN Rules Logical Operations Applications DIP Localizations Network Analysis
  56. 56. Steps in FIS
  57. 57. FIS Toolbox in MATLAB
  58. 58. Conventional FIS usage in DIP FIS(4Input) Image processor Edge
  59. 59. My usage Image Restoration Image Enhancement Noise Removal using LoG FIS OutDIP2 Edge Detection2 DIP 1 Edge detection1 Mat2Gray out1 FIS Image processor FIS Image Processor Edge Out Mat2Gray out Filtration Noise Removal Image enhancement Image restoration
  60. 60. FIS 1
  61. 61. Membership Function of Input
  62. 62. Membership of Output
  63. 63. IF-THEN Rule set = 16
  64. 64. FIS2
  65. 65. Membership Function of Input
  66. 66. Membership of Output
  67. 67. IF-THEN Ruleset = 28 +10
  68. 68. Final Outputs Compare d
  69. 69. Thank You

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