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DIGITAL IMAGE PROCESSING

Chapter 9 – Morphological Image Processing. DIGITAL IMAGE PROCESSING. J. Shanbehzadeh S.S.Nobakht. Khwarizmi University of Tehran. Table of Contents. Erosion . 2. (B) z = {c | c = b + z, for b є B}. Erosion. Boundary Extraction. Boundary Extraction. Table of Contents.

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DIGITAL IMAGE PROCESSING

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  1. Chapter 9 – Morphological Image Processing DIGITAL IMAGE PROCESSING J. Shanbehzadeh S.S.Nobakht Khwarizmi University of Tehran

  2. Table of Contents

  3. Erosion 2 (B)z = {c | c = b + z, for b є B} • Erosion

  4. Boundary Extraction

  5. Boundary Extraction

  6. Table of Contents

  7. Dilation 6 (B)z = {c | c = b + z, for b є B} • Dilation

  8. Hole Filling

  9. Hole Filling

  10. Table of Contents

  11. Extraction of Connected Components

  12. Extraction of Connected Components

  13. Table of Contents

  14. Convex Hull Closing Opening Erosion Dilation The Hit-or-Miss Transformation

  15. Convex Hull Convex Concave

  16. Convex Hull

  17. Table of Contents

  18. Thinning

  19. Thinning

  20. Table of Contents

  21. Thickening • where B is a structuring element suitable for thickening. As in thinning. thickening can be defined as a sequential operation: • The structuring elements used for thickening have the same form as those shown in Fig. 9.2l(a). but with all 1s and 0s interchanged. However, a separate algorithm for thickening is seldom used in practice. Instead, the usual procedure is to thin the background of the set in question and then complement the result. In other words. to thicken a set A. we form C = AC, thin C, and then form C C. Figure 9.22 illustrates this procedure. • Depending on the nature of A. this procedure can result in disconnected points, as Fig. 9.22(d) shows. Hence thickening by this method usually is followed by postprocessing to remove disconnected points Note from Fig. 9.22(c) that the thinned background forms a boundary for the thickening process • This useful feature is not present in the direct implementation of thickening using Eq. (9.5-I0). and it is one of the principal reasons for using background thinning to accomplish thickening.

  22. Thickening

  23. Table of Contents

  24. Skeleton Skeleton

  25. Applications Simplify a shape by pruning its skeleton:

  26. Skeletons Skeletonization is a process for reducing foreground regions in a binary image to a skeletal remnant that largely preserves the extent and connectivity of the original region while throwing away most of the original foreground pixels. How this works: imagine that the foreground regions in the input binary image are made of some uniform slow-burning material. Light fires simultaneously at all points along the boundary of this region and watch the fire move into the interior. At points where the fire traveling from two different boundaries meets itself, the fire will extinguish itself and the points at which this happens form the so called `quench line'. This line is the skeleton.

  27. Skeletons Skeleton of a rectangle defined in terms of bi-tangent circles.

  28. Skeletons The skeleton/MAT can be produced in two main ways. 1. to use some kind of morphological thinning that successively erodes away pixels from the boundary (while preserving the end points of line segments) until no more thinning is possible, at which point what is left approximates the skeleton. 2. to calculate the distance transform of the image. The skeleton then lies along the singularities (i.e. creases or curvature discontinuities) in the distance transform.

  29. Erosion Dilation Closing Opening The Hit-or-Miss Transformation

  30. Skeletons • Fig. 9.23 shows a skeleton S(A) of a set A. • (a) lf z is a point of S(A) and (D)z is the largest disk cantered at z and contained in A. one cannot find a larger disk (not necessarily centered at z) containing (D)z and included in A. The disk (D)z is called a maximum disk. • (b) The disk (D)Z touches the boundary of A at two or more different places. Opening Erosion

  31. Skeletons

  32. Skeletons

  33. Distance Transform The distance transform of a simple shape. Note that we are using the `chessboard' distance metric. The distance transform is an operator normally only applied to binary images. The result of the transform is a graylevel image that looks similar to the input image, except that the graylevel intensities of points inside foreground regions are changed to show the distance to the closest boundary from each point.

  34. Distance Transform

  35. Table of Contents

  36. Pruning https://reference.wolfram.com/mathematica/ref/Pruning.html

  37. Pruning Iteratively prune an image: https://reference.wolfram.com/mathematica/ref/Pruning.html

  38. Applictions Count the legs of a centipede Find the loops of a graph: https://reference.wolfram.com/mathematica/ref/Pruning.html

  39. Applictions Solve a maze puzzle by thinning all paths and pruning dead ends: https://reference.wolfram.com/mathematica/ref/Pruning.html

  40. Pruning Thinning The Hit-or-Miss Transformation

  41. Pruning Thinning The Hit-or-Miss Transformation Dilation H = 3x3 structuring element of 1’s

  42. Pruning

  43. Table of Contents

  44. Table of Contents

  45. Morphological Operations on Binary Images

  46. Morphological Operations on Binary Images

  47. Morphological Operations on Binary Images

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