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DIGITAL IMAGE PROCESSING J. Shanbehzadeh S.S.Nobakht Khwarizmi University of Tehran

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 1 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Boundary Extraction 3

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Boundary Extraction 4

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 5 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Hole Filling 7

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Hole Filling 8

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 9 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Extraction of Connected Components 10

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Extraction of Connected Components 11

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 12 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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Convex Hull 13 Erosion Dilation Opening Closing The Hit-or-Miss Transformation

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Convex Hull Convex Concave

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Convex Hull 15

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 16 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Thinning 17

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Thinning

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 19 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. 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 = A C, 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. Thickening 20

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Thickening

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 22 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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Skeleton 23 Skeleton

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Applications 24 Simplify a shape by pruning its skeleton:

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Skeletons 25 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.binary image 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.

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Skeletons 26 Skeleton of a rectangle defined in terms of bi-tangent circles.

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Skeletons 27 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.thinning 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.distance transform

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28 Erosion Dilation Opening Closing The Hit-or-Miss Transformation

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Skeletons 29 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. Erosion Opening

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Skeletons 30

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. SkeletonsSkeletons 31

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Distance Transform 32 The distance transform of a simple shape. Note that we are using the `chessboard' distance metric.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.

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Distance Transform 33

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 34 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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Pruning 35 https://reference.wolfram.com/mathematica/ref/Pruning.html

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Pruning 36 Iteratively prune an image: https://reference.wolfram.com/mathematica/ref/Pruning.html

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Applictions 37 Count the legs of a centipede Find the loops of a graph: https://reference.wolfram.com/mathematica/ref/Pruning.html

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Applictions 38 Solve a maze puzzle by thinning all paths and pruning dead ends: https://reference.wolfram.com/mathematica/ref/Pruning.html

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Pruning 39 The Hit-or-Miss Transformation Thinning

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Pruning 40 Thinning The Hit-or-Miss Transformation Dilation H = 3x3 structuring element of 1’s

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Pruning

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 42 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Table of Contents 43 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction 9.5.2 Hole Filling 9.5.3 Extraction of Connected Components 9.5.4 Convex Hull 9.5.5 Thinning 9.5.6 Thickening 9.5.7 Skeletons 9.5.8 Pruning 9.5.9 Morphological Reconstruction 9.5.10 Summary of Morphological Operations on Binary Images

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Morphological Operations on Binary Images 44

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Morphological Operations on Binary Images 45

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R. C. Gonzalez, and R. E. Woods, Digital Image Processing, New Jersey: Prentice Hall, 3 rd edition, 2008. Morphological Operations on Binary Images 46

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