DIGITAL IMAGE PROCESSING Chapter 9 – Morphological Image Processing J. Shanbehzadeh S.S.Nobakht Khwarizmi University of Tehran
Table of Contents 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
Erosion 2 (B)z = {c | c = b + z, for b є B} Erosion
Boundary Extraction
Boundary Extraction
Table of Contents 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
Dilation 6 (B)z = {c | c = b + z, for b є B} Dilation
Hole Filling
Hole Filling
Table of Contents 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
Extraction of Connected Components
Extraction of Connected Components تصویر سینه مرغ حاوی استخوان هایی است. تصویر اشعه ایکس است. ابتدا تصویر را باینری کرده ایم. سپس با استفاده از Connected Component عناصر با سایز کوچکتر از 5*5 را حذف کرده ایم. چون عناصر بزرگتر از این سایز برای ما اهمیت دارند.
Table of Contents 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
The Hit-or-Miss Transformation Convex Hull Closing Opening Dilation Erosion The Hit-or-Miss Transformation
Convex Hull Convex Concave تفاوت پوسته محدب و مجموعه اصلی را نقصان محدب S می نامند که برای توصیف اشیاء مهم بوده و در فصل Segmentation مورد بررسی قرار می گیرد.
Convex Hull
Table of Contents 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
Thinning
Thinning
Table of Contents 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
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.
Thickening
Table of Contents 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
Skeleton Skeleton
Applications Simplify a shape by pruning its skeleton:
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.
Skeleton of a rectangle defined in terms of bi-tangent circles. Skeletons Skeleton of a rectangle defined in terms of bi-tangent circles.
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.
The Hit-or-Miss Transformation Dilation Erosion Closing Opening The Hit-or-Miss Transformation
Skeletons Opening Erosion 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
Skeletons
Skeletons
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.
Distance Transform
Table of Contents 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
Pruning https://reference.wolfram.com/mathematica/ref/Pruning.html
Pruning Iteratively prune an image: https://reference.wolfram.com/mathematica/ref/Pruning.html
Applictions Count the legs of a centipede Find the loops of a graph: https://reference.wolfram.com/mathematica/ref/Pruning.html
Applictions Solve a maze puzzle by thinning all paths and pruning dead ends: https://reference.wolfram.com/mathematica/ref/Pruning.html
The Hit-or-Miss Transformation Pruning Thinning The Hit-or-Miss Transformation
The Hit-or-Miss Transformation Pruning Thinning The Hit-or-Miss Transformation Dilation H = 3x3 structuring element of 1’s
Pruning
Table of Contents 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
Table of Contents 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
Morphological Operations on Binary Images
Morphological Operations on Binary Images
Morphological Operations on Binary Images