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