11Extraction 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.
12Table of Contents 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction9.5.2 Hole Filling9.5.3 Extraction of Connected Components9.5.4 Convex Hull9.5.5 Thinning9.5.6 Thickening9.5.7 Skeletons9.5.8 Pruning9.5.9 Morphological ReconstructionSummary of Morphological Operations on Binary Images
19Table of Contents 9.5 Some Basic Morphological Algorithm 9.5.1 Boundary Extraction9.5.2 Hole Filling9.5.3 Extraction of Connected Components9.5.4 Convex Hull9.5.5 Thinning9.5.6 Thickening9.5.7 Skeletons9.5.8 Pruning9.5.9 Morphological ReconstructionSummary of Morphological Operations on Binary Images
20Thickeningwhere 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 processThis 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.
24ApplicationsSimplify a shape by pruning its skeleton:
25SkeletonsSkeletonization 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.
26Skeleton of a rectangle defined in terms of bi-tangent circles. SkeletonsSkeleton of a rectangle defined in terms of bi-tangent circles.
27Skeletons 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.
29Skeletons 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.ErosionOpening
32Distance TransformThe 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.