Abstract: This paper shows that images can be decomposed into a series of homotopic subsets by means of morphological erosions using a series of disk-like structuring elements, and the skeleton can be obtained from the homotopic subset by detecting the vertices of each homotopic subset. It is an affine transform to map objects into a series of subsets and the skeleton points can be obtained from the mapped subsets individually. When a digital disk is rotation-invariant, the mapping is rotation-invariant. Consequently, the skeleton is rotation-invariant. It is shown that the convex vertices of an object of which curvatures change significantly are the skeleton points. Two algorithms for detecting vertices are presented in this paper. A fast mapping algorithm and a reconstruction algorithm are presented. Compared to other morphological methods, this proposed skeletonization method generates more accurate skeletons, particularly in the cases involving rotated shapes. Based on the skeleton, we introduce a new concept of major points (MPs) for skeleton descriptions. This is a skeleton sampling method. MPs can be obtained through choosing skeleton points with maximally weighted self-information. The MPs emphasize the contribution of each skeleton point to original objects. This paper also presents a detailed description on selections of MPs, where an object can be partially reconstructed via MPs based on a proposed reconstruction criterion. !25
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