Abstract
This paper presents the analysis and the implementation algorithms of the morphological skeleton transform (MST) of binary images. A general MST algorithm is provided from which different subclasses of MSTs can be derived by choosing different structuring elements. Three subclasses of MSTs are discussed in this paper: the uniform-step-distance MST (USDMST), the periodically-uniform-step-distance MST (PUSDMST) and the pseudo-Euclidean MST (PEMST). A general discrete distance called morphological distance relates distance measures to the definitions of structuring elements. The PEMST is proposed which uses isotropic discrete structuring elements called quasi-circular structuring elements (QCSE). The QCSEs of all integer sizes are composed by a dilation interpolation method so that they can be decomposed into simplest elements in order to reduce computation. The PEMST has better performance in terms of rotation-invariance than any existing MSTs. The algorithm has an approximately linear computational complexity. Finally, the implementation of the three MSTs are discussed.
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