A Classification of Centres of Maximal Balls in ℤ3
A classification of centres of maximal balls (CMBs) in ℤ3 derived from generalizations of the chessboard and city block metrics to 3D, a weighted metric, and the Euclidean metric is presented. Using these metrics, the set of CMBs (the medial axis) can be extracted. One difficulty with skeletonization in 3D is that of guaranteeing reversibility. A reversible skeleton generally consists of both surfaces and curves. Previous attempts to construct connected skeletons including the CMBs uses conditions based on local neighbourhood configurations. However, a local neighbourhood might be too small and, most important, does not allow a consistent definition for surface- and curve-parts of the skeleton. The classification of the CMBs presented in this paper will be a tool for defining which parts of a 3D skeleton are surfaces and curves.
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