Exploiting curvatures to compute the medial axis for domains with smooth boundary

In the paper, strong proofs of some basics facts about the medial axis transform of a planar region Ω with smooth boundary curve(s) are given. In particular the decomposition of Choi et al. (1997) is derived from the set of regular disks. Two special algorithms to compute the medial axis are presented. Due to the decomposition, they can be applied to each part of Ω separately. Emphasis is given to the local analysis of the boundary's curvatures. This leads to an interesting connection to the theory of Dupin cyclides. With this mean, a predictor/corrector algorithm (as in the numerical analysis of ODE's) is developed. The examples show that the predictor yields already an excellent approximation; so only a few refining steps of the corrector are necessary.

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