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Medial Axes and Mean Curvature Motion II: Singularities

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Abstract

What happens to the medial axis of a curve that evolves through MCM (Mean Curvature Motion)? We explore some theoretical results regarding properties of both medial axes and curvature motions. Specifically, using singularity theory, we present all possible topological transitions of a symmetry set (of which the medial axis is a subset) whose originating curve undergoes MCM. All calculations are presented in a clear and organized fashion and are easily generalized for other front motions. A companion article deals with non-singular points of the medial axis through direct calculations.

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  1. Instituto de Matematica Pura e Aplicada, Rio de Janeiro, Brasil

    Ralph Costa Teixeira

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  1. Ralph Costa Teixeira
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Correspondence to Ralph Costa Teixeira.

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Teixeira, R.C. Medial Axes and Mean Curvature Motion II: Singularities. J Math Imaging Vis 23, 87–105 (2005). https://doi.org/10.1007/s10851-005-4969-0

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  • DOI: https://doi.org/10.1007/s10851-005-4969-0

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