Medial Axes and Mean Curvature Motion II: Singularities

Ralph Teixeira

Keywords: Computer Vision | medial axis | Curvature Motion | Distance Transform | Shape

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 medial axis 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.

Anexos:

• Maxis2.pdf