American Mathematical Monthly
Regularization of the medial axis transform
Proceedings of the 6th Workshop on Theoretical Foundations of Computer Vision
Curvature motions, medial axes and distance transforms
Curvature motions, medial axes and distance transforms
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Linear Time Algorithms for Exact Distance Transform
Journal of Mathematical Imaging and Vision
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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.