Geometrical image segmentation by the Allen-Cahn equation

Authors:
Michal Beneš;Vladimír Chalupecký;Karol Mikula
Affiliations:
Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University of Prague, Trojanova 13, 120 00 Prague, Czech Republic;Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University of Prague, Trojanova 13, 120 00 Prague, Czech Republic;Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

We present an algorithm of pattern recovery (image segmentation) based on the solution of the Allen-Cahn equation. The approach is usually understood as a regularization of the level-set motion by mean curvature where we impose a special forcing term which lets the initial level set closely surround the pattern in question. We show convergence of the numerical scheme and demonstrate function of the algorithm on several artificial as well as real examples.