Chambolle, Antonin; Cremers, Daniel; Pock, Thomas A convex approach to minimal partitions. (English) Zbl 1256.49040 SIAM J. Imaging Sci. 5, No. 4, 1113-1158 (2012). Summary: We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically: we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution: we give some arguments to explain why it should be so and also discuss some situations where it fails. Cited in 50 Documents MSC: 49M29 Numerical methods involving duality 49Q05 Minimal surfaces and optimization 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature 53C38 Calibrations and calibrated geometries 65D18 Numerical aspects of computer graphics, image analysis, and computational geometry 68U10 Computing methodologies for image processing Keywords:image segmentation; classification; minimal partitions; calibrations; convex relaxation PDFBibTeX XMLCite \textit{A. Chambolle} et al., SIAM J. Imaging Sci. 5, No. 4, 1113--1158 (2012; Zbl 1256.49040) Full Text: DOI