A Convex Formulation of Continuous Multi-label Problems

Thomas Pock, Thomas Schoenemann, Gottfried Graber, Horst Bischof, Daniel Cremers

Abstract: We propose a spatially continuous formulation of Ishikawa’s discrete multi-label problem. We show that the resulting non-convex variational problem can be reformulated as a convex variational problem via embedding in a higher dimensional space. This variational problem can be interpreted as a minimal surface problem in an anisotropic Riemannian space. In several stereo experiments we show that the proposed continuous formulation is superior to its discrete counterpart in terms of computing time, memory efficiency and metrication errors.