A Principled Approach for Coarse-to-Fine MAP Inference

In this work we reconsider labeling problems with (virtually) continuous state spaces, which are of relevance in low level computer vision. In order to cope with such huge state spaces multi-scale methods have been proposed to approximately solve such labeling tasks. Although performing well in many cases, these methods do usually not come with any guarantees on the returned solution. A general and principled approach to solve labeling problems is based on the well-known linear programming relaxation, which appears to be prohibitive for large state spaces at the first glance. We demonstrate that a coarse-to-fine exploration strategy in the label space is able to optimize the LP relaxation for non-trivial problem instances with reasonable run-times and moderate memory requirements.