Tight Convex Relaxations for Vector-Valued Labeling

Abstract

Multilabel problems are of fundamental importance in computer vision and image analysis. Yet, finding global minima of the associated energies is typically a hard computational challenge. Recently, progress has been made by reverting to spatially continuous formulations of respective problems and solving the arising convex relaxation globally. In practice this leads to solutions which are either optimal or within an a posteriori bound of the optimum. Unfortunately, in previous methods, both run time and memory requirements scale linearly in the total number of labels, making these methods very inefficient and often not applicable to problems with higher dimensional label spaces. In this paper, we propose a reduction technique for the case that the label space is a continuous product space and the regularizer is separable, i.e., a sum of regularizers for each dimension of the label space. In typical real-world labeling problems, the resulting convex relaxation requires orders of magnitude less memory and c...