Image Labeling and Grouping by Minimizing Linear Functionals over Cones

• Authors: Christian Schellewald;Jens Keuchel;Christoph Schnörr
• Venue: EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
• Year: 2001

We consider energy minimization problems related to image labeling, partitioning, and grouping, which typically show up at mid-level stages of computer vision systems. A common feature of these problems is their intrinsic combinatorial complexity from an optimization point-of-view. Rather than trying to compute the global minimum - a goal we consider as elusive in these cases - we wish to design optimization approaches which exhibit two relevant properties: First, in each application a solution with guaranteed degree of suboptimality can be computed. Secondly, the computations are based on clearly defined algorithms which do not comprise any (hidden) tuning parameters. In this paper, we focus on the second property and introduce a novel and general optimization technique to the field of computer vision which amounts to compute a suboptimal solution by just solving a convex optimization problem. As representative examples, we consider two binary quadratic energy functionals related to image labeling and perceptual grouping. Both problems can be considered as instances of a general quadratic functional in binary variables, which is embedded into a higher-dimensional space such that suboptimal solutions can be computed as minima of linear functionals over cones in that space (semidefinite programs). Extensive numerical results reveal that, on the average, suboptimal solutions can be computed which yield a gap below 5% with respect to the global optimum in case where this is known.