Sublabel-Accurate Relaxation of Nonconvex Energies
This work addresses multilabel energy minimization for computer vision applications, offering an incremental improvement over existing functional lifting methods.
The paper tackles the problem of multilabel optimization in computer vision by introducing a sublabel-accurate convex relaxation framework that reduces the need for many labels and minimizes grid bias, achieving efficient GPU-based optimization and demonstrating effectiveness on various vision tasks.
We propose a novel spatially continuous framework for convex relaxations based on functional lifting. Our method can be interpreted as a sublabel-accurate solution to multilabel problems. We show that previously proposed functional lifting methods optimize an energy which is linear between two labels and hence require (often infinitely) many labels for a faithful approximation. In contrast, the proposed formulation is based on a piecewise convex approximation and therefore needs far fewer labels. In comparison to recent MRF-based approaches, our method is formulated in a spatially continuous setting and shows less grid bias. Moreover, in a local sense, our formulation is the tightest possible convex relaxation. It is easy to implement and allows an efficient primal-dual optimization on GPUs. We show the effectiveness of our approach on several computer vision problems.