Sublabel-Accurate Relaxation of Nonconvex Energies

TL;DR

This paper introduces a spatially continuous convex relaxation framework for multilabel problems that is sublabel-accurate, requiring fewer labels and reducing grid bias compared to previous methods, with efficient GPU implementation.

Contribution

The authors present a novel piecewise convex approximation method for functional lifting that achieves sublabel accuracy and tight convex relaxation in a continuous setting.

Findings

Requires fewer labels than previous methods

Less grid bias compared to MRF-based approaches

Effective on various computer vision tasks

Abstract

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.