Sublabel-Accurate Convex Relaxation of Vectorial Multilabel Energies

TL;DR

This paper introduces a novel sublabel accurate convex relaxation method for vectorial multilabel problems, significantly improving solution quality and efficiency in computer vision tasks like optical flow and image denoising.

Contribution

It presents the first sublabel accurate convex relaxation approach that approximates the data term more faithfully, reducing memory and runtime requirements.

Findings

Superior solution quality in optical flow and denoising tasks

Lower memory and runtime compared to existing methods

More faithful approximation of the original cost function

Abstract

Convex relaxations of nonconvex multilabel problems have been demonstrated to produce superior (provably optimal or near-optimal) solutions to a variety of classical computer vision problems. Yet, they are of limited practical use as they require a fine discretization of the label space, entailing a huge demand in memory and runtime. In this work, we propose the first sublabel accurate convex relaxation for vectorial multilabel problems. The key idea is that we approximate the dataterm of the vectorial labeling problem in a piecewise convex (rather than piecewise linear) manner. As a result we have a more faithful approximation of the original cost function that provides a meaningful interpretation for the fractional solutions of the relaxed convex problem. In numerous experiments on large-displacement optical flow estimation and on color image denoising we demonstrate that the computed solutions have superior quality while requiring much lower memory and runtime.