Sublabel-Accurate Convex Relaxation of Vectorial Multilabel Energies
This addresses a practical bottleneck in computer vision for researchers and practitioners by enabling more efficient convex relaxations, though it is incremental as it builds on existing relaxation methods.
The paper tackles the high memory and runtime demands of convex relaxations for vectorial multilabel problems by proposing a sublabel-accurate convex relaxation that approximates the dataterm piecewise convexly, resulting in superior solution quality with much lower resource usage in optical flow and color image denoising experiments.
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.