Continuous Multiclass Labeling Approaches and Algorithms

TL;DR

This paper introduces convex relaxation methods for continuous image labeling problems, proposing algorithms that efficiently approximate solutions and recover near-optimal discrete labels, with demonstrated competitive performance on real images.

Contribution

It develops a flexible convex relaxation framework for image labeling, introduces a globally convergent Douglas-Rachford algorithm, and improves solution quality with an advanced binarization technique.

Findings

Achieves solutions within 1-5% of the global optimum.

Demonstrates competitive performance on synthetic and real images.

Provides a flexible relaxation framework applicable to various metrics.

Abstract

We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity -- one can be used to tightly relax any metric interaction potential, while the other one only covers Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent Douglas-Rachford scheme, and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other first-order methods, the approach shows competitive performance on synthetical and real-world images. By combining the method with an improved binarization technique for nonstandard potentials, we were able to routinely recover discrete solutions within 1%--5% of the global optimum for the combinatorial image labeling problem.