Efficient and Flexible Sublabel-Accurate Energy Minimization

TL;DR

This paper introduces an efficient hybrid optimization method that combines discrete and continuous approaches to achieve sublabel-accurate energy minimization with theoretical guarantees and practical efficiency for large label spaces.

Contribution

It proposes a novel two-step approach that first performs global discrete optimization and then local continuous refinement, improving efficiency while maintaining accuracy and guarantees.

Findings

Achieves faster and more memory-efficient energy minimization.

Maintains accuracy comparable to continuous convex relaxation methods.

Applicable to a wide range of regularization terms.

Abstract

We address the problem of minimizing a class of energy functions consisting of data and smoothness terms that commonly occur in machine learning, computer vision, and pattern recognition. While discrete optimization methods are able to give theoretical optimality guarantees, they can only handle a finite number of labels and therefore suffer from label discretization bias. Existing continuous optimization methods can find sublabel-accurate solutions, but they are not efficient for large label spaces. In this work, we propose an efficient sublabel-accurate method that utilizes the best properties of both continuous and discrete models. We separate the problem into two sequential steps: (i) global discrete optimization for selecting the label range, and (ii) efficient continuous sublabel-accurate local refinement of a convex approximation of the energy function in the chosen range. Doing so allows us to achieve a boost in time and memory efficiency while practically keeping the accuracy at the same level as continuous convex relaxation methods, and in addition, providing theoretical optimality guarantees at the level of discrete methods. Finally, we show the flexibility of the proposed approach to general pairwise smoothness terms, so that it is applicable to a wide range of regularizations. Experiments on the illustrating example of the image denoising problem demonstrate the properties of the proposed method. The code reproducing experiments is available at \url{https://github.com/nurlanov-zh/sublabel-accurate-alpha-expansion}.