Deterministic consensus maximization with biconvex programming

TL;DR

This paper introduces a deterministic biconvex programming-based algorithm that effectively enhances initial solutions in consensus maximization tasks, outperforming prior random or relaxation-based methods in computer vision.

Contribution

The authors develop a novel deterministic optimization algorithm using biconvex programming for consensus maximization, providing a more reliable improvement over initial solutions.

Findings

Consistently improves initial consensus solutions in experiments.

Outperforms previous random sampling and relaxation methods.

Operates efficiently with minimal computational cost.

Abstract

Consensus maximization is one of the most widely used robust fitting paradigms in computer vision, and the development of algorithms for consensus maximization is an active research topic. In this paper, we propose an efficient deterministic optimization algorithm for consensus maximization. Given an initial solution, our method conducts a deterministic search that forcibly increases the consensus of the initial solution. We show how each iteration of the update can be formulated as an instance of biconvex programming, which we solve efficiently using a novel biconvex optimization algorithm. In contrast to our algorithm, previous consensus improvement techniques rely on random sampling or relaxations of the objective function, which reduce their ability to significantly improve the initial consensus. In fact, on challenging instances, the previous techniques may even return a worse off solution. Comprehensive experiments show that our algorithm can consistently and greatly improve the quality of the initial solution, without substantial cost.