Deterministic consensus maximization with biconvex programming
This addresses robust fitting in computer vision, offering a deterministic alternative to previous random or relaxed methods, which is incremental but improves reliability on challenging instances.
The paper tackles the problem of consensus maximization in computer vision by proposing a deterministic optimization algorithm that forcibly increases consensus from an initial solution, showing it consistently and greatly improves solution quality without substantial cost.
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.