Consensus Maximization Tree Search Revisited

TL;DR

This paper improves the efficiency of A* tree search for consensus maximization in computer vision by removing redundant paths and introducing a more dimension-sensitive branch pruning technique, enabling it to handle larger inputs.

Contribution

The paper introduces two novel techniques: one to eliminate redundant paths in the search tree and another to enhance branch pruning, significantly accelerating A* tree search.

Findings

Accelerated A* tree search by removing non-adjacent level paths.

Developed a dimension-sensitive branch pruning method.

Enabled efficient exact solutions on larger problem inputs.

Abstract

Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is one of the most efficient exact methods, though it is still limited to small inputs. We make two key contributions towards improving A* tree search. First, we show that the consensus maximization tree structure used previously actually contains paths that connect nodes at both adjacent and non-adjacent levels. Crucially, paths connecting non-adjacent levels are redundant for tree search, but they were not avoided previously. We propose a new acceleration strategy that avoids such redundant paths. In the second contribution, we show that the existing branch pruning technique also deteriorates quickly with the problem dimension. We then propose a new branch pruning technique that is less dimension-sensitive to address this issue. Experiments show that both new techniques can significantly accelerate A* tree search, making it reasonably efficient on inputs that were previously out of reach.