Accelerating Globally Optimal Consensus Maximization in Geometric Vision

TL;DR

This paper introduces a novel technique to accelerate globally optimal consensus maximization in geometric vision problems by reducing the search space and applying efficient interval stabbing, significantly improving computational speed.

Contribution

The authors propose a general method that branches over an n-1 dimensional space and uses interval stabbing to solve the remaining degree of freedom globally, reducing computation time.

Findings

Achieved speed-up factors exceeding 100x in experiments.

Applied method to four fundamental geometric vision problems.

Demonstrated increased viability of global optimization in online scenarios.

Abstract

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an n-1 dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.