A clever elimination strategy for efficient minimal solvers

TL;DR

This paper introduces a novel elimination strategy that simplifies and accelerates minimal solvers in computer vision, especially for problems involving linear and polynomial equations, leading to more efficient algorithms.

Contribution

It proposes a systematic elimination approach for generating minimal solvers, applicable to both linear and non-linear systems, improving efficiency and revealing new constraints.

Findings

More efficient solvers for camera pose problems

New constraints on fundamental matrices

Faster computation in minimal problems

Abstract

We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.