Optimizing Elimination Templates by Greedy Parameter Search

TL;DR

This paper introduces a greedy parameter search method to optimize elimination templates, significantly reducing their size for polynomial system solving in computer vision tasks, leading to faster and more accurate algorithms.

Contribution

It presents a novel heuristic optimization approach for constructing smaller elimination templates, improving efficiency in solving minimal problems in computer vision.

Findings

Templates are 2.1 to 6.6 times smaller on average.

Achieved a 20-fold reduction for refractive absolute pose estimation.

New solvers are fast and numerically accurate.

Abstract

We propose a new method for constructing elimination templates for efficient polynomial system solving of minimal problems in structure from motion, image matching, and camera tracking. We first construct a particular affine parameterization of the elimination templates for systems with a finite number of distinct solutions. Then, we use a heuristic greedy optimization strategy over the space of parameters to get a template with a small size. We test our method on 34 minimal problems in computer vision. For all of them, we found the templates either of the same or smaller size compared to the state-of-the-art. For some difficult examples, our templates are, e.g., 2.1, 2.5, 3.8, 6.6 times smaller. For the problem of refractive absolute pose estimation with unknown focal length, we have found a template that is 20 times smaller. Our experiments on synthetic data also show that the new solvers are fast and numerically accurate. We also present a fast and numerically accurate solver for the problem of relative pose estimation with unknown common focal length and radial distortion.