The Five Points Pose Problem : A New and Accurate Solution Adapted to any Geometric Configuration

TL;DR

This paper introduces a new method for estimating rotation and translation between two stereoscopic images using five points, which is accurate across various geometric configurations, including challenging planar and panoramic scenes.

Contribution

The proposed approach directly estimates rotation and translation without relying on the essential matrix, improving accuracy in difficult scenarios.

Findings

Effective in planar and panoramic scenes

Comparable accuracy in standard cases

Uses algebraic solvers like Groebner bases

Abstract

The goal of this paper is to estimate directly the rotation and translation between two stereoscopic images with the help of five homologous points. The methodology presented does not mix the rotation and translation parameters, which is comparably an important advantage over the methods using the well-known essential matrix. This results in correct behavior and accuracy for situations otherwise known as quite unfavorable, such as planar scenes, or panoramic sets of images (with a null base length), while providing quite comparable results for more "standard" cases. The resolution of the algebraic polynomials resulting from the modeling of the coplanarity constraint is made with the help of powerful algebraic solver tools (the Groebner bases and the Rational Univariate Representation).