Euclidean Upgrade from a Minimal Number of Segments

TL;DR

This paper introduces an algebraic method to upgrade a projective reconstruction to a Euclidean one using only nine known-length segments, employing polynomial equations and Gr"obner bases for solution.

Contribution

It presents a novel minimal solver for Euclidean upgrade from nine segments, combining algebraic constraints and Gr"obner bases, with practical experiments demonstrating effectiveness.

Findings

Solver successfully computes Euclidean upgrade from minimal segments.

Method efficiently solves polynomial equations using Gr"obner bases.

Experimental results validate the approach's practicality.

Abstract

In this paper, we propose an algebraic approach to upgrade a projective reconstruction to a Euclidean one, and aim at computing the rectifying homography from a minimal number of 9 segments of known length. Constraints are derived from these segments which yield a set of polynomial equations that we solve by means of Gr\"obner bases. We explain how a solver for such a system of equations can be constructed from simplified template data. Moreover, we present experiments that demonstrate that the given problem can be solved in this way.