On Computing the Translations Norm in the Epipolar Graph

TL;DR

This paper presents a method to recover the unknown translation norms between cameras using relative rotations and directions, involving a cycle basis approach and linear system solving, validated through experiments.

Contribution

It introduces a novel two-stage approach for computing translation norms in epipolar graphs, with theoretical conditions and practical algorithms.

Findings

Accurate translation norm recovery demonstrated on synthetic data.

Method effective on real camera data.

Theoretical conditions for solvability established.

Abstract

This paper deals with the problem of recovering the unknown norm of relative translations between cameras based on the knowledge of relative rotations and translation directions. We provide theoretical conditions for the solvability of such a problem, and we propose a two-stage method to solve it. First, a cycle basis for the epipolar graph is computed, then all the scaling factors are recovered simultaneously by solving a homogeneous linear system. We demonstrate the accuracy of our solution by means of synthetic and real experiments.