An Algorithmic Solution to the Five-Point Pose Problem Based on the Cayley Representation of Rotations

TL;DR

This paper introduces a novel algorithm for the five-point pose problem that leverages the Cayley representation of rotations, avoiding the traditional cubic constraint on the essential matrix, and derives solutions from a polynomial system.

Contribution

It presents a new approach using Cayley representation to formulate a polynomial system, providing a direct algebraic solution to the five-point pose problem.

Findings

Derives a 10th degree polynomial for pose parameters

Provides a polynomial-based solution avoiding cubic constraints

Enables direct computation of camera rotation and translation

Abstract

We give a new algorithmic solution to the well-known five-point relative pose problem. Our approach does not deal with the famous cubic constraint on an essential matrix. Instead, we use the Cayley representation of rotations in order to obtain a polynomial system from epipolar constraints. Solving that system, we directly get relative rotation and translation parameters of the cameras in terms of roots of a 10th degree polynomial.