An efficient solution to the five-point relative pose problem

TLDR

The five‑point relative pose problem seeks the possible camera poses between two calibrated views from five point correspondences. The paper presents an efficient algorithmic solution to the classical five‑point relative pose problem. The algorithm derives a closed‑form tenth‑degree polynomial, solves for its roots, and is evaluated for numerical precision, noise robustness, and speed against 8‑, 7‑, and 6‑point methods, then integrated into a real‑time hypothesize‑and‑test framework for structure‑and‑motion estimation. The algorithm is the first numerically efficient solution matching the problem’s inherent complexity and has been demonstrated in a real‑time, vision‑only system at major conferences.

Abstract

An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well-known 8 and 7-point methods and a 6-point scheme. The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay. The real-time system uses solely visual input and has been demonstrated at major conferences.