Fast and Robust Certifiable Estimation of the Relative Pose Between Two Calibrated Cameras

TL;DR

This paper presents a fast, certifiable algorithm for estimating the relative pose between two calibrated cameras that is robust to noise and mismatches, with proven optimality certification and extensive experimental validation.

Contribution

It introduces a novel certifiable pipeline for relative pose estimation that is both fast and robust, integrating new certifiers and a robust optimization framework.

Findings

The proposed method achieves high accuracy in synthetic and real data experiments.

It significantly increases the ratio of detected optimal solutions.

The framework demonstrates robustness against noisy and corrupted feature matches.

Abstract

This work contributes an efficient algorithm to compute the Relative Pose problem (RPp) between calibrated cameras and certify the optimality of the solution, given a set of pair-wise feature correspondences affected by noise and probably corrupted by wrong matches. We propose a family of certifiers that is shown to increase the ratio of detected optimal solutions. This set of certifiers is incorporated into a fast essential matrix estimation pipeline that, given any initial guess for the RPp, refines it iteratively on the product space of 3D rotations and 2-sphere. In addition, this fast certifiable pipeline is integrated into a robust framework that combines Graduated Non-convexity and the Black-Rangarajan duality between robust functions and line processes. We proved through extensive experiments on synthetic and real data that the proposed framework provides a fast and robust relative pose estimation. We make the code publicly available \url{https://github.com/mergarsal/FastCertRelPose.git}.