# From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation

arXiv: https://arxiv.org/abs/2312.05995 · HTML: https://mlsanity.com/paper/2312.05995/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 69 references that are in the map.
- First posted on arXiv 10 Dec 2023.

## Builds on (most cited first, 26 of 26)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [DKM: Dense Kernelized Feature Matching for Geometry Estimation](https://mlsanity.com/paper/2202.00667/) (2022)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [PDC-Net+: Enhanced Probabilistic Dense Correspondence Network](https://mlsanity.com/paper/2109.13912/) (2021)
- [The non-convex Burer-Monteiro approach works on smooth semidefinite programs](https://mlsanity.com/paper/1606.04970/) (2016)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [An Efficient Solution to Non-Minimal Case Essential Matrix Estimation](https://mlsanity.com/paper/1903.09067/) (2019)
- [On the local stability of semidefinite relaxations](https://mlsanity.com/paper/1710.04287/) (2017)
- [Certifiable Relative Pose Estimation](https://mlsanity.com/paper/2003.13732/) (2020)
- [Triangulation: Why Optimize?](https://mlsanity.com/paper/1907.11917/) (2019)
- [Semidefinite descriptions of the convex hull of rotation matrices](https://mlsanity.com/paper/1403.4914/) (2014)
- [The Probabilistic Normal Epipolar Constraint for Frame-To-Frame Rotation Optimization under Uncertain Feature Positions](https://mlsanity.com/paper/2204.02256/) (2022)
- [Geometric Interpretations of the Normalized Epipolar Error](https://mlsanity.com/paper/2008.01254/) (2020)
- [Fast and Robust Certifiable Estimation of the Relative Pose Between Two Calibrated Cameras](https://mlsanity.com/paper/2101.08524/) (2021)
- [Semidefinite Relaxations for Robust Multiview Triangulation](https://mlsanity.com/paper/2301.11431/) (2023)
- [A Strengthened SDP Relaxation for Quadratic Optimization Over the Stiefel Manifold](https://mlsanity.com/paper/2208.03125/) (2022)

## Built on by (most cited first, 4 of 4)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Six-Point Method for Multi-Camera Systems with Reduced Solution Space](https://mlsanity.com/paper/2402.18066/) (2024)
- [Differential 6-DOF Pose Estimation with Provable First-Order Immunity to Camera Calibration Errors](https://mlsanity.com/paper/2608.04673/) (2026)
- [Non-Minimal Sampling and Consensus for Prohibitively Large Datasets](https://mlsanity.com/paper/2604.22518/) (2026)

## Abstract (arXiv)

Estimating the relative camera pose from n ≥ 5 correspondences between two calibrated views is a fundamental task in computer vision. This process typically involves two stages: 1) estimating the essential matrix between the views, and 2) disambiguating among the four candidate relative poses that satisfy the epipolar geometry. In this paper, we demonstrate a novel approach that, for the first time, bypasses the second stage. Specifically, we show that it is possible to directly estimate the correct relative camera pose from correspondences without needing a post-processing step to enforce the cheirality constraint on the correspondences. Building on recent advances in certifiable non-minimal optimization, we frame the relative pose estimation as a Quadratically Constrained Quadratic Program (QCQP). By applying the appropriate constraints, we ensure the estimation of a camera pose that corresponds to a valid 3D geometry and that is globally optimal when certified. We validate our method through exhaustive synthetic and real-world experiments, confirming the efficacy, efficiency and accuracy of the proposed approach. Code is available at https://github.com/javrtg/C2P.