# Semidefinite Relaxations for Robust Multiview Triangulation

arXiv: https://arxiv.org/abs/2301.11431 · HTML: https://mlsanity.com/paper/2301.11431/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## Builds on (most cited first, 15 of 15)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming](https://mlsanity.com/paper/2010.11645/) (2020)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications](https://mlsanity.com/paper/2007.15109/) (2020)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [In Perfect Shape: Certifiably Optimal 3D Shape Reconstruction from 2D Landmarks](https://mlsanity.com/paper/1911.11924/) (2019)
- [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)
- [A convex relaxation to compute the nearest structured rank deficient matrix](https://mlsanity.com/paper/1904.09661/) (2019)
- [Certifiably Optimal Monocular Hand-Eye Calibration](https://mlsanity.com/paper/2005.08298/) (2020)
- [Optimal least-squares solution to the hand-eye calibration problem](https://mlsanity.com/paper/2002.10838/) (2020)
- [Robust Uncertainty-Aware Multiview Triangulation](https://mlsanity.com/paper/2008.01258/) (2020)
- [Globally Optimal Multi-Scale Monocular Hand-Eye Calibration Using Dual Quaternions](https://mlsanity.com/paper/2201.04473/) (2022)

## Built on by (most cited first, 3 of 3)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [GlobalPointer: Large-Scale Plane Adjustment with Bi-Convex Relaxation](https://mlsanity.com/paper/2407.13537/) (2024)
- [From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation](https://mlsanity.com/paper/2312.05995/) (2023)

## Abstract (arXiv)

We propose an approach based on convex relaxations for certifiably optimal robust multiview triangulation. To this end, we extend existing relaxation approaches to non-robust multiview triangulation by incorporating a truncated least squares cost function. We propose two formulations, one based on epipolar constraints and one based on fractional reprojection constraints. The first is lower dimensional and remains tight under moderate noise and outlier levels, while the second is higher dimensional and therefore slower but remains tight even under extreme noise and outlier levels. We demonstrate through extensive experiments that the proposed approaches allow us to compute provably optimal reconstructions even under significant noise and a large percentage of outliers.