# Robust Camera Location Estimation by Convex Programming

arXiv: https://arxiv.org/abs/1412.0165 · HTML: https://mlsanity.com/paper/1412.0165/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2014.

## Built on by (most cited first, 30 of 41)

- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [Visual Geometry Grounded Deep Structure From Motion](https://mlsanity.com/paper/2312.04563/) (2023)
- [Global Structure-from-Motion Revisited](https://mlsanity.com/paper/2407.20219/) (2024)
- [ParticleSfM: Exploiting Dense Point Trajectories for Localizing Moving Cameras in the Wild](https://mlsanity.com/paper/2207.09137/) (2022)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [A Pose-only Solution to Visual Reconstruction and Navigation](https://mlsanity.com/paper/2103.01530/) (2021)
- [Hybrid Rotation Averaging: A Fast and Robust Rotation Averaging Approach](https://mlsanity.com/paper/2101.09116/) (2021)
- [End2End Multi-View Feature Matching with Differentiable Pose Optimization](https://mlsanity.com/paper/2205.01694/) (2022)
- [Deep Permutation Equivariant Structure from Motion](https://mlsanity.com/paper/2104.06703/) (2021)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Robust Group Synchronization via Quadratic Programming](https://mlsanity.com/paper/2206.08994/) (2022)
- [EC-SfM: Efficient Covisibility-based Structure-from-Motion for Both Sequential and Unordered Images](https://mlsanity.com/paper/2302.10544/) (2023)
- [Regist3R: Incremental Registration with Stereo Foundation Model](https://mlsanity.com/paper/2504.12356/) (2025)
- [Fast, Accurate and Memory-Efficient Partial Permutation Synchronization](https://mlsanity.com/paper/2203.16505/) (2022)
- [Lazy Visual Localization via Motion Averaging](https://mlsanity.com/paper/2307.09981/) (2023)
- [A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion](https://mlsanity.com/paper/2404.11590/) (2024)
- [FastMap: Revisiting Structure from Motion through First-Order Optimization](https://mlsanity.com/paper/2505.04612/) (2025)
- [Global Structure-from-Motion Meets Feedforward Reconstruction](https://mlsanity.com/paper/2605.26103/) (2026)
- [Vision-Based Environmental Perception for Autonomous Driving](https://mlsanity.com/paper/2212.11453/) (2022)
- [Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching](https://mlsanity.com/paper/2201.04797/) (2022)
- [TC-SfM: Robust Track-Community-Based Structure-from-Motion](https://mlsanity.com/paper/2206.05866/) (2022)
- [AdaSfM: From Coarse Global to Fine Incremental Adaptive Structure from Motion](https://mlsanity.com/paper/2301.12135/) (2023)
- [Efficient Detection of Long Consistent Cycles and its Application to Distributed Synchronization](https://mlsanity.com/paper/2407.04260/) (2024)
- [DATAP-SfM: Dynamic-Aware Tracking Any Point for Robust Structure from Motion in the Wild](https://mlsanity.com/paper/2411.13291/) (2024)
- [Semihierarchical Reconstruction and Weak-area Revisiting for Robotic Visual Seafloor Mapping](https://mlsanity.com/paper/2308.06147/) (2023)
- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [Cycle-Sync: Robust Global Camera Pose Estimation through Enhanced Cycle-Consistent Synchronization](https://mlsanity.com/paper/2511.02329/) (2025)
- [RESfM: Robust Deep Equivariant Structure from Motion](https://mlsanity.com/paper/2404.14280/) (2024)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [Incremental Rotation Averaging Revisited](https://mlsanity.com/paper/2309.16924/) (2023)

## Abstract (arXiv)

3D structure recovery from a collection of 2D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation part, which can be formulated as the inverse problem of estimating n locations t1, t2, ldots, tn in ℝ3 from noisy measurements of a subset of the pairwise directions fracti - tj|ti - tj|, are sensitive to outliers in direction measurements. In this paper, we firstly provide a complete characterization of well-posed instances of the location estimation problem, by presenting its relation to the existing theory of parallel rigidity. For robust estimation of camera locations, we introduce a two-step approach, comprised of a pairwise direction estimation method robust to outliers in point correspondences between image pairs, and a convex program to maintain robustness to outlier directions. In the presence of partially corrupted measurements, we empirically demonstrate that our convex formulation can even recover the locations exactly. Lastly, we demonstrate the utility of our formulations through experiments on Internet photo collections.