# A New Rank Constraint on Multi-view Fundamental Matrices, and its Application to Camera Location Recovery

arXiv: https://arxiv.org/abs/1702.03023 · HTML: https://mlsanity.com/paper/1702.03023/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2017.

## Built on by (most cited first, 10 of 10)

- [Deep Permutation Equivariant Structure from Motion](https://mlsanity.com/paper/2104.06703/) (2021)
- [Fast, Accurate and Memory-Efficient Partial Permutation Synchronization](https://mlsanity.com/paper/2203.16505/) (2022)
- [A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion](https://mlsanity.com/paper/2404.11590/) (2024)
- [Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching](https://mlsanity.com/paper/2201.04797/) (2022)
- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [Higher-Order Group Synchronization](https://mlsanity.com/paper/2505.21932/) (2025)
- [An Algebraic Geometry Approach to Viewing Graph Solvability](https://mlsanity.com/paper/2504.03637/) (2025)
- [QuadSync: Quadrifocal Tensor Synchronization via Tucker Decomposition](https://mlsanity.com/paper/2602.22639/) (2026)
- [Multiprojective Geometry of Compatible Triples of Fundamental and Essential Matrices](https://mlsanity.com/paper/2602.23450/) (2026)

## Abstract (arXiv)

Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with the selection of proper scale factors, a matrix formed by stacking fundamental matrices between pairs of images has rank 6. Moreover, this matrix forms the symmetric part of a rank 3 matrix whose factors relate directly to the corresponding camera matrices. We use this new characterization to produce better estimations of fundamental matrices by optimizing an L1-cost function using Iterative Re-weighted Least Squares and Alternate Direction Method of Multiplier. We further show that this procedure can improve the recovery of camera locations, particularly in multi-view settings in which fewer images are available.