# Rotation Synchronization via Deep Matrix Factorization

arXiv: https://arxiv.org/abs/2305.05268 · HTML: https://mlsanity.com/paper/2305.05268/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 9 May 2023.

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

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [Low-Rank Matrix Completion: A Contemporary Survey](https://mlsanity.com/paper/1907.11705/) (2019)
- [Why Having 10,000 Parameters in Your Camera Model is Better Than Twelve](https://mlsanity.com/paper/1912.02908/) (2019)
- [NeuRoRA: Neural Robust Rotation Averaging](https://mlsanity.com/paper/1912.04485/) (2019)
- [Message Passing Least Squares Framework and its Application to Rotation Synchronization](https://mlsanity.com/paper/2007.13638/) (2020)
- [Synchronizing Probability Measures on Rotations via Optimal Transport](https://mlsanity.com/paper/2004.00663/) (2020)
- [Deep Permutation Equivariant Structure from Motion](https://mlsanity.com/paper/2104.06703/) (2021)
- [Rotation Coordinate Descent for Fast Globally Optimal Rotation Averaging](https://mlsanity.com/paper/2103.08292/) (2021)
- [Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs](https://mlsanity.com/paper/2109.08046/) (2021)
- [On the Distribution of Minima in Intrinsic-Metric Rotation Averaging](https://mlsanity.com/paper/2003.08310/) (2020)
- [Deep matrix factorizations](https://mlsanity.com/paper/2010.00380/) (2020)

## Built on by (most cited first, 7 of 7)

- [Global Structure-from-Motion Revisited](https://mlsanity.com/paper/2407.20219/) (2024)
- [Multiway Point Cloud Mosaicking with Diffusion and Global Optimization](https://mlsanity.com/paper/2404.00429/) (2024)
- [GeoNLF: Geometry guided Pose-Free Neural LiDAR Fields](https://mlsanity.com/paper/2407.05597/) (2024)
- [Gravity-aligned Rotation Averaging with Circular Regression](https://mlsanity.com/paper/2410.12763/) (2024)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [PRAGO: Differentiable Multi-View Pose Optimization From Objectness Detections](https://mlsanity.com/paper/2403.08586/) (2024)
- [Multiple Rotation Averaging with Constrained Reweighting Deep Matrix Factorization](https://mlsanity.com/paper/2409.09790/) (2024)

## Abstract (arXiv)

In this paper we address the rotation synchronization problem, where the objective is to recover absolute rotations starting from pairwise ones, where the unknowns and the measures are represented as nodes and edges of a graph, respectively. This problem is an essential task for structure from motion and simultaneous localization and mapping. We focus on the formulation of synchronization via neural networks, which has only recently begun to be explored in the literature. Inspired by deep matrix completion, we express rotation synchronization in terms of matrix factorization with a deep neural network. Our formulation exhibits implicit regularization properties and, more importantly, is unsupervised, whereas previous deep approaches are supervised. Our experiments show that we achieve comparable accuracy to the closest competitors in most scenes, while working under weaker assumptions.