# TriP: A Triangle Puzzle Approach to Robust Translation Averaging

arXiv: https://arxiv.org/abs/2605.07143 · HTML: https://mlsanity.com/paper/2605.07143/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 12 of 12)

- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Robust Camera Location Estimation by Convex Programming](https://mlsanity.com/paper/1412.0165/) (2014)
- [Baseline Desensitizing In Translation Averaging](https://mlsanity.com/paper/1901.00643/) (2019)
- [Message Passing Least Squares Framework and its Application to Rotation Synchronization](https://mlsanity.com/paper/2007.13638/) (2020)
- [Robust Group Synchronization via Cycle-Edge Message Passing](https://mlsanity.com/paper/1912.11347/) (2019)
- [ShapeFit and ShapeKick for Robust, Scalable Structure from Motion](https://mlsanity.com/paper/1608.02165/) (2016)
- [A Unified Approach to Synchronization Problems over Subgroups of the Orthogonal Group](https://mlsanity.com/paper/2009.07514/) (2020)
- [Estimation of Camera Locations in Highly Corrupted Scenarios: All About that Base, No Shape Trouble](https://mlsanity.com/paper/1804.02591/) (2018)
- [ShapeFit: Exact location recovery from corrupted pairwise directions](https://mlsanity.com/paper/1506.01437/) (2015)
- [Exact Camera Location Recovery by Least Unsquared Deviations](https://mlsanity.com/paper/1709.09683/) (2017)
- [Cycle-Sync: Robust Global Camera Pose Estimation through Enhanced Cycle-Consistent Synchronization](https://mlsanity.com/paper/2511.02329/) (2025)

## Abstract (arXiv)

Translation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain no distance information, making the estimation problem highly ill-conditioned and highly sensitive to corrupted observations. In this paper, we propose TriP, a triangle-based framework for robust translation averaging. TriP first infers local relative edge scales from triangle geometry, and then synchronizes the scales of overlapping triangles in the logarithmic domain to recover globally consistent edge lengths and camera locations. By leveraging higher-order consistency across triangles, the proposed method is robust to adversarial, cycle-consistent, and other structured corruptions. In addition, TriP avoids the collapse issue without requiring any extra anti-collapse constraints, since log-scale synchronization excludes the degenerate zero-scale solution by construction. These structural advantages enable a particularly strong theory for exact location recovery. On the practical side, TriP is fully parallelizable, computationally efficient, and naturally scalable to graphs with millions of cameras. Moreover, it outperforms all previous translation averaging methods by a large margin on both synthetic and real datasets.