# A Solution for Multi-Alignment by Transformation Synchronisation

arXiv: https://arxiv.org/abs/1410.8546 · HTML: https://mlsanity.com/paper/1410.8546/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2014.

## Built on by (most cited first, 15 of 15)

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- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [Learning Iterative Robust Transformation Synchronization](https://mlsanity.com/paper/2111.00728/) (2021)
- [A Comparative Study of Graph Matching Algorithms in Computer Vision](https://mlsanity.com/paper/2207.00291/) (2022)
- [Multiway Point Cloud Mosaicking with Diffusion and Global Optimization](https://mlsanity.com/paper/2404.00429/) (2024)
- [A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts](https://mlsanity.com/paper/2410.14770/) (2024)
- [Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation](https://mlsanity.com/paper/2110.00053/) (2021)
- [CombAlign: Enhancing Model Expressiveness in Unsupervised Graph Alignment](https://mlsanity.com/paper/2406.13216/) (2024)
- [Non-Negative Spherical Relaxations for Universe-Free Multi-Matching and Clustering](https://mlsanity.com/paper/2310.13311/) (2023)
- [Incremental Multiview Point Cloud Registration](https://mlsanity.com/paper/2407.05021/) (2024)
- [Multiview Point Cloud Registration via Optimization in an Autoencoder Latent Space](https://mlsanity.com/paper/2504.21467/) (2025)
- [Shortest Paths in Graphs with Matrix-Valued Edges: Concepts, Algorithm and Application to 3D Multi-Shape Analysis](https://mlsanity.com/paper/2112.04165/) (2021)
- [DisPOSE: Projected Polystochastic Diffusion for Self-Supervised Multi-View 3D Human Pose Estimation](https://mlsanity.com/paper/2606.07419/) (2026)

## Abstract (arXiv)

The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations can be retrieved from the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are transitively consistent. Simulations demonstrate that for noisy transformations, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results.