# Synchronization over Cartan motion groups via contraction

arXiv: https://arxiv.org/abs/1612.00059 · HTML: https://mlsanity.com/paper/1612.00059/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2016.

## Built on by (most cited first, 3 of 3)

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Chordal Averaging on Flag Manifolds and Its Applications](https://mlsanity.com/paper/2303.13501/) (2023)
- [Unrolled algorithms for group synchronization](https://mlsanity.com/paper/2207.09418/) (2022)

## Abstract (arXiv)

Group contraction is an algebraic map that relates two classes of Lie groups by a limiting process. We utilize this notion for the compactification of the class of Cartan motion groups. The compactification process is then applied to reduce a non-compact synchronization problem to a problem where the solution can be obtained by means of a unitary, faithful representation. We describe this method of synchronization via contraction in detail and analyze several important aspects of this application. One important special case of Cartan motion groups is the group of rigid motions, also called the special Euclidean group. We thoroughly discuss the synchronization over this group and show numerically the advantages of our approach compared to some current state-of-the-art synchronization methods on both synthetic and real data.