# Convex Relaxations of SE(2) and SE(3) for Visual Pose Estimation

arXiv: https://arxiv.org/abs/1401.3700 · HTML: https://mlsanity.com/paper/1401.3700/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2014.

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

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representations](https://mlsanity.com/paper/2210.02045/) (2022)
- [Certifiably Optimal Anisotropic Rotation Averaging](https://mlsanity.com/paper/2503.07353/) (2025)

## Abstract (arXiv)

This paper proposes a new method for rigid body pose estimation based on spectrahedral representations of the tautological orbitopes of SE(2) and SE(3). The approach can use dense point cloud data from stereo vision or an RGB-D sensor (such as the Microsoft Kinect), as well as visual appearance data. The method is a convex relaxation of the classical pose estimation problem, and is based on explicit linear matrix inequality (LMI) representations for the convex hulls of SE(2) and SE(3). Given these representations, the relaxed pose estimation problem can be framed as a robust least squares problem with the optimization variable constrained to these convex sets. Although this formulation is a relaxation of the original problem, numerical experiments indicate that it is indeed exact - i.e. its solution is a member of SE(2) or SE(3) - in many interesting settings. We additionally show that this method is guaranteed to be exact for a large class of pose estimation problems.