# Efficient Global Point Cloud Alignment using Bayesian Nonparametric Mixtures

arXiv: https://arxiv.org/abs/1603.04868 · HTML: https://mlsanity.com/paper/1603.04868/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2016.

## Built on by (most cited first, 9 of 9)

- [DeepDPM: Deep Clustering With an Unknown Number of Clusters](https://mlsanity.com/paper/2203.14309/) (2022)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [Efficient and Deterministic Search Strategy Based on Residual Projections for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/2305.11716/) (2023)
- [Transformation Decoupling Strategy based on Screw Theory for Deterministic Point Cloud Registration with Gravity Prior](https://mlsanity.com/paper/2311.01432/) (2023)
- [Hybrid Trilinear and Bilinear Programming for Aligning Partially Overlapping Point Sets](https://mlsanity.com/paper/2101.07458/) (2021)
- [Correspondence-Free Fast and Robust Spherical Point Pattern Registration](https://mlsanity.com/paper/2508.02339/) (2025)
- [Decomposed Global Optimization for Robust Point Matching with Low-Dimensional Branching](https://mlsanity.com/paper/2405.08589/) (2024)

## Abstract (arXiv)

Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from 3D object recognition to reconstruction. We propose a novel approach to the alignment problem that utilizes Bayesian nonparametrics to describe the point cloud and surface normal densities, and branch and bound (BB) optimization to recover the relative transformation. BB uses a novel, refinable, near-uniform tessellation of rotation space using 4D tetrahedra, leading to more efficient optimization compared to the common axis-angle tessellation. We provide objective function bounds for pruning given the proposed tessellation, and prove that BB converges to the optimum of the cost function along with providing its computational complexity. Finally, we empirically demonstrate the efficiency of the proposed approach as well as its robustness to real-world conditions such as missing data and partial overlap.