# GOGMA: Globally-Optimal Gaussian Mixture Alignment

arXiv: https://arxiv.org/abs/1603.00150 · HTML: https://mlsanity.com/paper/1603.00150/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2016.

## Built on by (most cited first, 22 of 22)

- [Robust Point Cloud Registration Framework Based on Deep Graph Matching](https://mlsanity.com/paper/2103.04256/) (2021)
- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (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)
- [Self-Supervised Point Cloud Registration with Deep Versatile Descriptors](https://mlsanity.com/paper/2201.10034/) (2022)
- [Coarse-to-Fine Point Cloud Registration with SE(3)-Equivariant Representations](https://mlsanity.com/paper/2210.02045/) (2022)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [Full Transformer Framework for Robust Point Cloud Registration with Deep Information Interaction](https://mlsanity.com/paper/2112.09385/) (2021)
- [Efficient Globally-Optimal Correspondence-Less Visual Odometry for Planar Ground Vehicles](https://mlsanity.com/paper/2203.00291/) (2022)
- [Efficient and Deterministic Search Strategy Based on Residual Projections for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/2305.11716/) (2023)
- [Adaptive Multi-step Refinement Network for Robust Point Cloud Registration](https://mlsanity.com/paper/2312.03053/) (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)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [A Comprehensive Survey for Real-World Industrial Defect Detection: Challenges, Approaches, and Prospects](https://mlsanity.com/paper/2507.13378/) (2025)
- [Correspondence-Free Fast and Robust Spherical Point Pattern Registration](https://mlsanity.com/paper/2508.02339/) (2025)
- [Fast Semantic-Assisted Outlier Removal for Large-scale Point Cloud Registration](https://mlsanity.com/paper/2202.10579/) (2022)
- [Robust Point Cloud Registration Framework Based on Deep Graph Matching(TPAMI Version)](https://mlsanity.com/paper/2211.04696/) (2022)
- [Decomposed Global Optimization for Robust Point Matching with Low-Dimensional Branching](https://mlsanity.com/paper/2405.08589/) (2024)
- [Gaussian Alignment for Relative Camera Pose Estimation via Single-View Reconstruction](https://mlsanity.com/paper/2509.13652/) (2025)
- [Group Invariant Spectral Embedding](https://mlsanity.com/paper/2607.08987/) (2026)
- [Efficient and Robust Absolute Pose Estimation via Gravity-Prior-Driven Transformation Decoupling and Pose Refinement](https://mlsanity.com/paper/2609.00713/) (2026)

## Abstract (arXiv)

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.