# Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization

arXiv: https://arxiv.org/abs/2206.03410 · HTML: https://mlsanity.com/paper/2206.03410/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 71 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 19 of 19)

- [DoubleFusion: Real-time Capture of Human Performances with Inner Body Shapes from a Single Depth Sensor](https://mlsanity.com/paper/1804.06023/) (2018)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [DeepDeform: Learning Non-rigid RGB-D Reconstruction with Semi-supervised Data](https://mlsanity.com/paper/1912.04302/) (2019)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Neural Non-Rigid Tracking](https://mlsanity.com/paper/2006.13240/) (2020)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Robust 3D Self-portraits in Seconds](https://mlsanity.com/paper/2004.02460/) (2020)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Recurrent Multi-view Alignment Network for Unsupervised Surface Registration](https://mlsanity.com/paper/2011.12104/) (2020)
- [AA-ICP: Iterative Closest Point with Anderson Acceleration](https://mlsanity.com/paper/1709.05479/) (2017)
- [Quasi-Newton Solver for Robust Non-Rigid Registration](https://mlsanity.com/paper/2004.04322/) (2020)
- [Learning to Optimize Non-Rigid Tracking](https://mlsanity.com/paper/2003.12230/) (2020)
- [Topology-Aware Non-Rigid Point Cloud Registration](https://mlsanity.com/paper/1811.07014/) (2018)
- [DispVoxNets: Non-Rigid Point Set Alignment with Supervised Learning Proxies](https://mlsanity.com/paper/1907.10367/) (2019)
- [Accelerating ADMM for Efficient Simulation and Optimization](https://mlsanity.com/paper/1909.00470/) (2019)
- [Anderson Acceleration for Geometry Optimization and Physics Simulation](https://mlsanity.com/paper/1805.05715/) (2018)
- [Anderson Acceleration for Nonconvex ADMM Based on Douglas-Rachford Splitting](https://mlsanity.com/paper/2006.14539/) (2020)
- [Static/Dynamic Filtering for Mesh Geometry](https://mlsanity.com/paper/1712.03574/) (2017)

## Built on by (most cited first, 12 of 12)

- [Non-Rigid Shape Registration via Deep Functional Maps Prior](https://mlsanity.com/paper/2311.04494/) (2023)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis](https://mlsanity.com/paper/2406.18817/) (2024)
- [DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Features](https://mlsanity.com/paper/2408.08568/) (2024)
- [DynoSurf: Neural Deformation-based Temporally Consistent Dynamic Surface Reconstruction](https://mlsanity.com/paper/2403.11586/) (2024)
- [DDM: A Metric for Comparing 3D Shapes Using Directional Distance Fields](https://mlsanity.com/paper/2401.09736/) (2024)
- [Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy](https://mlsanity.com/paper/2502.10704/) (2025)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration](https://mlsanity.com/paper/2405.20188/) (2024)
- [SemICP: Semantic Non-Rigid Point Cloud Registration with Elastic Energy Regularization](https://mlsanity.com/paper/2503.00972/) (2025)
- [NFR: Neural Feature-Guided Non-Rigid Shape Registration](https://mlsanity.com/paper/2505.22445/) (2025)
- [DualReg: Dual-Space Filtering and Reinforcement for Rigid Registration](https://mlsanity.com/paper/2508.17034/) (2025)

## Abstract (arXiv)

Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way to align with a target 3D shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and partial overlap) and high degrees of freedom. Existing methods typically adopt the ℓp type robust norm to measure the alignment error and regularize the smoothness of deformation, and use a proximal algorithm to solve the resulting non-smooth optimization problem. However, the slow convergence of such algorithms limits their wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust norm for alignment and regularization, which can effectively handle outliers and partial overlaps. The problem is solved using the majorization-minimization algorithm, which reduces each iteration to a convex quadratic problem with a closed-form solution. We further apply Anderson acceleration to speed up the convergence of the solver, enabling the solver to run efficiently on devices with limited compute capability. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlaps, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/yaoyx689/AMMNRR.