# Quasi-Newton Solver for Robust Non-Rigid Registration

arXiv: https://arxiv.org/abs/2004.04322 · HTML: https://mlsanity.com/paper/2004.04322/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2020.

## Built on by (most cited first, 17 of 17)

- [GeoTransformer: Fast and Robust Point Cloud Registration with Geometric Transformer](https://mlsanity.com/paper/2308.03768/) (2023)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization](https://mlsanity.com/paper/2206.03410/) (2022)
- [Towards Autonomous Atlas-based Ultrasound Acquisitions in Presence of Articulated Motion](https://mlsanity.com/paper/2208.05399/) (2022)
- [Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis](https://mlsanity.com/paper/2406.18817/) (2024)
- [SPEAL: Skeletal Prior Embedded Attention Learning for Cross-Source Point Cloud Registration](https://mlsanity.com/paper/2312.08664/) (2023)
- [DynoSurf: Neural Deformation-based Temporally Consistent Dynamic Surface Reconstruction](https://mlsanity.com/paper/2403.11586/) (2024)
- [3D Face Morphing Attacks: Generation, Vulnerability and Detection](https://mlsanity.com/paper/2201.03454/) (2022)
- [Semantic Human Mesh Reconstruction with Textures](https://mlsanity.com/paper/2403.02561/) (2024)
- [Spatiotemporal Texture Reconstruction for Dynamic Objects Using a Single RGB-D Camera](https://mlsanity.com/paper/2108.09007/) (2021)
- [Anatomical Landmarks Localization for 3D Foot Point Clouds](https://mlsanity.com/paper/2110.00937/) (2021)
- [HumanReg: Self-supervised Non-rigid Registration of Human Point Cloud](https://mlsanity.com/paper/2312.05462/) (2023)
- [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)
- [DualReg: Dual-Space Filtering and Reinforcement for Rigid Registration](https://mlsanity.com/paper/2508.17034/) (2025)

## Abstract (arXiv)

Imperfect data (noise, outliers and partial overlap) and high degrees of freedom make non-rigid registration a classical challenging problem in computer vision. Existing methods typically adopt the ℓp type robust estimator to regularize the fitting and smoothness, and the proximal operator is used to solve the resulting non-smooth problem. However, the slow convergence of these algorithms limits its wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust estimator for data fitting and regularization, which can handle outliers and partial overlaps. We apply the majorization-minimization algorithm to the problem, which reduces each iteration to solving a simple least-squares problem with L-BFGS. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlap, 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/Juyong/FastRNRR.