# Non-rigid Point Cloud Registration with Neural Deformation Pyramid

arXiv: https://arxiv.org/abs/2205.12796 · HTML: https://mlsanity.com/paper/2205.12796/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [Neural Scene Flow Prior](https://mlsanity.com/paper/2111.01253/) (2021)
- [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)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Neural Non-Rigid Tracking](https://mlsanity.com/paper/2006.13240/) (2020)
- [PointPWC-Net: A Coarse-to-Fine Network for Supervised and Self-Supervised Scene Flow Estimation on 3D Point Clouds](https://mlsanity.com/paper/1911.12408/) (2019)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Learning to Optimize Non-Rigid Tracking](https://mlsanity.com/paper/2003.12230/) (2020)

## Built on by (most cited first, 30 of 42)

- [BlockFusion: Expandable 3D Scene Generation using Latent Tri-plane Extrapolation](https://mlsanity.com/paper/2401.17053/) (2024)
- [Dynamic Point Fields](https://mlsanity.com/paper/2304.02626/) (2023)
- [Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registration](https://mlsanity.com/paper/2303.09950/) (2023)
- [Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization](https://mlsanity.com/paper/2206.03410/) (2022)
- [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)
- [Thinking in Blender: Staged Executable Inverse Graphics with Vision-Language Models](https://mlsanity.com/paper/2606.02580/) (2026)
- [Category-Agnostic Neural Object Rigging](https://mlsanity.com/paper/2505.20283/) (2025)
- [Root Pose Decomposition Towards Generic Non-rigid 3D Reconstruction with Monocular Videos](https://mlsanity.com/paper/2308.10089/) (2023)
- [DynoSurf: Neural Deformation-based Temporally Consistent Dynamic Surface Reconstruction](https://mlsanity.com/paper/2403.11586/) (2024)
- [Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondence](https://mlsanity.com/paper/2503.21766/) (2025)
- [Landmark-Free Preoperative-to-Intraoperative Registration in Laparoscopic Liver Resection](https://mlsanity.com/paper/2504.15152/) (2025)
- [Leveraging Intrinsic Properties for Non-Rigid Garment Alignment](https://mlsanity.com/paper/2308.09519/) (2023)
- [ADoPT: LiDAR Spoofing Attack Detection Based on Point-Level Temporal Consistency](https://mlsanity.com/paper/2310.14504/) (2023)
- [Degrees of Freedom Matter: Inferring Dynamics from Point Trajectories](https://mlsanity.com/paper/2406.03625/) (2024)
- [Robust-DefReg: A Robust Deformable Point Cloud Registration Method based on Graph Convolutional Neural Networks](https://mlsanity.com/paper/2306.04701/) (2023)
- [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)
- [Diff-Reg v1: Diffusion Matching Model for Registration Problem](https://mlsanity.com/paper/2403.19919/) (2024)
- [Toward Reliable AR-Guided Surgical Navigation: Interactive Deformation Modeling with Data-Driven Biomechanics and Prompts](https://mlsanity.com/paper/2506.08048/) (2025)
- [FUSE: A Flow-based Mapping Between Shapes](https://mlsanity.com/paper/2511.13431/) (2025)
- [Non-rigid Point Cloud Registration for Middle Ear Diagnostics with Endoscopic Optical Coherence Tomography](https://mlsanity.com/paper/2304.13618/) (2023)
- [Prim2Room: Layout-Controllable Room Mesh Generation from Primitives](https://mlsanity.com/paper/2409.05380/) (2024)
- [DefTransNet: A Transformer-based Method for Non-Rigid Point Cloud Registration in the Simulation of Soft Tissue Deformation](https://mlsanity.com/paper/2502.06336/) (2025)
- [SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration](https://mlsanity.com/paper/2405.20188/) (2024)
- [COSMU: Complete 3D human shape from monocular unconstrained images](https://mlsanity.com/paper/2407.10586/) (2024)
- [Preconditioned Deformation Grids](https://mlsanity.com/paper/2509.18097/) (2025)
- [ERNet: Efficient Non-Rigid Registration Network for Point Sequences](https://mlsanity.com/paper/2510.15800/) (2025)

## Abstract (arXiv)

Non-rigid point cloud registration is a key component in many computer vision and computer graphics applications. The high complexity of the unknown non-rigid motion make this task a challenging problem. In this paper, we break down this problem via hierarchical motion decomposition. Our method called Neural Deformation Pyramid (NDP) represents non-rigid motion using a pyramid architecture. Each pyramid level, denoted by a Multi-Layer Perception (MLP), takes as input a sinusoidally encoded 3D point and outputs its motion increments from the previous level. The sinusoidal function starts with a low input frequency and gradually increases when the pyramid level goes down. This allows a multi-level rigid to nonrigid motion decomposition and also speeds up the solving by 50 times compared to the existing MLP-based approach. Our method achieves advanced partialto-partial non-rigid point cloud registration results on the 4DMatch/4DLoMatch benchmark under both no-learned and supervised settings.