# Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization

arXiv: https://arxiv.org/abs/2111.12878 · HTML: https://mlsanity.com/paper/2111.12878/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 96 references that are in the map.
- First posted on arXiv 25 Nov 2021.

## Builds on (most cited first, 30 of 46)

- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration](https://mlsanity.com/paper/2011.12149/) (2020)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [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)
- [Efficient Learning on Point Clouds with Basis Point Sets](https://mlsanity.com/paper/1908.09186/) (2019)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [Learning multiview 3D point cloud registration](https://mlsanity.com/paper/2001.05119/) (2020)
- [DeepDeform: Learning Non-rigid RGB-D Reconstruction with Semi-supervised Data](https://mlsanity.com/paper/1912.04302/) (2019)
- [Deep Shells: Unsupervised Shape Correspondence with Optimal Transport](https://mlsanity.com/paper/2010.15261/) (2020)
- [Neural Deformation Graphs for Globally-consistent Non-rigid Reconstruction](https://mlsanity.com/paper/2012.01451/) (2020)
- [Weakly Supervised Learning of Rigid 3D Scene Flow](https://mlsanity.com/paper/2102.08945/) (2021)
- [Correspondence Learning via Linearly-invariant Embedding](https://mlsanity.com/paper/2010.13136/) (2020)
- [MultiBodySync: Multi-Body Segmentation and Motion Estimation via 3D Scan Synchronization](https://mlsanity.com/paper/2101.06605/) (2021)
- [Quaternion Equivariant Capsule Networks for 3D Point Clouds](https://mlsanity.com/paper/1912.12098/) (2019)
- [Locally Aware Piecewise Transformation Fields for 3D Human Mesh Registration](https://mlsanity.com/paper/2104.08160/) (2021)
- [HCRF-Flow: Scene Flow from Point Clouds with Continuous High-order CRFs and Position-aware Flow Embedding](https://mlsanity.com/paper/2105.07751/) (2021)

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

- [Dynamic 3D Scene Analysis by Point Cloud Accumulation](https://mlsanity.com/paper/2207.12394/) (2022)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Spatially and Spectrally Consistent Deep Functional Maps](https://mlsanity.com/paper/2308.08871/) (2023)
- [NICP: Neural ICP for 3D Human Registration at Scale](https://mlsanity.com/paper/2312.14024/) (2023)
- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (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)
- [Dimensions of Motion: Monocular Prediction through Flow Subspaces](https://mlsanity.com/paper/2112.01502/) (2021)
- [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)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [G-MSM: Unsupervised Multi-Shape Matching with Graph-based Affinity Priors](https://mlsanity.com/paper/2212.02910/) (2022)
- [Diffusion Shape Prior for Wrinkle-Accurate Cloth Registration](https://mlsanity.com/paper/2311.05828/) (2023)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [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)
- [Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transform](https://mlsanity.com/paper/2404.11156/) (2024)
- [Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondence](https://mlsanity.com/paper/2404.00959/) (2024)
- [TourPhysics: Bringing Physics to World Models for Exploration and Manipulation from a Single Image](https://mlsanity.com/paper/2609.04911/) (2026)
- [Riemannian Functional Map Synchronization for Probabilistic Partial Correspondence in Shape Networks](https://mlsanity.com/paper/2111.14762/) (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)
- [SynBench: A Synthetic Benchmark for Non-rigid 3D Point Cloud Registration](https://mlsanity.com/paper/2409.14474/) (2024)
- [NFR: Neural Feature-Guided Non-Rigid Shape Registration](https://mlsanity.com/paper/2505.22445/) (2025)
- [3D Human Mesh Estimation from Single View RGBD](https://mlsanity.com/paper/2508.08178/) (2025)
- [DisPOSE: Projected Polystochastic Diffusion for Self-Supervised Multi-View 3D Human Pose Estimation](https://mlsanity.com/paper/2606.07419/) (2026)
- [BridgeMatch: Conditional Transport Bridges in Matching Matrix Space for 3D Deformable Registration](https://mlsanity.com/paper/2609.11472/) (2026)

## Abstract (arXiv)

We present SyNoRiM, a novel way to jointly register multiple non-rigid shapes by synchronizing the maps relating learned functions defined on the point clouds. Even though the ability to process non-rigid shapes is critical in various applications ranging from computer animation to 3D digitization, the literature still lacks a robust and flexible framework to match and align a collection of real, noisy scans observed under occlusions. Given a set of such point clouds, our method first computes the pairwise correspondences parameterized via functional maps. We simultaneously learn potentially non-orthogonal basis functions to effectively regularize the deformations, while handling the occlusions in an elegant way. To maximally benefit from the multi-way information provided by the inferred pairwise deformation fields, we synchronize the pairwise functional maps into a cycle-consistent whole thanks to our novel and principled optimization formulation. We demonstrate via extensive experiments that our method achieves a state-of-the-art performance in registration accuracy, while being flexible and efficient as we handle both non-rigid and multi-body cases in a unified framework and avoid the costly optimization over point-wise permutations by the use of basis function maps.