# Non-Rigid Shape Registration via Deep Functional Maps Prior arXiv: https://arxiv.org/abs/2311.04494 ยท HTML: https://mlsanity.com/paper/2311.04494/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Builds on 38 of its 59 references that are in the map. - First posted on arXiv 8 Nov 2023. ## Builds on (most cited first, 30 of 38) - [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016) - [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017) - [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018) - [PointContrast: Unsupervised Pre-training for 3D Point Cloud Understanding](https://mlsanity.com/paper/2007.10985/) (2020) - [Learning from Synthetic Humans](https://mlsanity.com/paper/1701.01370/) (2017) - [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021) - [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) - [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017) - [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020) - [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) - [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018) - [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021) - [Continuous and Orientation-preserving Correspondences via Functional Maps](https://mlsanity.com/paper/1806.04455/) (2018) - [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) - [Smooth Shells: Multi-Scale Shape Registration with Functional Maps](https://mlsanity.com/paper/1905.12512/) (2019) - [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023) - [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019) - [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021) - [Neural Non-Rigid Tracking](https://mlsanity.com/paper/2006.13240/) (2020) - [Correspondence Learning via Linearly-invariant Embedding](https://mlsanity.com/paper/2010.13136/) (2020) - [CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds](https://mlsanity.com/paper/2012.15638/) (2020) - [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022) - [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022) - [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022) - [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022) - [Dual Geometric Graph Network (DG2N) -- Iterative network for deformable shape alignment](https://mlsanity.com/paper/2011.14723/) (2020) - [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (2022) ## Built on by (most cited first, 12 of 12) - [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024) - [DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Features](https://mlsanity.com/paper/2408.08568/) (2024) - [Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2407.08244/) (2024) - [Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondence](https://mlsanity.com/paper/2503.21766/) (2025) - [Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy](https://mlsanity.com/paper/2502.10704/) (2025) - [ARMO: Autoregressive Rigging for Multi-Category Objects](https://mlsanity.com/paper/2503.20663/) (2025) - [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026) - [FUSE: A Flow-based Mapping Between Shapes](https://mlsanity.com/paper/2511.13431/) (2025) - [Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondence](https://mlsanity.com/paper/2404.00959/) (2024) - [MeshLoom: Feed-Forward Non-Rigid Registration of Mesh Sequences](https://mlsanity.com/paper/2606.17027/) (2026) - [Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matching](https://mlsanity.com/paper/2606.30131/) (2026) - [NFR: Neural Feature-Guided Non-Rigid Shape Registration](https://mlsanity.com/paper/2505.22445/) (2025) ## Abstract (arXiv) In this paper, we propose a learning-based framework for non-rigid shape registration without correspondence supervision. Traditional shape registration techniques typically rely on correspondences induced by extrinsic proximity, therefore can fail in the presence of large intrinsic deformations. Spectral mapping methods overcome this challenge by embedding shapes into, geometric or learned, high-dimensional spaces, where shapes are easier to align. However, due to the dependency on abstract, non-linear embedding schemes, the latter can be vulnerable with respect to perturbed or alien input. In light of this, our framework takes the best of both worlds. Namely, we deform source mesh towards the target point cloud, guided by correspondences induced by high-dimensional embeddings learned from deep functional maps (DFM). In particular, the correspondences are dynamically updated according to the intermediate registrations and filtered by consistency prior, which prominently robustify the overall pipeline. Moreover, in order to alleviate the requirement of extrinsically aligned input, we train an orientation regressor on a set of aligned synthetic shapes independent of the training shapes for DFM. Empirical results show that, with as few as dozens of training shapes of limited variability, our pipeline achieves state-of-the-art results on several benchmarks of non-rigid point cloud matching, but also delivers high-quality correspondences between unseen challenging shape pairs that undergo both significant extrinsic and intrinsic deformations, in which case neither traditional registration methods nor intrinsic methods work. The code is available at https://github.com/rqhuang88/DFR.