Awesome Shape Matching

A curated list of awesome spectral shape matching methods, inspired by awesome-computer-vision

Why awesome shape matching?

This is a collection of papers and resources I curated when learning how to solve shape matching problem with spectral method. I will be continuously updating this list with the latest papers and resources.

Papers

Since many works possess multiple attributes simultaneously, they are categorized here based on their primary contributions.

Survey

• A Survey on Shape Correspondence, van Kaick et al. CGF 2011

• Registration of 3D point clouds and meshes: A survey from rigid to nonrigid, Tam et al. TVCG 2012

• Recent advances in shape correspondence, Sahillioğlu et al. TVC 2020

• A Survey of Non-Rigid 3D Registration, Deng et al. 2022

Axiomatic Methods

• Non-rigid registration under isometric deformation, Huang et al. SGP 2008

• Topologically-Robust 3D Shape Matching Based on Diffusion Geometry and Seed Growing, Sharma et al. CVPR 2011

• Geometrically consistent elastic matching of 3d shapes: A linear programming solution, Windheuser et al. ICCV 2011

• Large-Scale Integer Linear Programming for Orientation Preserving 3D Shape Matching, Windheuser et al. SGP 2011

• [FMaps] Functional Maps: A Flexible Representation of Maps Between Shapes, Ovsjanikov et a l. ACM TOG 2012

• [CQHB] Coupled quasi-harmonic bases, Kovnatsky et al. EG 2013

• Image Co-Segmentation via Consistent Functional Maps, Wang et al. ICCV 2013

• [CFM] Coupled Functional Maps, Eynard et al. 3DV 2016

• [PMSDP] Point Registration via Efficient Convex Relaxation, Maron et al. SIGGRAPH 2016 | Code

• [AMRSAM] Adjoint Map Representation for Shape Analysis and Matching, Huang et al. SGP 2017

• Deblurring and Denoising of Maps between Shapes, Ezuz et al. SGP 2017

• Informative Descriptor Preservation via Commutativity for Shape Matching, Nogneng et al. EG 2017

• [PMF] Product Manifold Filter: Non-Rigid Shape Correspondence via Kernel Density Estimation in the Product Space, Vestner et al. CVPR 2017

• Spatial Maps: From Low Rank Spectral to Sparse Spatial Functional Representations, Gasparetto et al. 3DV 2017

• Efficient Deformable Shape Correspondence via Kernel Matching, Vestner et al. 3DV 2017

• [BCICP] Continuous and Orientation-preserving Correspondences via Functional Maps, Ren et al. ACM TOG 2018 | Code

• [ZoomOut] ZoomOut: Spectral Upsampling for Efficient Shape Correspondence, Melzi et al. 2019 ACM TOG | Code

• Reversible Harmonic Maps between Discrete Surfaces, Ezuz et al. ACM TOG 2019

• [HFM] Hierarchical Functional Maps between Subdivision Surfaces, Shoham et al. SGP 2019

• Elastic Correspondence between Triangle Meshes, Ezuz et al. CGF 2019

• Structured Regularization of Functional Map Computations, Ren et al. SGP 2019

• [Smooth Shells] Smooth Shells: Multi-Scale Shape Registration with Functional Maps, Eisenberger et al. CVPR 2020 (Oral) | Code

• [MINA] MINA: Convex Mixed-Integer Programming for Non-Rigid Shape Alignment, Bernard et al. CVPR 2020

• [DiscrteOP] Discrete Optimization for Shape Matching, Ren et al. SGP 2021 | Code | Pytorch

• [MWP] Efficient deformable shape correspondence via multiscale spectral manifold wavelets preservation, Hu et al. CVPR 2021

• Fast Sinkhorn Filters: Using Matrix Scaling for Non-Rigid ShapeCorrespondence with Functional Maps, Pai et al. CVPR 2021 | Code

• [SmoothFM] Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization, Magnet et al. 3DV 2022 | Code

• [ComplexFM] Complex Functional Maps : a Conformal Link Between Tangent Bundles, Donati et al. EG 2022 | Code

• [SM-Comb] A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching, Roetzer et al. CVPR 2022 | Code

• [Scalable ZoomOut] Scalable and Efficient Functional Map Computations on Dense Meshes, Magnet et al. EG 2023 | Code

• [SIGMA] ΣIGMA: Scale-Invariant Global Sparse Shape Matching, Gao et al. ICCV 2023 | Code

• [Elastic Basis] An Elastic Basis for Spectral Shape Correspondence, Hartwig et al. SIGGRAPH 2023 | Code

Learning-based Methods

• [FMNet] Deep Functional Maps: Structured Prediction for Dense Shape Correspondence, Litany et al. ICCV 2017

• [UnsupFMNet] Unsupervised Learning of Dense Shape Correspondence, Halimi et al. CVPR 2019 (Oral) | Code

• [SURFMNet] Unsupervised Deep Learning for Structured Shape Matching, Roufosse et al. ICCV 2019 | Code

• Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapes, Ginzburg et al. ECCV 2020

• [GeomFmaps] Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence, Donati et al. CVPR 2020 | Code

• [WSupFMNet] Weakly Supervised Deep Functional Map for Shape Matching, Sharma et al. NeurIPS 2020 | Code

• [Deep Shells] Deep Shells: Unsupervised Shape Correspondence with Optimal Transport, Eisenberger et al. NeurIPS 2020 | Code

• Spectral Shape Recovery and Analysis Via Data-driven Connections, Marin et al. IJCV 2021

• [NCP] NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching, Attaiki et al. NeurIPS 2022 | Code

• [SRFeat] SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondence, Li et al. 3DV 2022

• [AttentiveFMaps] Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching, Li et al. NeurIPS 2022 | Code

• [DUO-FMNet] Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching, Donati et al. CVPR 2022 | Code

• [IFMatch] Implicit Field Supervision For Robust Non-Rigid Shape Matching, Sundararaman et al. CVPR 2022 | Code

• [ULRSSM] Unsupervised Learning of Robust Spectral Shape Matching, Cao et al. ACM TOG 2023 | Code

• [Differentiable ZoomOut] Memory-Scalable and Simplified Functional Map Learning, Magnet et al. CVPR 2024 | Code

• Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching, Bastian et al. CVPR 2024 | Code

• [SpiderMatch] SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency, Roetzer et al. CVPR 2024 (Best Student Paper Runner-Up) | Code

• Revisiting Map Relations for Unsupervised Non-Rigid Shape Matching, Cao et al. 3DV 2024

• Synchronous Diffusion for Unsupervised Smooth Non-rigid 3D Shape Matching, Cao et al. ECCV 2024

• [DiscoMatch] DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matching, Roetzer et al. ECCV 2024 | Code

Partial Shape Matching

• [FSP] Fully Spectral Partial Shape Matching, Litany et al. EG 2017

• [PSM] Partial Functional Correspondence, Rodola et al. CGF 2017

• [DIR] A Dual Iterative Refinement Method for Non-rigid Shape Matching, Xiang et al. CVPR 2021 | Code

• [DPFM] DPFM: Deep Partial Functional Maps, Attaiki et al. 3DV 2021 (Best Paper) | Code

• Learning Spectral Unions of Partial Deformable 3D Shapes, Moschella et al. EG 2022 | Code

• Geometrically Consistent Partial Shape Matching, Ehm et al. 3DV 2024

• Partial-to-Partial Shape Matching with Geometric Consistency, Ehm et al. CVPR 2024 | Code

Shape Interpolation

• Divergence-Free Shape Correspondence by Deformation, Eisenberger et al. SGP 2019 | Code

• Hamiltonian Dynamics for Real-World Shape Interpolation, Eisenberger et al. ECCV 2020 (Spotlight) | Code

• [Neuromorph] NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go, Eisenberger et al. CVPR 2021 | Code

• Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation, Cao et al. CVPR 2024 | Code

• [SRIF] SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation, Sun et al. SIGGRAPH Asia 2024 | Code

• Implicit Neural Surface Deformation with Explicit Velocity Fields, Sang et al. ICLR 2025 | Code

Pointcloud Matching

• [3D-CODED] 3D-CODED : 3D Correspondences by Deep Deformation, Groueix et al. ECCV 2018 | Code

• [Elementary] Learning elementary structures for 3D shape generation and matching, Deprelle et al. NeurIPS 2019

• [LIE] Correspondence Learning via Linearly-invariant Embedding, Marin et al. NeurIPS 2020 | Code | Pytorch

• [CorrNet3D] CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds, Zeng et al. CVPR 2021 | Code

• [DPC] DPC: Unsupervised Deep Point Correspondence via Cross and Self Constructio, Lang et al. 3DV 2021 | Code

• [NIE] Neural Intrinsic Embedding for Non-rigid Point Cloud Matching, Jiang et al. CVPR 2023 | Code

• [SSMSM] Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching, Cao et al. CVPR 2023 (Spotlight) | Code

• [DFR] Non-Rigid Shape Registration via Deep Functional Maps Prior Jiang et al. NeurIPS 2023 | Code

• [COE] CoE: Deep Coupled Embedding for Non-Rigid Point Cloud Correspondences Zeng et al. 3DV 2025 | Code

Shape Collections

• Consistent Shape Maps via Semidefinite Programming, Huang et al. SGP 2013

• Functional Map Networks for Analyzing and Exploring Large Shape Collections, Huang et al. ACM TOG 2014

• Unsupervised cycle-consistent deformation for shape matching, Groueix et al. SGP 2019

• [Consistent ZoomOut] CONSISTENT ZOOMOUT: Efficient Spectral Map Synchronization, Huang et al. SGP 2020

• [IsoMuSh] Isometric Multi-Shape Matching, Gao et al. CVPR 2021 (Oral) | Code

• [UDMSM] Unsupervised deep multi-shape matching, Cao et al. ECCV 2022 | Code

• [SyNoRiM] Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization, Huang et al. TPAMI 2022 | Code

• [G-MSM] G-MSM: Unsupervised Multi-Shape Matching with Graph-Based Affinity Priors, Eisenberger et al. CVPR 2023 | Code

• [SSCDFM] Spatially and Spectrally Consistent Deep Functional Maps, Sun et al. ICCV 2023 | Code

• Unsupervised Representation Learning for Diverse Deformable Shape Collections, Hahner et al. 3DV 2024 | Code

Zero-Shot Correspondence

• [SNK] Shape Non-rigid Kinematics (SNK): A Zero-Shot Method for Non-Rigid Shape Matching via Unsupervised Functional Map Regularized Reconstruction, Attaiki et al. NeurIPS 2023 | Code

• [SATR] SATR: Zero-Shot Semantic Segmentation of 3D Shapes, Abdelreheem et al. ICCV 2023 | Code

• Zero-Shot 3D Shape Correspondence, Abdelreheem et al. SIGGRAPH Asia 2023

Feature Backbone

• [PointNet++] PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space, Qi et al. NeurIPS 2017 | Pytorch

• [DGCNN] Dynamic Graph CNN for Learning on Point Clouds, Wang et al. ACM TOG 2018 | Pytorch

• [ACSCNN] Shape correspondence using anisotropic Chebyshev spectral CNNs Li et al. CVPR 2020

• [HSN] CNNs on Surfaces using Rotation-Equivariant Features, Wiersma et al. ACM TOG 2020

• [DiffusionNet] DiffusionNet: Discretization Agnostic Learning on Surfaces, Sharp et al. ACM TOG 2021 | Code

• Understanding and Improving Features Learned in Deep Functional Maps, Attaiki et al. CVPR 2023 | Code

Dataset

• [SCAPE] SCAPE: Shape Completion and Animation of People, Anguelov et al. SIGGRAPH 2005 | Website

• [FAUST] FAUST: Dataset and Evaluation for 3D Mesh Registration, Bogo et al. CVPR 2014 | Website

• [SURREAL] SURREAL: Open-Source Reinforcement Learning Framework and Robot Manipulation Benchmark, Varol et al. ECCV 2018 | Website

• [SMAL] 3D Menagerie: Modeling the 3D Shape and Pose of Animals, Zuffi et al. CVPR 2017 | Website

• [TOPKIDS] SHREC’16: Matching of Deformable Shapes with Topological Noise, Lähner et al. | Website

• [SHREC16] SHREC’16: Partial Matching of Deformable Shapes, Cosmo et al. | Website

• [SHREC19] SHREC 2019: Matching Humans with Different Connectivity, Melzi et al. | Website

• [SHREC20] SHREC’20: Shape correspondence with non-isometric deformations, Dyke et al. | Website

• [DT4D] 4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface, Li et al. ICCV 2021 | Website

TODO: Collect dataset with anonymous link, include various version (remeshed, anisotropic etc.)

courses

• Computing and Processing Correspondences with Functional Maps, Maks Ovsjanikov et al. SIGGRAPH Asia 2016

TODO: Add more resource (public course, talk etc.)

Tools

TODO: Add open-source toolbox for geometry processing and shape analysis.