mlsanityData to 7 Oct 2026

Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence

arXiv 2003.14286 ↗First posted 31 Mar 2020stat.ML cs.LGcited by 125

Not on the map. Why?

Abstract (arXiv)

We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly across diverse datasets, our approach is both accurate and robust to changes in shape structure. Key to our method is a feature-extraction network that learns directly from raw shape geometry, combined with a novel regularized map extraction layer and loss, based on the functional map representation. We demonstrate through extensive experiments in challenging shape matching scenarios that our method can learn from less training data than existing supervised approaches and generalizes significantly better than current descriptor-based learning methods. Our source code is available at: https://github.com/LIX-shape-analysis/GeomFmaps.

Key facts. Cited by 125 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Mar 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 22; 2022: 20; 2023: 28; 2024: 15; 2025: 20; 2026: 20.

125 papers.

Sort:

By area:

  1. 2021Lepard: Learning partial point cloud matching in rigid and deformable scenescited by 85
  2. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  3. 2021Subdivision-Based Mesh Convolution Networkscited by 60
  4. 2022A Survey of Non-Rigid 3D Registrationcited by 59
  5. 2021DPFM: Deep Partial Functional Mapscited by 58
  6. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  7. 2023Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Featurescited by 55
  8. 2021Shape registration in the time of transformerscited by 51
  9. 2022Non-rigid Point Cloud Registration with Neural Deformation Pyramidcited by 41
  10. 2022Unsupervised Deep Multi-Shape Matchingcited by 39
  11. 2021Accurate Point Cloud Registration with Robust Optimal Transportcited by 38
  12. 2022Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimizationcited by 37
38 more
  1. 2022Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matchingcited by 36
  2. 2022Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matchingcited by 35
  3. 2021Neural Surface Mapscited by 34
  4. 2023Zero-Shot 3D Shape Correspondencecited by 33
  5. 2021Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronizationcited by 30
  6. 2023Spatially and Spectrally Consistent Deep Functional Mapscited by 30
  7. 2024Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolationcited by 26
  8. 2022Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transportcited by 24
  9. 2022ACID: Action-Conditional Implicit Visual Dynamics for Deformable Object Manipulationcited by 24
  10. 2023Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matchingcited by 23
  11. 2023NICP: Neural ICP for 3D Human Registration at Scalecited by 21
  12. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  13. 2022A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matchingcited by 19
  14. 2023NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matchingcited by 18
  15. 2023Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matchingcited by 18
  16. 2021Complex Functional Maps : a Conformal Link Between Tangent Bundlescited by 17
  17. 2024Partial-to-Partial Shape Matching with Geometric Consistencycited by 16
  18. 2021Field Convolutions for Surface CNNscited by 14
  19. 2023Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registrationcited by 14
  20. 2023Point2SSM: Learning Morphological Variations of Anatomies from Point Cloudcited by 14
  21. 2024Memory-Scalable and Simplified Functional Map Learningcited by 14
  22. 2025Denoising Functional Maps: Diffusion Models for Shape Correspondencecited by 14
  23. 2025Hierarchical Neural Semantic Representation for 3D Semantic Correspondencecited by 14
  24. 2021ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networkscited by 13
  25. 2022Implicit field supervision for robust non-rigid shape matchingcited by 13
  26. 2022SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondencecited by 13
  27. 2023Neural Semantic Surface Mapscited by 13
  28. 2023Non-Rigid Shape Registration via Deep Functional Maps Priorcited by 12
  29. 2024Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learningcited by 12
  30. 2024SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimationcited by 12
  31. 2024Wormhole Loss for Partial Shape Matchingcited by 12
  32. 2023S3M: Scalable Statistical Shape Modeling through Unsupervised Correspondencescited by 11
  33. 2023GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Modelscited by 11
  34. 2023On Unsupervised Partial Shape Correspondencecited by 11
  35. 2024Finsler-Laplace-Beltrami Operators with Application to Shape Analysiscited by 10
  36. 2025DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matchingcited by 10
  37. 2023Neural Intrinsic Embedding for Non-rigid Point Cloud Matchingcited by 9
  38. 2023GAPS: Geometry-Aware, Physics-Based, Self-Supervised Neural Garment Drapingcited by 9

50 most cited of 125 All 125 (JSON)