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Partial Functional Correspondence

arXiv 1506.05274 ↗First posted 17 Jun 2015cs.CVcited by 61

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Abstract (arXiv)

In this paper, we propose a method for computing partial functional correspondence between non-rigid shapes. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. Corresponding parts are optimization variables in our problem and are used to weight the functional correspondence; we are looking for the largest and most regular (in the Mumford-Shah sense) parts that minimize correspondence distortion. We show that our approach can cope with very challenging correspondence settings.

Key facts. Cited by 61 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Jun 2015.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 11; 2022: 11; 2023: 11; 2024: 12; 2025: 7; 2026: 9.

61 papers.

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  1. 2021Rethinking Graph Transformers with Spectral Attentioncited by 473
  2. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  3. 2022A Survey of Non-Rigid 3D Registrationcited by 59
  4. 2021DPFM: Deep Partial Functional Mapscited by 58
  5. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  6. 2022Unsupervised Deep Multi-Shape Matchingcited by 39
  7. 2022Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matchingcited by 36
  8. 2023Spatially and Spectrally Consistent Deep Functional Mapscited by 30
  9. 2022Neural Shape Deformation Priorscited by 27
  10. 2024Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolationcited by 26
  11. 2022Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transportcited by 24
  12. 2023Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matchingcited by 23
38 more
  1. 2023NICP: Neural ICP for 3D Human Registration at Scalecited by 21
  2. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  3. 2022Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical frameworkcited by 19
  4. 2023NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matchingcited by 18
  5. 2021Complex Functional Maps : a Conformal Link Between Tangent Bundlescited by 17
  6. 2024Partial-to-Partial Shape Matching with Geometric Consistencycited by 16
  7. 2025Denoising Functional Maps: Diffusion Models for Shape Correspondencecited by 14
  8. 2021ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networkscited by 13
  9. 2022SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondencecited by 13
  10. 2023Geometrically Consistent Partial Shape Matchingcited by 13
  11. 2024Wormhole Loss for Partial Shape Matchingcited by 12
  12. 2023On Unsupervised Partial Shape Correspondencecited by 11
  13. 2024Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithmscited by 11
  14. 2024Zero-Shot Image Feature Consensus with Deep Functional Mapscited by 10
  15. 2024DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Featurescited by 10
  16. 2025DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matchingcited by 10
  17. 2024Generating Graphs via Spectral Diffusioncited by 8
  18. 2024Shape Non-rigid Kinematics (SNK): A Zero-Shot Method for Non-Rigid Shape Matching via Unsupervised Functional Map Regularized Reconstructioncited by 7
  19. 2024Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matchingcited by 7
  20. 2023Latent Spectral Regularization for Continual Learningcited by 6
  21. 2023Outlier-Robust Gromov-Wasserstein for Graph Datacited by 6
  22. 2023Generalizable Local Feature Pre-training for Deformable Shape Analysiscited by 6
  23. 2021Learning Spectral Unions of Partial Deformable 3D Shapescited by 4
  24. 2025FRIDU: Functional Map Refinement with Guided Image Diffusioncited by 4
  25. 2026Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunitiescited by 4
  26. 2021Partial Matching in the Space of Varifoldscited by 3
  27. 2021Disentangling Geometric Deformation Spaces in Generative Latent Shape Modelscited by 2
  28. 2022Spectral Maps for Learning on Subgraphscited by 2
  29. 2024DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domaincited by 2
  30. 2026SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularizationcited by 2
  31. 2021Learning Canonical Embedding for Non-rigid Shape Matchingcited by 1
  32. 2022Partial Shape Similarity via Alignment of Multi-Metric Hamiltonian Spectracited by 1
  33. 2022Semantic keypoint extraction for scanned animals using multi-depth-camera systemscited by 1
  34. 2024Latent Functional Maps: a spectral framework for representation alignmentcited by 1
  35. 2025ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fieldscited by 1
  36. 2026An Integer Linear Programming Approach to Geometrically Consistent Partial-Partial Shape Matchingcited by 1
  37. 2026Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matchingcited by 1
  38. 2021U-mesh: Human Correspondence Matching with Mesh Convolutional Networkscited by 0

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