mlsanityData to 14 Oct 2026

Smooth Shells: Multi-Scale Shape Registration with Functional Maps

arXiv 1905.12512 ↗First posted 29 May 2019cs.CV cs.GRcited by 72

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Abstract (arXiv)

We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main idea is to first align rough approximations of the geometry and then add more and more details to refine the correspondence. We fuse classical shape registration with Functional Maps by embedding the input shapes into an intrinsic-extrinsic product space. Moreover, we disambiguate intrinsic symmetries by applying a surrogate based Markov chain Monte Carlo initialization. Our method naturally handles various types of noise that commonly occur in real scans, like non-isometry or incompatible meshing. Finally, we demonstrate state-of-the-art quantitative results on several datasets and show that our pipeline produces smoother, more realistic results than other automatic matching methods in real world applications.

Key facts. Cited by 72 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 May 2019.

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Citing papers per year: 2021: 8; 2022: 13; 2023: 14; 2024: 11; 2025: 16; 2026: 10.

72 papers.

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  1. 2021Neural Scene Flow Priorcited by 91
  2. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  3. 2022A Survey of Non-Rigid 3D Registrationcited by 59
  4. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  5. 2021Shape registration in the time of transformerscited by 51
  6. 2022Unsupervised Deep Multi-Shape Matchingcited by 39
  7. 2022Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimizationcited by 37
  8. 2022Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matchingcited by 35
  9. 2023Spatially and Spectrally Consistent Deep Functional Mapscited by 30
  10. 2024Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolationcited by 26
  11. 2023Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matchingcited by 23
  12. 2022Intrinsic Neural Fields: Learning Functions on Manifoldscited by 20
38 more
  1. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  2. 2022A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matchingcited by 19
  3. 2023NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matchingcited by 18
  4. 2023Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matchingcited by 18
  5. 2021Complex Functional Maps : a Conformal Link Between Tangent Bundlescited by 17
  6. 2023Re-Evaluating LiDAR Scene Flow for Autonomous Drivingcited by 17
  7. 2024Partial-to-Partial Shape Matching with Geometric Consistencycited by 16
  8. 2023ZeroFlow: Scalable Scene Flow via Distillationcited by 14
  9. 2024Memory-Scalable and Simplified Functional Map Learningcited by 14
  10. 2025Denoising Functional Maps: Diffusion Models for Shape Correspondencecited by 14
  11. 2025Hierarchical Neural Semantic Representation for 3D Semantic Correspondencecited by 14
  12. 2022Implicit field supervision for robust non-rigid shape matchingcited by 13
  13. 2022SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondencecited by 13
  14. 2023Neural Semantic Surface Mapscited by 13
  15. 2023Geometrically Consistent Partial Shape Matchingcited by 13
  16. 2023Non-Rigid Shape Registration via Deep Functional Maps Priorcited by 12
  17. 2024Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learningcited by 12
  18. 2024SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimationcited by 12
  19. 2023GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Modelscited by 11
  20. 2024NeRF Analogies: Example-Based Visual Attribute Transfer for NeRFscited by 11
  21. 2024Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithmscited by 11
  22. 2022Neural Vector Fields for Implicit Surface Representation and Inferencecited by 10
  23. 2025DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matchingcited by 10
  24. 2022Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matchingcited by 8
  25. 2022G-MSM: Unsupervised Multi-Shape Matching with Graph-based Affinity Priorscited by 8
  26. 2023Revisiting Map Relations for Unsupervised Non-Rigid Shape Matchingcited by 8
  27. 2021Deep Virtual Markers for Articulated 3D Shapescited by 7
  28. 2024Shape Non-rigid Kinematics (SNK): A Zero-Shot Method for Non-Rigid Shape Matching via Unsupervised Functional Map Regularized Reconstructioncited by 7
  29. 2024Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matchingcited by 7
  30. 2025Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondencecited by 7
  31. 2022Garment Avatars: Realistic Cloth Driving using Pattern Registrationcited by 6
  32. 2023Leveraging Intrinsic Properties for Non-Rigid Garment Alignmentcited by 6
  33. 2025Textured 3D Regenerative Morphing with 3D Diffusion Priorcited by 6
  34. 2025Surface-Aware Distilled 3D Semantic Featurescited by 5
  35. 2021Mesh Draping: Parametrization-Free Neural Mesh Transfercited by 4
  36. 2025ARMO: Autoregressive Rigging for Multi-Category Objectscited by 4
  37. 2025Fast Globally Optimal and Geometrically Consistent 3D Shape Matchingcited by 4
  38. 2025FRIDU: Functional Map Refinement with Guided Image Diffusioncited by 4

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