mlsanityData to 7 Oct 2026

Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching

arXiv 2211.14604 ↗First posted 26 Nov 2022cs.CV cs.GRcited by 8

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Abstract (arXiv)

In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/DeformationBasis.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 39 of its 102 references that are in the map. First posted on arXiv 26 Nov 2022.

Builds on

39 of 102 references.

References · 39

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  2. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  4. 2020Nerfies: Deformable Neural Radiance Fieldscited by 1,194
  5. 2018AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generationcited by 539
  6. 2017Learning from Synthetic Humanscited by 358
  7. 20163D Menagerie: Modeling the 3D shape and pose of animalscited by 310
  8. 2016Panoptic Studio: A Massively Multiview System for Social Interaction Capturecited by 173
  9. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 163
  10. 20183D-CODED : 3D Correspondences by Deep Deformationcited by 160
  11. 2017Deep Functional Maps: Structured Prediction for Dense Shape Correspondencecited by 134
  12. 2020Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondencecited by 125
27 more
  1. 2020Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondencecited by 119
  2. 2019Neural Cages for Detail-Preserving 3D Deformationscited by 105
  3. 2019Learning elementary structures for 3D shape generation and matchingcited by 98
  4. 2016Learning shape correspondence with anisotropic convolutional neural networkscited by 95
  5. 2020Deep Implicit Templates for 3D Shape Representationcited by 86
  6. 2018Unsupervised Deep Learning for Structured Shape Matchingcited by 81
  7. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  8. 2018Continuous and Orientation-preserving Correspondences via Functional Mapscited by 77
  9. 2016VolumeDeform: Real-time Volumetric Non-rigid Reconstructioncited by 75
  10. 2020Deep Shells: Unsupervised Shape Correspondence with Optimal Transportcited by 74
  11. 2019Smooth Shells: Multi-Scale Shape Registration with Functional Mapscited by 72
  12. 20193DN: 3D Deformation Networkcited by 60
  13. 2020LIMP: Learning Latent Shape Representations with Metric Preservation Priorscited by 54
  14. 2021Shape registration in the time of transformerscited by 51
  15. 2020Correspondence Learning via Linearly-invariant Embeddingcited by 48
  16. 2020CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Cloudscited by 47
  17. 2021Joint Learning of 3D Shape Retrieval and Deformationcited by 41
  18. 2019ZoomOut: Spectral Upsampling for Efficient Shape Correspondencecited by 30
  19. 2020ShapeFlow: Learnable Deformations Among 3D Shapescited by 28
  20. 2018FARM: Functional Automatic Registration Method for 3D Human Bodiescited by 26
  21. 2019Unsupervised cycle-consistent deformation for shape matchingcited by 23
  22. 2021Augmenting Implicit Neural Shape Representations with Explicit Deformation Fieldscited by 19
  23. 2017Large-Scale 3D Shape Reconstruction and Segmentation from ShapeNet Core55cited by 15
  24. 2020Hamiltonian Dynamics for Real-World Shape Interpolationcited by 13
  25. 2019Realtime Simulation of Thin-Shell Deformable Materials using CNN-Based Mesh Embeddingcited by 9
  26. 2020Intrinsic Point Cloud Interpolation via Dual Latent Space Navigationcited by 8
  27. 2015Shape Aware Matching of Implicit Surfaces based on Thin Shell Energiescited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 1; 2025: 0; 2026: 3.

8 papers.

  1. 2023Template Free Reconstruction of Human-object Interaction with Procedural Interaction Generationcited by 37
  2. 2023NICP: Neural ICP for 3D Human Registration at Scalecited by 21
  3. 2023Advancing Bayesian Optimization via Learning Correlated Latent Spacecited by 18
  4. 2023textttNePhi: Neural Deformation Fields for Approximately Diffeomorphic Medical Image Registrationcited by 8
  5. 2026Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunitiescited by 4
  6. 2024SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registrationcited by 1
  7. 2026Ordered Diffusion for 3D Human Registrationcited by 1
  8. 2026MeshLoom: Feed-Forward Non-Rigid Registration of Mesh Sequencescited by 0