mlsanityData to 14 Oct 2026

Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching

arXiv 2204.13453 ↗First posted 28 Apr 2022cs.CV math.DG math.SPcited by 36

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Abstract (arXiv)

State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework allow to enforce orientation preservation using a functional representation for tangent vector field transfer, through so-called complex functional maps. Using this representation, we propose a new deep learning approach to learn orientation-aware features in a fully unsupervised setting. Our architecture is built on top of DiffusionNet, making it robust to discretization changes. Additionally, we introduce a vector field-based loss, which promotes orientation preservation without using (often unstable) extrinsic descriptors.

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). Builds on 22 of its 52 references that are in the map. First posted on arXiv 28 Apr 2022.

Builds on

22 of 52 references.

References · 22

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  3. 20163D Menagerie: Modeling the 3D shape and pose of animalscited by 312
  4. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 164
  5. 2017SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernelscited by 161
  6. 20183D-CODED : 3D Correspondences by Deep Deformationcited by 160
  7. 2017Deep Functional Maps: Structured Prediction for Dense Shape Correspondencecited by 134
  8. 2020Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondencecited by 125
  9. 2016Learning shape correspondence with anisotropic convolutional neural networkscited by 95
  10. 2018Unsupervised Deep Learning for Structured Shape Matchingcited by 81
  11. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  12. 2018Continuous and Orientation-preserving Correspondences via Functional Mapscited by 77
10 more
  1. 2020Deep Shells: Unsupervised Shape Correspondence with Optimal Transportcited by 74
  2. 2015Partial Functional Correspondencecited by 61
  3. 2020Correspondence Learning via Linearly-invariant Embeddingcited by 48
  4. 2015Building Statistical Shape Spaces for 3D Human Modelingcited by 47
  5. 2020CNNs on Surfaces using Rotation-Equivariant Featurescited by 43
  6. 2018Multi-directional Geodesic Neural Networks via Equivariant Convolutioncited by 32
  7. 2018The Vector Heat Methodcited by 31
  8. 2019Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapescited by 30
  9. 2021Complex Functional Maps : a Conformal Link Between Tangent Bundlescited by 17
  10. 2020Unsupervised Dense Shape Correspondence using Heat Kernelscited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 9; 2024: 11; 2025: 6; 2026: 7.

36 papers.

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  1. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  2. 2022Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matchingcited by 35
  3. 2023Spatially and Spectrally Consistent Deep Functional Mapscited by 30
  4. 2024Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolationcited by 26
  5. 2023Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matchingcited by 23
  6. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  7. 2023Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matchingcited by 18
  8. 2024Partial-to-Partial Shape Matching with Geometric Consistencycited by 16
  9. 2024Memory-Scalable and Simplified Functional Map Learningcited by 14
  10. 2025Denoising Functional Maps: Diffusion Models for Shape Correspondencecited by 14
  11. 2023Non-Rigid Shape Registration via Deep Functional Maps Priorcited by 12
  12. 2024Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learningcited by 12
24 more
  1. 2024SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimationcited by 12
  2. 2024Zero-Shot Image Feature Consensus with Deep Functional Mapscited by 10
  3. 2024DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Featurescited by 10
  4. 2023Revisiting Map Relations for Unsupervised Non-Rigid Shape Matchingcited by 8
  5. 2023DiscoMatch: Fast Discrete Optimisation for Geometrically Consistent 3D Shape Matchingcited by 7
  6. 2024Shape Non-rigid Kinematics (SNK): A Zero-Shot Method for Non-Rigid Shape Matching via Unsupervised Functional Map Regularized Reconstructioncited by 7
  7. 2024Synchronous Diffusion for Unsupervised Smooth Non-Rigid 3D Shape Matchingcited by 7
  8. 2025Fast Globally Optimal and Geometrically Consistent 3D Shape Matchingcited by 4
  9. 2025FRIDU: Functional Map Refinement with Guided Image Diffusioncited by 4
  10. 2023Deformation-Guided Unsupervised Non-Rigid Shape Matchingcited by 3
  11. 2025FUSE: A Flow-based Mapping Between Shapescited by 3
  12. 2022Learning Canonical Embeddings for Unsupervised Shape Correspondence with Locally Linear Transformationscited by 2
  13. 2022Anisotropic Multi-Scale Graph Convolutional Network for Dense Shape Correspondencecited by 2
  14. 2024Equivariant Local Reference Frames for Unsupervised Non-rigid Point Cloud Shape Correspondencecited by 2
  15. 2026SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularizationcited by 2
  16. 2026RINO: Rotation-Invariant Non-Rigid Correspondencescited by 2
  17. 2025DcMatch: Unsupervised Multi-Shape Matching with Dual-Level Consistencycited by 1
  18. 2026DeepShapeMatchingKit: Accelerated Functional Map Solver and Shape Matching Pipelines Revisitedcited by 1
  19. 2026Hyper-Network Neural Functional Maps for Unsupervised Robust 3D Shape Matchingcited by 1
  20. 2024Deep Frequency-Aware Functional Maps for Robust Shape Matchingcited by 0
  21. 2025Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approachcited by 0
  22. 2026GenSP: Consistent Spherical Parameterization via Learning Shape Generative Modelscited by 0
  23. 2026MDND: Unsupervised Learning Guided by Non-Differentiable Refinement for Shape Correspondencecited by 0
  24. 2026TokenMatch: 3D Mesh Correspondence Transformer with Curvature-Guided Tokenisationcited by 0