mlsanityData to 14 Oct 2026

Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures

arXiv 2306.15762 ↗First posted 27 Jun 2023cs.CVcited by 6

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Abstract (arXiv)

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning algorithms require correspondence between each point when comparing the predicted shape and the target shape. We propose an architecture able to cope with different parameterizations, even during the training phase. In particular, our loss function is built upon a kernel-based metric over a representation of meshes using geometric measures such as currents and varifolds. The latter allows to implement an efficient dissimilarity measure with many desirable properties such as robustness to resampling of the mesh or point cloud. We demonstrate the efficiency and resilience of our model with a generative learning task of human faces.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 36 of its 58 references that are in the map. First posted on arXiv 27 Jun 2023.

Builds on

36 of 58 references.

References · 36

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24 more
  1. 2016Volumetric and Multi-View CNNs for Object Classification on 3D Datacited by 240
  2. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 164
  3. 20183D-CODED : 3D Correspondences by Deep Deformationcited by 160
  4. 20163D Shape Induction from 2D Views of Multiple Objectscited by 121
  5. 2021Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completioncited by 112
  6. 2020Kernel Operations on the GPU, with Autodiff, without Memory Overflowscited by 104
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  8. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 92
  9. 2019Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generationcited by 90
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  13. 2022Unsupervised Deep Multi-Shape Matchingcited by 39
  14. 20193D Face Modeling From Diverse Raw Scan Datacited by 25
  15. 2013The varifold representation of non-oriented shapes for diffeomorphic registrationcited by 24
  16. 2019Deep Unsupervised Learning of 3D Point Clouds via Graph Topology Inference and Filteringcited by 21
  17. 2021Sparse to Dense Dynamic 3D Facial Expression Generationcited by 19
  18. 2022Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical frameworkcited by 19
  19. 2022Fine Detailed Texture Learning for 3D Meshes with Generative Modelscited by 15
  20. 2020Shape My Face: Registering 3D Face Scans by Surface-to-Surface Translationcited by 14
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  22. 2021DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Cloudscited by 10
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 1; 2026: 1.

6 papers.

  1. 2024ScanTalk: 3D Talking Heads from Unregistered Scanscited by 24
  2. 2023Basis restricted elastic shape analysis on the space of unregistered surfacescited by 5
  3. 2024Beyond Fixed Topologies: Unregistered Training and Comprehensive Evaluation Metrics for 3D Talking Headscited by 5
  4. 2023VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Datacited by 4
  5. 2025SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Datacited by 1
  6. 2026FreeTalk: Emotional Topology-Free 3D Talking Headscited by 0