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

arXiv: https://arxiv.org/abs/2306.15762 · HTML: https://mlsanity.com/paper/2306.15762/

## 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 (most cited first, 30 of 36)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [3D Shape Induction from 2D Views of Multiple Objects](https://mlsanity.com/paper/1612.05872/) (2016)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Image GANs meet Differentiable Rendering for Inverse Graphics and Interpretable 3D Neural Rendering](https://mlsanity.com/paper/2010.09125/) (2020)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [Deep Shells: Unsupervised Shape Correspondence with Optimal Transport](https://mlsanity.com/paper/2010.15261/) (2020)
- [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [3D Face Modeling From Diverse Raw Scan Data](https://mlsanity.com/paper/1902.04943/) (2019)
- [The varifold representation of non-oriented shapes for diffeomorphic registration](https://mlsanity.com/paper/1304.6108/) (2013)
- [Deep Unsupervised Learning of 3D Point Clouds via Graph Topology Inference and Filtering](https://mlsanity.com/paper/1905.04571/) (2019)
- [Sparse to Dense Dynamic 3D Facial Expression Generation](https://mlsanity.com/paper/2105.07463/) (2021)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)

## Built on by (most cited first, 6 of 6)

- [ScanTalk: 3D Talking Heads from Unregistered Scans](https://mlsanity.com/paper/2403.10942/) (2024)
- [Basis restricted elastic shape analysis on the space of unregistered surfaces](https://mlsanity.com/paper/2311.04382/) (2023)
- [Beyond Fixed Topologies: Unregistered Training and Comprehensive Evaluation Metrics for 3D Talking Heads](https://mlsanity.com/paper/2410.11041/) (2024)
- [VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data](https://mlsanity.com/paper/2307.03553/) (2023)
- [SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data](https://mlsanity.com/paper/2506.01189/) (2025)
- [FreeTalk: Emotional Topology-Free 3D Talking Heads](https://mlsanity.com/paper/2603.15512/) (2026)

## 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.