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

TL;DR

This paper introduces a mesh-invariant 3D generative model that uses geometric measures like currents and varifolds to handle unregistered meshes and point clouds, improving robustness and flexibility.

Contribution

The authors propose a novel architecture with a kernel-based loss function based on geometric measures, enabling training on unregistered 3D data without correspondence constraints.

Findings

Effective generation of human face meshes

Robustness to mesh resampling and unregistered data

Outperforms existing methods in handling geometric variability

Abstract

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.