Learning Joint Surface Atlases;

Abstract

This paper describes new techniques for learning atlas-like representations of 3D surfaces, i.e. homeomorphic transformations from a 2D domain to surfaces. Compared to prior work, we propose two major contributions. First, instead of mapping a fixed 2D domain, such as a set of square patches, to the surface, we learn a continuous 2D domain with arbitrary topology by optimizing a point sampling distribution represented as a mixture of Gaussians. Second, we learn consistent mappings in both directions: charts, from the 3D surface to 2D domain, and parametrizations, their inverse. We demonstrate that this improves the quality of the learned surface represen- tation, as well as its consistency in a collection of related shapes. It thus leads to improvements for applications such as correspondence estimation, texture transfer, and consistent UV mapping. As an additional technical contribution, we outline that, while incorporating normal consistency has clear benefits, it leads to issues in the optimization, and that these issues can be mitigated using a simple repulsive regularization. We demonstrate that our contributions provide better surface representation than existing baselines.

Results

We are able to generate constistent joint surface atlases for a collection of shapes.

Citing this work

If you find this work useful in your research, please consider citing :

@article{deprelle2022learning,
  title={Learning Joint Surface Atlases},
  author={Deprelle, Theo and Groueix, Thibault and Aigerman, Noam and Kim, Vladimir G and Aubry, Mathieu},
  journal={arXiv preprint arXiv:2206.06273},
  year={2022}
}

Method

We aim to jointly learn the surface parametrizations and their inverse functions, the charts-mappings; (ii) we learn a 2D domain relevant to a family of shapes by optimizing a probability density function in the 2D Euclidean plane. We also differ in two novel losses that correctly orient the normals of the reconstructed surface and fix point-collapse in 3D which is a common artifact of AtlasNet-type of approaches.

Code

We provide source codes for the project on http://github.com/TheoDEPRELLE/Joint-Atlas-Surfaces.