# Learning Joint Surface Atlases

arXiv: https://arxiv.org/abs/2206.06273 · HTML: https://mlsanity.com/paper/2206.06273/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Shape Reconstruction by Learning Differentiable Surface Representations](https://mlsanity.com/paper/1911.11227/) (2019)
- [Meshlet Priors for 3D Mesh Reconstruction](https://mlsanity.com/paper/2001.01744/) (2020)
- [TearingNet: Point Cloud Autoencoder to Learn Topology-Friendly Representations](https://mlsanity.com/paper/2006.10187/) (2020)
- [Better Patch Stitching for Parametric Surface Reconstruction](https://mlsanity.com/paper/2010.07021/) (2020)
- [Temporally-Coherent Surface Reconstruction via Metric-Consistent Atlases](https://mlsanity.com/paper/2104.06950/) (2021)

## Built on by (most cited first, 2 of 2)

- [An Object is Worth 64x64 Pixels: Generating 3D Object via Image Diffusion](https://mlsanity.com/paper/2408.03178/) (2024)
- [CN-DHF: Compact Neural Double Height-Field Representations of 3D Shapes](https://mlsanity.com/paper/2304.13141/) (2023)

## Abstract (arXiv)

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 representation, 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.