# Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion

arXiv: https://arxiv.org/abs/2207.14782 · HTML: https://mlsanity.com/paper/2207.14782/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Shape Reconstruction by Learning Differentiable Surface Representations](https://mlsanity.com/paper/1911.11227/) (2019)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [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)
- [NeeDrop: Self-supervised Shape Representation from Sparse Point Clouds using Needle Dropping](https://mlsanity.com/paper/2111.15207/) (2021)

## Built on by (most cited first, 5 of 5)

- [StableVideo: Text-driven Consistency-aware Diffusion Video Editing](https://mlsanity.com/paper/2308.09592/) (2023)
- [Robust e-NeRF: NeRF from Sparse & Noisy Events under Non-Uniform Motion](https://mlsanity.com/paper/2309.08596/) (2023)
- [Diffusion Shape Prior for Wrinkle-Accurate Cloth Registration](https://mlsanity.com/paper/2311.05828/) (2023)
- [Parameterization-driven Neural Surface Reconstruction for Object-oriented Editing in Neural Rendering](https://mlsanity.com/paper/2310.05524/) (2023)
- [Advances in Neural 3D Mesh Texturing: A Survey](https://mlsanity.com/paper/2606.00137/) (2026)

## Abstract (arXiv)

Explicit neural surface representations allow for exact and efficient extraction of the encoded surface at arbitrary precision, as well as analytic derivation of differential geometric properties such as surface normal and curvature. Such desirable properties, which are absent in its implicit counterpart, makes it ideal for various applications in computer vision, graphics and robotics. However, SOTA works are limited in terms of the topology it can effectively describe, distortion it introduces to reconstruct complex surfaces and model efficiency. In this work, we present Minimal Neural Atlas, a novel atlas-based explicit neural surface representation. At its core is a fully learnable parametric domain, given by an implicit probabilistic occupancy field defined on an open square of the parametric space. In contrast, prior works generally predefine the parametric domain. The added flexibility enables charts to admit arbitrary topology and boundary. Thus, our representation can learn a minimal atlas of 3 charts with distortion-minimal parameterization for surfaces of arbitrary topology, including closed and open surfaces with arbitrary connected components. Our experiments support the hypotheses and show that our reconstructions are more accurate in terms of the overall geometry, due to the separation of concerns on topology and geometry.