# Neural Surface Maps

arXiv: https://arxiv.org/abs/2103.16942 · HTML: https://mlsanity.com/paper/2103.16942/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 63 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [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)
- [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)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (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)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Deep Meta Functionals for Shape Representation](https://mlsanity.com/paper/1908.06277/) (2019)
- [Scan2Mesh: From Unstructured Range Scans to 3D Meshes](https://mlsanity.com/paper/1811.10464/) (2018)
- [Neural Subdivision](https://mlsanity.com/paper/2005.01819/) (2020)
- [Shape Reconstruction by Learning Differentiable Surface Representations](https://mlsanity.com/paper/1911.11227/) (2019)
- [On the Effectiveness of Weight-Encoded Neural Implicit 3D Shapes](https://mlsanity.com/paper/2009.09808/) (2020)
- [Multi-chart Generative Surface Modeling](https://mlsanity.com/paper/1806.02143/) (2018)
- [Surface Networks via General Covers](https://mlsanity.com/paper/1812.10705/) (2018)
- [Coupling Explicit and Implicit Surface Representations for Generative 3D Modeling](https://mlsanity.com/paper/2007.10294/) (2020)
- [Interactive 3D Modeling with a Generative Adversarial Network](https://mlsanity.com/paper/1706.05170/) (2017)

## Built on by (most cited first, 30 of 34)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [ReLU Fields: The Little Non-linearity That Could](https://mlsanity.com/paper/2205.10824/) (2022)
- [Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features](https://mlsanity.com/paper/2311.17024/) (2023)
- [Nuvo: Neural UV Mapping for Unruly 3D Representations](https://mlsanity.com/paper/2312.05283/) (2023)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [NeuForm: Adaptive Overfitting for Neural Shape Editing](https://mlsanity.com/paper/2207.08890/) (2022)
- [Flatten Anything: Unsupervised Neural Surface Parameterization](https://mlsanity.com/paper/2405.14633/) (2024)
- [Differentiable Surface Triangulation](https://mlsanity.com/paper/2109.10695/) (2021)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [Neural Semantic Surface Maps](https://mlsanity.com/paper/2309.04836/) (2023)
- [NeRF Analogies: Example-Based Visual Attribute Transfer for NeRFs](https://mlsanity.com/paper/2402.08622/) (2024)
- [Neural Convolutional Surfaces](https://mlsanity.com/paper/2204.02289/) (2022)
- [PartUV: Part-Based UV Unwrapping of 3D Meshes](https://mlsanity.com/paper/2511.16659/) (2025)
- [NeuroGF: A Neural Representation for Fast Geodesic Distance and Path Queries](https://mlsanity.com/paper/2306.00658/) (2023)
- [Neural Light Spheres for Implicit Image Stitching and View Synthesis](https://mlsanity.com/paper/2409.17924/) (2024)
- [Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion](https://mlsanity.com/paper/2207.14782/) (2022)
- [Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis](https://mlsanity.com/paper/2503.03132/) (2025)
- [Adaptive Local Basis Functions for Shape Completion](https://mlsanity.com/paper/2307.08348/) (2023)
- [Learning 3D Scene Analogies with Neural Contextual Scene Maps](https://mlsanity.com/paper/2503.15897/) (2025)
- [FlexPara: Flexible Neural Surface Parameterization](https://mlsanity.com/paper/2504.19210/) (2025)
- [MeshTailor: Cutting Seams via Generative Mesh Traversal](https://mlsanity.com/paper/2603.27309/) (2026)
- [TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations](https://mlsanity.com/paper/2406.12121/) (2024)
- [Learning Neural Implicit Representations with Surface Signal Parameterizations](https://mlsanity.com/paper/2211.00519/) (2022)
- [ParaPoint: Learning Global Free-Boundary Surface Parameterization of 3D Point Clouds](https://mlsanity.com/paper/2403.10349/) (2024)
- [Advances and Trends in the 3D Reconstruction of the Shape and Motion of Animals](https://mlsanity.com/paper/2508.16062/) (2025)
- [Learning to Solve PDEs on Neural Shape Representations](https://mlsanity.com/paper/2512.21311/) (2025)
- [GradientSurf: Gradient-Domain Neural Surface Reconstruction from RGB Video](https://mlsanity.com/paper/2310.05406/) (2023)
- [NC-Reg : Neural Cortical Maps for Rigid Registration](https://mlsanity.com/paper/2601.19042/) (2026)
- [Neural parametric representations for thin-shell shape optimisation](https://mlsanity.com/paper/2604.06612/) (2026)

## Abstract (arXiv)

Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as paramterization, shape analysis, remeshing, and deformation. Unfortunately, most computational representations of surface maps do not lend themselves to manipulation and optimization, usually entailing hard, discrete problems. While algorithms exist to solve these problems, they are problem-specific, and a general framework for surface maps is still in need. In this paper, we advocate considering neural networks as encoding surface maps. Since neural networks can be composed on one another and are differentiable, we show it is easy to use them to define surfaces via atlases, compose them for surface-to-surface mappings, and optimize differentiable objectives relating to them, such as any notion of distortion, in a trivial manner. In our experiments, we represent surfaces by generating a neural map that approximates a UV parameterization of a 3D model. Then, we compose this map with other neural maps which we optimize with respect to distortion measures. We show that our formulation enables trivial optimization of rather elusive mapping tasks, such as maps between a collection of surfaces.