# Modeling 3D Surface Manifolds with a Locally Conditioned Atlas

arXiv: https://arxiv.org/abs/2102.05984 · HTML: https://mlsanity.com/paper/2102.05984/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 49 references that are in the map.
- First posted on arXiv 11 Feb 2021.

## Builds on (most cited first, 30 of 38)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [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)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [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)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [PIXOR: Real-time 3D Object Detection from Point Clouds](https://mlsanity.com/paper/1902.06326/) (2019)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Neural Cages for Detail-Preserving 3D Deformations](https://mlsanity.com/paper/1912.06395/) (2019)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Hierarchical Surface Prediction for 3D Object Reconstruction](https://mlsanity.com/paper/1704.00710/) (2017)
- [Point Cloud GAN](https://mlsanity.com/paper/1810.05795/) (2018)
- [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020)
- [GarNet: A Two-Stream Network for Fast and Accurate 3D Cloth Draping](https://mlsanity.com/paper/1811.10983/) (2018)
- [Shape Reconstruction by Learning Differentiable Surface Representations](https://mlsanity.com/paper/1911.11227/) (2019)
- [Marr Revisited: 2D-3D Alignment via Surface Normal Prediction](https://mlsanity.com/paper/1604.01347/) (2016)
- [Deep Parametric Shape Predictions using Distance Fields](https://mlsanity.com/paper/1904.08921/) (2019)

## Built on by (most cited first, 3 of 3)

- [Points2NeRF: Generating Neural Radiance Fields from 3D point cloud](https://mlsanity.com/paper/2206.01290/) (2022)
- [BIGS: Bimanual Category-agnostic Interaction Reconstruction from Monocular Videos via 3D Gaussian Splatting](https://mlsanity.com/paper/2504.09097/) (2025)
- [HyperCube: Implicit Field Representations of Voxelized 3D Models](https://mlsanity.com/paper/2110.05770/) (2021)

## Abstract (arXiv)

Recently proposed 3D object reconstruction methods represent a mesh with an atlas - a set of planar patches approximating the surface. However, their application in a real-world scenario is limited since the surfaces of reconstructed objects contain discontinuities, which degrades the quality of the final mesh. This is mainly caused by independent processing of individual patches, and in this work, we postulate to mitigate this limitation by preserving local consistency around patch vertices. To that end, we introduce a Locally Conditioned Atlas (LoCondA), a framework for representing a 3D object hierarchically in a generative model. Firstly, the model maps a point cloud of an object into a sphere. Secondly, by leveraging a spherical prior, we enforce the mapping to be locally consistent on the sphere and on the target object. This way, we can sample a mesh quad on that sphere and project it back onto the object's manifold. With LoCondA, we can produce topologically diverse objects while maintaining quads to be stitched together. We show that the proposed approach provides structurally coherent reconstructions while producing meshes of quality comparable to the competitors.