# NeuralODF: Learning Omnidirectional Distance Fields for 3D Shape Representation

arXiv: https://arxiv.org/abs/2206.05837 · HTML: https://mlsanity.com/paper/2206.05837/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 59 references that are in the map.
- First posted on arXiv 12 Jun 2022.

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

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [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)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [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)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [Deep Convolutional Neural Fields for Depth Estimation from a Single Image](https://mlsanity.com/paper/1411.6387/) (2014)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Multiresolution Tree Networks for 3D Point Cloud Processing](https://mlsanity.com/paper/1807.03520/) (2018)
- [Point Cloud GAN](https://mlsanity.com/paper/1810.05795/) (2018)
- [Unsupervised Learning of 3D Structure from Images](https://mlsanity.com/paper/1607.00662/) (2016)

## Built on by (most cited first, 7 of 7)

- [DDF-HO: Hand-Held Object Reconstruction via Conditional Directed Distance Field](https://mlsanity.com/paper/2308.08231/) (2023)
- [Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes](https://mlsanity.com/paper/2403.01414/) (2024)
- [Reconstructive Latent-Space Neural Radiance Fields for Efficient 3D Scene Representations](https://mlsanity.com/paper/2310.17880/) (2023)
- [OmniNeRF: Hybriding Omnidirectional Distance and Radiance fields for Neural Surface Reconstruction](https://mlsanity.com/paper/2209.13433/) (2022)
- [Efficient Visibility Approximation for Game AI using Neural Omnidirectional Distance Fields](https://mlsanity.com/paper/2407.03330/) (2024)
- [Probabilistic Directed Distance Fields for Ray-Based Shape Representations](https://mlsanity.com/paper/2404.09081/) (2024)
- [Learning Scene-Level Signed Directional Distance Function with Ellipsoidal Priors and Neural Residuals](https://mlsanity.com/paper/2503.20066/) (2025)

## Abstract (arXiv)

In visual computing, 3D geometry is represented in many different forms including meshes, point clouds, voxel grids, level sets, and depth images. Each representation is suited for different tasks thus making the transformation of one representation into another (forward map) an important and common problem. We propose Omnidirectional Distance Fields (ODFs), a new 3D shape representation that encodes geometry by storing the depth to the object's surface from any 3D position in any viewing direction. Since rays are the fundamental unit of an ODF, it can be used to easily transform to and from common 3D representations like meshes or point clouds. Different from level set methods that are limited to representing closed surfaces, ODFs are unsigned and can thus model open surfaces (e.g., garments). We demonstrate that ODFs can be effectively learned with a neural network (NeuralODF) despite the inherent discontinuities at occlusion boundaries. We also introduce efficient forward mapping algorithms for transforming ODFs to and from common 3D representations. Specifically, we introduce an efficient Jumping Cubes algorithm for generating meshes from ODFs. Experiments demonstrate that NeuralODF can learn to capture high-quality shape by overfitting to a single object, and also learn to generalize on common shape categories.