# OctField: Hierarchical Implicit Functions for 3D Modeling

arXiv: https://arxiv.org/abs/2111.01067 · HTML: https://mlsanity.com/paper/2111.01067/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 69 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 30 of 46)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [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)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [End-to-end Recovery of Human Shape and Pose](https://mlsanity.com/paper/1712.06584/) (2017)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [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)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [3D-FRONT: 3D Furnished Rooms with layOuts and semaNTics](https://mlsanity.com/paper/2011.09127/) (2020)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)

## Built on by (most cited first, 25 of 25)

- [XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies](https://mlsanity.com/paper/2312.03806/) (2023)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations](https://mlsanity.com/paper/2205.02825/) (2022)
- [ImFace: A Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2203.14510/) (2022)
- [OctreeOcc: Efficient and Multi-Granularity Occupancy Prediction Using Octree Queries](https://mlsanity.com/paper/2312.03774/) (2023)
- [Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian](https://mlsanity.com/paper/2309.01793/) (2023)
- [OcTr: Octree-based Transformer for 3D Object Detection](https://mlsanity.com/paper/2303.12621/) (2023)
- [3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2205.15572/) (2022)
- [PINs: Progressive Implicit Networks for Multi-Scale Neural Representations](https://mlsanity.com/paper/2202.04713/) (2022)
- [3D Equivariant Graph Implicit Functions](https://mlsanity.com/paper/2203.17178/) (2022)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature](https://mlsanity.com/paper/2404.13420/) (2024)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2312.04028/) (2023)
- [Surf-D: Generating High-Quality Surfaces of Arbitrary Topologies Using Diffusion Models](https://mlsanity.com/paper/2311.17050/) (2023)
- [Unified Cross-Scale 3D Generation and Understanding via Autoregressive Modeling](https://mlsanity.com/paper/2503.16278/) (2025)
- [ROAD: Learning an Implicit Recursive Octree Auto-Decoder to Efficiently Encode 3D Shapes](https://mlsanity.com/paper/2212.06193/) (2022)
- [Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes](https://mlsanity.com/paper/2403.01414/) (2024)
- [CoFie: Learning Compact Neural Surface Representations with Coordinate Fields](https://mlsanity.com/paper/2406.03417/) (2024)
- [Implicit Neural Deformation for Sparse-View Face Reconstruction](https://mlsanity.com/paper/2112.02494/) (2021)
- [A Review of Deep Learning-Powered Mesh Reconstruction Methods](https://mlsanity.com/paper/2303.02879/) (2023)
- [ReFiNe: Recursive Field Networks for Cross-modal Multi-scene Representation](https://mlsanity.com/paper/2406.04309/) (2024)
- [Mesh Compression with Quantized Neural Displacement Fields](https://mlsanity.com/paper/2504.01027/) (2025)
- [On Optimal Sampling for Learning SDF Using MLPs Equipped with Positional Encoding](https://mlsanity.com/paper/2401.01391/) (2024)
- [CARA: Collision-Aware Resolution Adaptation for Multiresolution Hash Encoding Based Image Fitting](https://mlsanity.com/paper/2609.18554/) (2026)

## Abstract (arXiv)

Recent advances in localized implicit functions have enabled neural implicit representation to be scalable to large scenes. However, the regular subdivision of 3D space employed by these approaches fails to take into account the sparsity of the surface occupancy and the varying granularities of geometric details. As a result, its memory footprint grows cubically with the input volume, leading to a prohibitive computational cost even at a moderately dense decomposition. In this work, we present a learnable hierarchical implicit representation for 3D surfaces, coded OctField, that allows high-precision encoding of intricate surfaces with low memory and computational budget. The key to our approach is an adaptive decomposition of 3D scenes that only distributes local implicit functions around the surface of interest. We achieve this goal by introducing a hierarchical octree structure to adaptively subdivide the 3D space according to the surface occupancy and the richness of part geometry. As octree is discrete and non-differentiable, we further propose a novel hierarchical network that models the subdivision of octree cells as a probabilistic process and recursively encodes and decodes both octree structure and surface geometry in a differentiable manner. We demonstrate the value of OctField for a range of shape modeling and reconstruction tasks, showing superiority over alternative approaches.