# ROAD: Learning an Implicit Recursive Octree Auto-Decoder to Efficiently Encode 3D Shapes

arXiv: https://arxiv.org/abs/2212.06193 · HTML: https://mlsanity.com/paper/2212.06193/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 77 references that are in the map.
- First posted on arXiv 12 Dec 2022.

## Builds on (most cited first, 30 of 62)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)

## Built on by (most cited first, 6 of 6)

- [CARTO: Category and Joint Agnostic Reconstruction of ARTiculated Objects](https://mlsanity.com/paper/2303.15782/) (2023)
- [NeO 360: Neural Fields for Sparse View Synthesis of Outdoor Scenes](https://mlsanity.com/paper/2308.12967/) (2023)
- [FSD: Fast Self-Supervised Single RGB-D to Categorical 3D Objects](https://mlsanity.com/paper/2310.12974/) (2023)
- [ReFiNe: Recursive Field Networks for Cross-modal Multi-scene Representation](https://mlsanity.com/paper/2406.04309/) (2024)
- [INRet: A General Framework for Accurate Retrieval of INRs for Shapes](https://mlsanity.com/paper/2501.15722/) (2025)
- [Squeeze3D: Extreme Neural Compression with Latent Space Bridging](https://mlsanity.com/paper/2506.07932/) (2025)

## Abstract (arXiv)

Compact and accurate representations of 3D shapes are central to many perception and robotics tasks. State-of-the-art learning-based methods can reconstruct single objects but scale poorly to large datasets. We present a novel recursive implicit representation to efficiently and accurately encode large datasets of complex 3D shapes by recursively traversing an implicit octree in latent space. Our implicit Recursive Octree Auto-Decoder (ROAD) learns a hierarchically structured latent space enabling state-of-the-art reconstruction results at a compression ratio above 99%. We also propose an efficient curriculum learning scheme that naturally exploits the coarse-to-fine properties of the underlying octree spatial representation. We explore the scaling law relating latent space dimension, dataset size, and reconstruction accuracy, showing that increasing the latent space dimension is enough to scale to large shape datasets. Finally, we show that our learned latent space encodes a coarse-to-fine hierarchical structure yielding reusable latents across different levels of details, and we provide qualitative evidence of generalization to novel shapes outside the training set.