# CN-DHF: Compact Neural Double Height-Field Representations of 3D Shapes

arXiv: https://arxiv.org/abs/2304.13141 · HTML: https://mlsanity.com/paper/2304.13141/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 57 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 25 of 25)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [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)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [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)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Variable Bitrate Neural Fields](https://mlsanity.com/paper/2206.07707/) (2022)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [RGB-D Local Implicit Function for Depth Completion of Transparent Objects](https://mlsanity.com/paper/2104.00622/) (2021)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [Dense RGB SLAM with Neural Implicit Maps](https://mlsanity.com/paper/2301.08930/) (2023)
- [Canonical Capsules: Self-Supervised Capsules in Canonical Pose](https://mlsanity.com/paper/2012.04718/) (2020)
- [On the Effectiveness of Weight-Encoded Neural Implicit 3D Shapes](https://mlsanity.com/paper/2009.09808/) (2020)
- [Learning Joint Surface Atlases](https://mlsanity.com/paper/2206.06273/) (2022)

## Abstract (arXiv)

We introduce CN-DHF (Compact Neural Double-Height-Field), a novel hybrid neural implicit 3D shape representation that is dramatically more compact than the current state of the art. Our representation leverages Double-Height-Field (DHF) geometries, defined as closed shapes bounded by a pair of oppositely oriented height-fields that share a common axis, and leverages the following key observations: DHFs can be compactly encoded as 2D neural implicits that capture the maximal and minimal heights along the DHF axis; and typical closed 3D shapes are well represented as intersections of a very small number (three or fewer) of DHFs. We represent input geometries as CNDHFs by first computing the set of DHFs whose intersection well approximates each input shape, and then encoding these DHFs via neural fields. Our approach delivers high-quality reconstructions, and reduces the reconstruction error by a factor of 2:5 on average compared to the state-of-the-art, given the same parameter count or storage capacity. Compared to the best-performing alternative, our method produced higher accuracy models on 94% of the 400 input shape and parameter count combinations tested.