# NESI: Shape Representation via Neural Explicit Surface Intersection

arXiv: https://arxiv.org/abs/2409.06030 · HTML: https://mlsanity.com/paper/2409.06030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 79 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 19 of 19)

- [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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [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)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [Shape Reconstruction by Learning Differentiable Surface Representations](https://mlsanity.com/paper/1911.11227/) (2019)
- [Matryoshka Networks: Predicting 3D Geometry via Nested Shape Layers](https://mlsanity.com/paper/1804.10975/) (2018)
- [Better Patch Stitching for Parametric Surface Reconstruction](https://mlsanity.com/paper/2010.07021/) (2020)
- [Compact Neural Graphics Primitives with Learned Hash Probing](https://mlsanity.com/paper/2312.17241/) (2023)
- [NeuForm: Adaptive Overfitting for Neural Shape Editing](https://mlsanity.com/paper/2207.08890/) (2022)
- [Neural Parametric Surfaces for Shape Modeling](https://mlsanity.com/paper/2309.09911/) (2023)
- [High-fidelity 3D Model Compression based on Key Spheres](https://mlsanity.com/paper/2201.07486/) (2022)

## Abstract (arXiv)

Compressed representations of 3D shapes that are compact, accurate, and can be processed efficiently directly in compressed form, are extremely useful for digital media applications. Recent approaches in this space focus on learned implicit or parametric representations. While implicits are well suited for tasks such as in-out queries, they lack natural 2D parameterization, complicating tasks such as texture or normal mapping. Conversely, parametric representations support the latter tasks but are ill-suited for occupancy queries. We propose a novel learned alternative to these approaches, based on intersections of localized explicit, or height-field, surfaces. Since explicits can be trivially expressed both implicitly and parametrically, NESI directly supports a wider range of processing operations than implicit alternatives, including occupancy queries and parametric access. We represent input shapes using a collection of differently oriented height-field bounded half-spaces combined using volumetric Boolean intersections. We first tightly bound each input using a pair of oppositely oriented height-fields, forming a Double Height-Field (DHF) Hull. We refine this hull by intersecting it with additional localized height-fields (HFs) that capture surface regions in its interior. We minimize the number of HFs necessary to accurately capture each input and compactly encode both the DHF hull and the local HFs as neural functions defined over subdomains of R^2. This reduced dimensionality encoding delivers high-quality compact approximations. Given similar parameter count, or storage capacity, NESI significantly reduces approximation error compared to the state of the art, especially at lower parameter counts.