# Coupling Explicit and Implicit Surface Representations for Generative 3D Modeling

arXiv: https://arxiv.org/abs/2007.10294 · HTML: https://mlsanity.com/paper/2007.10294/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2020.

## Built on by (most cited first, 19 of 19)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [NeuTex: Neural Texture Mapping for Volumetric Neural Rendering](https://mlsanity.com/paper/2103.00762/) (2021)
- [Towards Implicit Text-Guided 3D Shape Generation](https://mlsanity.com/paper/2203.14622/) (2022)
- [Sketch2Mesh: Reconstructing and Editing 3D Shapes from Sketches](https://mlsanity.com/paper/2104.00482/) (2021)
- [HPNet: Deep Primitive Segmentation Using Hybrid Representations](https://mlsanity.com/paper/2105.10620/) (2021)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [Learning Parallel Dense Correspondence from Spatio-Temporal Descriptors for Efficient and Robust 4D Reconstruction](https://mlsanity.com/paper/2103.16341/) (2021)
- [NeuForm: Adaptive Overfitting for Neural Shape Editing](https://mlsanity.com/paper/2207.08890/) (2022)
- [DeepDT: Learning Geometry From Delaunay Triangulation for Surface Reconstruction](https://mlsanity.com/paper/2101.10353/) (2021)
- [Neural Convolutional Surfaces](https://mlsanity.com/paper/2204.02289/) (2022)
- [Ray-ONet: Efficient 3D Reconstruction From A Single RGB Image](https://mlsanity.com/paper/2107.01899/) (2021)
- [DeepMend: Learning Occupancy Functions to Represent Shape for Repair](https://mlsanity.com/paper/2210.05728/) (2022)
- [DeepJoin: Learning a Joint Occupancy, Signed Distance, and Normal Field Function for Shape Repair](https://mlsanity.com/paper/2211.12400/) (2022)
- [Dynamic NeRF: A Review](https://mlsanity.com/paper/2405.08609/) (2024)
- [Modeling 3D Surface Manifolds with a Locally Conditioned Atlas](https://mlsanity.com/paper/2102.05984/) (2021)
- [Towards Generalising Neural Implicit Representations](https://mlsanity.com/paper/2101.12690/) (2021)
- [Contextualising Implicit Representations for Semantic Tasks](https://mlsanity.com/paper/2305.13312/) (2023)
- [3D Shape Completion with Test-Time Training](https://mlsanity.com/paper/2410.18668/) (2024)

## Abstract (arXiv)

We propose a novel neural architecture for representing 3D surfaces, which harnesses two complementary shape representations: (i) an explicit representation via an atlas, i.e., embeddings of 2D domains into 3D; (ii) an implicit-function representation, i.e., a scalar function over the 3D volume, with its levels denoting surfaces. We make these two representations synergistic by introducing novel consistency losses that ensure that the surface created from the atlas aligns with the level-set of the implicit function. Our hybrid architecture outputs results which are superior to the output of the two equivalent single-representation networks, yielding smoother explicit surfaces with more accurate normals, and a more accurate implicit occupancy function. Additionally, our surface reconstruction step can directly leverage the explicit atlas-based representation. This process is computationally efficient, and can be directly used by differentiable rasterizers, enabling training our hybrid representation with image-based losses.