# Neural Vector Fields: Generalizing Distance Vector Fields by Codebooks and Zero-Curl Regularization

arXiv: https://arxiv.org/abs/2309.01512 · HTML: https://mlsanity.com/paper/2309.01512/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 80 of its 92 references that are in the map.
- First posted on arXiv 4 Sep 2023.

## Builds on (most cited first, 30 of 80)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [CogVideo: Large-scale Pretraining for Text-to-Video Generation via Transformers](https://mlsanity.com/paper/2205.15868/) (2022)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [CogView: Mastering Text-to-Image Generation via Transformers](https://mlsanity.com/paper/2105.13290/) (2021)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [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)
- [RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds](https://mlsanity.com/paper/1911.11236/) (2019)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [PIFuHD: Multi-Level Pixel-Aligned Implicit Function for High-Resolution 3D Human Digitization](https://mlsanity.com/paper/2004.00452/) (2020)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)

## Built on by (most cited first, 2 of 2)

- [Spatio-Temporal Field Neural Networks for Air Quality Inference](https://mlsanity.com/paper/2403.02354/) (2024)
- [Towards Point Cloud Compression for Machine Perception: A Simple and Strong Baseline by Learning the Octree Depth Level Predictor](https://mlsanity.com/paper/2406.00791/) (2024)

## Abstract (arXiv)

Recent neural networks based surface reconstruction can be roughly divided into two categories, one warping templates explicitly and the other representing 3D surfaces implicitly. To enjoy the advantages of both, we propose a novel 3D representation, Neural Vector Fields (NVF), which adopts the explicit learning process to manipulate meshes and implicit unsigned distance function (UDF) representation to break the barriers in resolution and topology. This is achieved by directly predicting the displacements from surface queries and modeling shapes as Vector Fields, rather than relying on network differentiation to obtain direction fields as most existing UDF-based methods do. In this way, our approach is capable of encoding both the distance and the direction fields so that the calculation of direction fields is differentiation-free, circumventing the non-trivial surface extraction step. Furthermore, building upon NVFs, we propose to incorporate two types of shape codebooks, ie, NVFs (Lite or Ultra), to promote cross-category reconstruction through encoding cross-object priors. Moreover, we propose a new regularization based on analyzing the zero-curl property of NVFs, and implement this through the fully differentiable framework of our NVF (ultra). We evaluate both NVFs on four surface reconstruction scenarios, including watertight vs non-watertight shapes, category-agnostic reconstruction vs category-unseen reconstruction, category-specific, and cross-domain reconstruction.