# Neural Vector Fields for Implicit Surface Representation and Inference

arXiv: https://arxiv.org/abs/2204.06552 · HTML: https://mlsanity.com/paper/2204.06552/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 84 references that are in the map.
- First posted on arXiv 13 Apr 2022.

## Builds on (most cited first, 30 of 49)

- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (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)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Gibson Env: Real-World Perception for Embodied Agents](https://mlsanity.com/paper/1808.10654/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [StyleSDF: High-Resolution 3D-Consistent Image and Geometry Generation](https://mlsanity.com/paper/2112.11427/) (2021)
- [ICON: Implicit Clothed humans Obtained from Normals](https://mlsanity.com/paper/2112.09127/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [Learning a Multi-View Stereo Machine](https://mlsanity.com/paper/1708.05375/) (2017)
- [Multi-view Supervision for Single-view Reconstruction via Differentiable Ray Consistency](https://mlsanity.com/paper/1704.06254/) (2017)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)

## Built on by (most cited first, 10 of 10)

- [PolyGNN: Polyhedron-based Graph Neural Network for 3D Building Reconstruction from Point Clouds](https://mlsanity.com/paper/2307.08636/) (2023)
- [Pairwise-Constrained Implicit Functions for 3D Human Heart Modelling](https://mlsanity.com/paper/2307.08716/) (2023)
- [VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation](https://mlsanity.com/paper/2603.18797/) (2026)
- [3D Compression Using Neural Fields](https://mlsanity.com/paper/2311.13009/) (2023)
- [Extracting Complex Topology from Multivariate Functional Approximation: Contours, Jacobi Sets, and Ridge-Valley Graphs](https://mlsanity.com/paper/2508.07637/) (2025)
- [CEI-3D: Collaborative Explicit-Implicit 3D Reconstruction for Realistic and Fine-Grained Object Editing](https://mlsanity.com/paper/2603.11810/) (2026)
- [Implicit Neural Representations: A Signal Processing Perspective](https://mlsanity.com/paper/2604.15047/) (2026)
- [VF-NeRF: Learning Neural Vector Fields for Indoor Scene Reconstruction](https://mlsanity.com/paper/2408.08766/) (2024)
- [Direct Topology Tracking in Continuous Implicit Models](https://mlsanity.com/paper/2609.12157/) (2026)
- [Projective Normal Fields: A Convex Optimization Method for Constructing Smooth UDFs](https://mlsanity.com/paper/2609.34784/) (2026)

## Abstract (arXiv)

Implicit fields have recently shown increasing success in representing and learning 3D shapes accurately. Signed distance fields and occupancy fields are decades old and still the preferred representations, both with well-studied properties, despite their restriction to closed surfaces. With neural networks, several other variations and training principles have been proposed with the goal to represent all classes of shapes. In this paper, we develop a novel and yet a fundamental representation considering unit vectors in 3D space and call it Vector Field (VF): at each point in ℝ3, VF is directed at the closest point on the surface. We theoretically demonstrate that VF can be easily transformed to surface density by computing the flux density. Unlike other standard representations, VF directly encodes an important physical property of the surface, its normal. We further show the advantages of VF representation, in learning open, closed, or multi-layered as well as piecewise planar surfaces. We compare our method on several datasets including ShapeNet where the proposed new neural implicit field shows superior accuracy in representing any type of shape, outperforming other standard methods. Code is available at https://github.com/edomel/ImplicitVF.