# NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions

arXiv: https://arxiv.org/abs/2309.15426 · HTML: https://mlsanity.com/paper/2309.15426/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Builds on 70 of its 89 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 30 of 70)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [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)
- [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)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [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)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)

## Built on by (most cited first, 30 of 65)

- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [DNGaussian: Optimizing Sparse-View 3D Gaussian Radiance Fields with Global-Local Depth Normalization](https://mlsanity.com/paper/2403.06912/) (2024)
- [CoR-GS: Sparse-View 3D Gaussian Splatting via Co-Regularization](https://mlsanity.com/paper/2405.12110/) (2024)
- [Pixel-GS: Density Control with Pixel-aware Gradient for 3D Gaussian Splatting](https://mlsanity.com/paper/2403.15530/) (2024)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [Spec-Gaussian: Anisotropic View-Dependent Appearance for 3D Gaussian Splatting](https://mlsanity.com/paper/2402.15870/) (2024)
- [Structure-Aware Sparse-View X-ray 3D Reconstruction](https://mlsanity.com/paper/2311.10959/) (2023)
- [InstantSplat: Sparse-view Gaussian Splatting in Seconds](https://mlsanity.com/paper/2403.20309/) (2024)
- [MesonGS: Post-training Compression of 3D Gaussians via Efficient Attribute Transformation](https://mlsanity.com/paper/2409.09756/) (2024)
- [Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set](https://mlsanity.com/paper/2410.14189/) (2024)
- [GStex: Per-Primitive Texturing of 2D Gaussian Splatting for Decoupled Appearance and Geometry Modeling](https://mlsanity.com/paper/2409.12954/) (2024)
- [NARUTO: Neural Active Reconstruction from Uncertain Target Observations](https://mlsanity.com/paper/2402.18771/) (2024)
- [Lighting Every Darkness with 3DGS: Fast Training and Real-Time Rendering for HDR View Synthesis](https://mlsanity.com/paper/2406.06216/) (2024)
- [IntrinsicAvatar: Physically Based Inverse Rendering of Dynamic Humans from Monocular Videos via Explicit Ray Tracing](https://mlsanity.com/paper/2312.05210/) (2023)
- [EvGGS: A Collaborative Learning Framework for Event-based Generalizable Gaussian Splatting](https://mlsanity.com/paper/2405.14959/) (2024)
- [Efficient-NeRF2NeRF: Streamlining Text-Driven 3D Editing with Multiview Correspondence-Enhanced Diffusion Models](https://mlsanity.com/paper/2312.08563/) (2023)
- [3D Reconstruction with Fast Dipole Sums](https://mlsanity.com/paper/2405.16788/) (2024)
- [Implicit-Zoo: A Large-Scale Dataset of Neural Implicit Functions for 2D Images and 3D Scenes](https://mlsanity.com/paper/2406.17438/) (2024)
- [MiraGe: Editable 2D Images using Gaussian Splatting](https://mlsanity.com/paper/2410.01521/) (2024)
- [RayGauss: Volumetric Gaussian-Based Ray Casting for Photorealistic Novel View Synthesis](https://mlsanity.com/paper/2408.03356/) (2024)
- [Learnable Infinite Taylor Gaussian for Dynamic View Rendering](https://mlsanity.com/paper/2412.04282/) (2024)
- [PIG: Physics-Informed Gaussians as Adaptive Parametric Mesh Representations](https://mlsanity.com/paper/2412.05994/) (2024)
- [ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2312.04028/) (2023)
- [PINGS: Gaussian Splatting Meets Distance Fields within a Point-Based Implicit Neural Map](https://mlsanity.com/paper/2502.05752/) (2025)
- [Grounding and Enhancing Grid-based Models for Neural Fields](https://mlsanity.com/paper/2403.20002/) (2024)
- [E-3DGS: Event-Based Novel View Rendering of Large-Scale Scenes Using 3D Gaussian Splatting](https://mlsanity.com/paper/2502.10827/) (2025)
- [VideoLifter: Lifting Videos to 3D with Fast Hierarchical Stereo Alignment](https://mlsanity.com/paper/2501.01949/) (2025)
- [Sparfels: Fast Reconstruction from Sparse Unposed Imagery](https://mlsanity.com/paper/2505.02178/) (2025)
- [Optimizing Rank for High-Fidelity Implicit Neural Representations](https://mlsanity.com/paper/2512.14366/) (2025)

## Abstract (arXiv)

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.