# Neural Directional Encoding for Efficient and Accurate View-Dependent Appearance Modeling

arXiv: https://arxiv.org/abs/2405.14847 · HTML: https://mlsanity.com/paper/2405.14847/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 64 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 30 of 51)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [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)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [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)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [One-2-3-45: Any Single Image to 3D Mesh in 45 Seconds without Per-Shape Optimization](https://mlsanity.com/paper/2306.16928/) (2023)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)

## Built on by (most cited first, 16 of 16)

- [EnvGS: Modeling View-Dependent Appearance with Environment Gaussian](https://mlsanity.com/paper/2412.15215/) (2024)
- [Ref-GS: Directional Factorization for 2D Gaussian Splatting](https://mlsanity.com/paper/2412.00905/) (2024)
- [LIRM: Large Inverse Rendering Model for Progressive Reconstruction of Shape, Materials and View-dependent Radiance Fields](https://mlsanity.com/paper/2504.20026/) (2025)
- [Generative Multiview Relighting for 3D Reconstruction under Extreme Illumination Variation](https://mlsanity.com/paper/2412.15211/) (2024)
- [Spherical Voronoi: Directional Appearance as a Differentiable Partition of the Sphere](https://mlsanity.com/paper/2512.14180/) (2025)
- [ProbeSDF: Light Field Probes for Neural Surface Reconstruction](https://mlsanity.com/paper/2412.10084/) (2024)
- [Inverse Rendering using Multi-Bounce Path Tracing and Reservoir Sampling](https://mlsanity.com/paper/2406.16360/) (2024)
- [Car-GS: Addressing Reflective and Transparent Surface Challenges in 3D Car Reconstruction](https://mlsanity.com/paper/2501.11020/) (2025)
- [PBIR-NIE: Glossy Object Capture under Non-Distant Lighting](https://mlsanity.com/paper/2408.06878/) (2024)
- [RISE-SDF: a Relightable Information-Shared Signed Distance Field for Glossy Object Inverse Rendering](https://mlsanity.com/paper/2409.20140/) (2024)
- [NeRFs are Mirror Detectors: Using Structural Similarity for Multi-View Mirror Scene Reconstruction with 3D Surface Primitives](https://mlsanity.com/paper/2501.04074/) (2025)
- [8DNA: 8D Neural Asset Light Transport by Distribution Learning](https://mlsanity.com/paper/2604.25129/) (2026)
- [Spectral Prefiltering of Neural Fields](https://mlsanity.com/paper/2510.08394/) (2025)
- [Augmented Radiance Field: A General Framework for Enhanced Gaussian Splatting](https://mlsanity.com/paper/2602.19916/) (2026)
- [PhyGaP: Physically-Grounded Gaussians with Polarization Cues](https://mlsanity.com/paper/2603.14001/) (2026)
- [Gaussian Splatting with Reflections Guided by What is Seen](https://mlsanity.com/paper/2610.13757/) (2026)

## Abstract (arXiv)

Novel-view synthesis of specular objects like shiny metals or glossy paints remains a significant challenge. Not only the glossy appearance but also global illumination effects, including reflections of other objects in the environment, are critical components to faithfully reproduce a scene. In this paper, we present Neural Directional Encoding (NDE), a view-dependent appearance encoding of neural radiance fields (NeRF) for rendering specular objects. NDE transfers the concept of feature-grid-based spatial encoding to the angular domain, significantly improving the ability to model high-frequency angular signals. In contrast to previous methods that use encoding functions with only angular input, we additionally cone-trace spatial features to obtain a spatially varying directional encoding, which addresses the challenging interreflection effects. Extensive experiments on both synthetic and real datasets show that a NeRF model with NDE (1) outperforms the state of the art on view synthesis of specular objects, and (2) works with small networks to allow fast (real-time) inference. The project webpage and source code are available at: urlhttps://lwwu2.github.io/nde/.