# Beyond Spherical Harmonics: Rethinking Appearance Models for Radiance Reconstruction

arXiv: https://arxiv.org/abs/2606.09794 · HTML: https://mlsanity.com/paper/2606.09794/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 88 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 30 of 39)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [NeRF in the Dark: High Dynamic Range View Synthesis from Noisy Raw Images](https://mlsanity.com/paper/2111.13679/) (2021)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [Mixture of Volumetric Primitives for Efficient Neural Rendering](https://mlsanity.com/paper/2103.01954/) (2021)
- [BakedSDF: Meshing Neural SDFs for Real-Time View Synthesis](https://mlsanity.com/paper/2302.14859/) (2023)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [A Hierarchical 3D Gaussian Representation for Real-Time Rendering of Very Large Datasets](https://mlsanity.com/paper/2406.12080/) (2024)
- [3D Gaussian Ray Tracing: Fast Tracing of Particle Scenes](https://mlsanity.com/paper/2407.07090/) (2024)
- [3DGUT: Enabling Distorted Cameras and Secondary Rays in Gaussian Splatting](https://mlsanity.com/paper/2412.12507/) (2024)
- [Neural Point Catacaustics for Novel-View Synthesis of Reflections](https://mlsanity.com/paper/2301.01087/) (2023)
- [Spec-Gaussian: Anisotropic View-Dependent Appearance for 3D Gaussian Splatting](https://mlsanity.com/paper/2402.15870/) (2024)
- [Deformable Beta Splatting](https://mlsanity.com/paper/2501.18630/) (2025)
- [Don't Splat your Gaussians: Volumetric Ray-Traced Primitives for Modeling and Rendering Scattering and Emissive Media](https://mlsanity.com/paper/2405.15425/) (2024)
- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [GlossyGS: Inverse Rendering of Glossy Objects with 3D Gaussian Splatting](https://mlsanity.com/paper/2410.13349/) (2024)
- [Cinematic Gaussians: Real-Time HDR Radiance Fields with Depth of Field](https://mlsanity.com/paper/2406.07329/) (2024)

## Built on by (most cited first, 1 of 1)

- [Compact Neural Appearance Models for Efficient Gaussian Splatting](https://mlsanity.com/paper/2609.05255/) (2026)

## Abstract (arXiv)

View-dependent appearance modeling remains a challenging problem in novel-view synthesis and reconstruction. Accurately representing complex angular effects often requires substantial memory and computational resources. For new learning-based methods, a common approach is to rely on SH. However, capturing high-frequency phenomena such as specular reflections demands high-order expansions, which increase memory usage and computational cost. Consequently, most methods employ low-order SH, which limits the ability to model complex view-dependent effects, resulting in overly smooth or diffuse representations. To address these limitations, we systematically evaluate a wide range of spherical functions in the context of scene reconstruction. Some of them are introduced to graphics and computer vision for the first time in this paper. Based on the insights from the experiment, we develop a novel spherical formulation, the Normalized Anisotropic Spherical Gabor function that enables efficient modeling and learning of high-frequency appearance effects while maintaining compact representation. Compared to existing approaches, our function achieves higher-quality reconstruction of view-dependent phenomena such as glints, while being up to five times more memory-efficient and more efficient to evaluate. We validate its performance in radiance-field reconstruction tasks.