# Affine-Equivariant Kernel Space Encoding for NeRF Editing

arXiv: https://arxiv.org/abs/2508.02831 · HTML: https://mlsanity.com/paper/2508.02831/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 51 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 30 of 44)

- [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)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Instruct-NeRF2NeRF: Editing 3D Scenes with Instructions](https://mlsanity.com/paper/2303.12789/) (2023)
- [HumanNeRF: Free-viewpoint Rendering of Moving People from Monocular Video](https://mlsanity.com/paper/2201.04127/) (2022)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [Decomposing NeRF for Editing via Feature Field Distillation](https://mlsanity.com/paper/2205.15585/) (2022)
- [CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fields](https://mlsanity.com/paper/2112.05139/) (2021)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [NeuMesh: Learning Disentangled Neural Mesh-based Implicit Field for Geometry and Texture Editing](https://mlsanity.com/paper/2207.11911/) (2022)
- [NeRF for Outdoor Scene Relighting](https://mlsanity.com/paper/2112.05140/) (2021)
- [SINE: Semantic-driven Image-based NeRF Editing with Prior-guided Editing Field](https://mlsanity.com/paper/2303.13277/) (2023)
- [Deforming Radiance Fields with Cages](https://mlsanity.com/paper/2207.12298/) (2022)
- [SKED: Sketch-guided Text-based 3D Editing](https://mlsanity.com/paper/2303.10735/) (2023)
- [Forward Flow for Novel View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2309.17390/) (2023)
- [ViCA-NeRF: View-Consistency-Aware 3D Editing of Neural Radiance Fields](https://mlsanity.com/paper/2402.00864/) (2024)
- [Removing Objects From Neural Radiance Fields](https://mlsanity.com/paper/2212.11966/) (2022)
- [CoNeRF: Controllable Neural Radiance Fields](https://mlsanity.com/paper/2112.01983/) (2021)
- [NeRFiller: Completing Scenes via Generative 3D Inpainting](https://mlsanity.com/paper/2312.04560/) (2023)
- [Control-NeRF: Editable Feature Volumes for Scene Rendering and Manipulation](https://mlsanity.com/paper/2204.10850/) (2022)
- [PIE-NeRF: Physics-based Interactive Elastodynamics with NeRF](https://mlsanity.com/paper/2311.13099/) (2023)
- [NeuPhysics: Editable Neural Geometry and Physics from Monocular Videos](https://mlsanity.com/paper/2210.12352/) (2022)
- [NeuralEditor: Editing Neural Radiance Fields via Manipulating Point Clouds](https://mlsanity.com/paper/2305.03049/) (2023)

## Built on by (most cited first, 4 of 4)

- [GS-Verse: Mesh-based Gaussian Splatting for Physics-aware Interaction in Virtual Reality](https://mlsanity.com/paper/2510.11878/) (2025)
- [IRIS: Intersection-aware Ray-based Implicit Editable Scenes](https://mlsanity.com/paper/2603.15368/) (2026)
- [Floating Radiance Networks](https://mlsanity.com/paper/2608.05920/) (2026)
- [ORCA: Occlusion-Aware Refinement and Completion for Novel View Synthesis](https://mlsanity.com/paper/2609.17450/) (2026)

## Abstract (arXiv)

Neural scene representations achieve high-fidelity rendering by encoding 3D scenes as continuous functions, but their latent spaces are typically implicit and globally entangled, making localized editing and physically grounded manipulation difficult. While several works introduce explicit control structures or point-based latent representations to improve editability, these approaches often suffer from limited locality, sensitivity to deformations, or visual artifacts. In this paper, we introduce Affine-Equivariant Kernel Space Encoding (EKS), a spatial encoding for neural radiance fields that provides localized, deformation-aware feature representations. Instead of querying latent features directly at discrete points or grid vertices, our encoding aggregates features through a field of anisotropic Gaussian kernels, each defining a localized region of influence. This kernel-based formulation enables stable feature interpolation under spatial transformations while preserving continuity and high reconstruction quality. To preserve detail without sacrificing editability, we further propose a training-time feature distillation mechanism that transfers information from multi-resolution hash grid encodings into the kernel field, yielding a compact and fully grid-free representation at inference. This enables intuitive, localized scene editing directly via Gaussian kernels without retraining, while maintaining high-quality rendering. The code can be found under (https://github.com/MikolajZielinski/eks)