Affine-Equivariant Kernel Space Encoding for NeRF Editing

Mikołaj Zieliński1, Krzysztof Byrski2, Tomasz Szczepanik2, Dominik Belter1 Przemysław Spurek2, 3
1Poznan University of Technology, 2Jagiellonian University, 3IDEAS Research Institute
Paper arXiv Code Data Demo Data
Teaser Image

EKS allows for editing of NeRFs by moving jointly trained Gaussians.

Abstract

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.

Editing

EKS makes it super easy to edit 3D scenes - just move or tweak the Gaussians directly! In this demo, the Gaussians are visually exaggerated to show how they follow the motion of the dozer and animate the scoop, all driven by simple mesh deformation.

Manual Edits

EKS lets you manually adjust parts of a scene by moving Gaussians directly. Here, we tweaked the hotdogs on a plate to make it fly just by dragging points around.

Physical Simulations

With EKS, you can apply physical simulations like soft body dynamics or cloth drops. This clip shows a Lego dozer being dropped, with the deformation driven entirely by a mesh-based simulation.

Real World Edits

This section shows two examples of real-world edits using EKS. In one demo, a plant pot falls and bounces off a tilted table as part of a physics simulation. In the other, a soft plasticine Lego dozer is squashed by applying a force.

Interactive Demo

This demo lets you play with a pre-rendered animation of a fox from InstantNGP. Use the slider below to smoothly adjust the fox’s head position.

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NeuralEditor

In our paper, we compare EKS with NeuralEditor. Here, you can see the NeRF-Synthetic objects edited in the same way.

Citation

If you find this work useful, please consider citing it: 

@misc{zielinski2025eks,
      title     = {Affine-Equivariant Kernel Space Encoding for NeRF Editing},
      author    = {Miko\l{}aj Zieli\'{n}ski and Krzysztof Byrski and Tomasz Szczepanik and Dominik Belter and Przemys\l{}aw Spurek},
      year      = {2025},
      eprint    = {2508.02831},
      archivePrefix = {arXiv},
      primaryClass  = {cs.CV},
      url       = {https://arxiv.org/abs/2508.02831}
    }