Fourier Splatting:
Generalized Fourier Encoded Primitives for Scalable Radiance Fields

Abstract

Novel view synthesis has recently been revolutionized by 3D Gaussian Splatting (3DGS), which enables real-time rendering through explicit primitive rasterization. However, existing methods tie visual fidelity strictly to the number of primitives: quality downscaling is achieved only through pruning primitives. We propose the first inherently scalable primitive for radiance field rendering. Fourier Splatting employs scalable primitives with arbitrary closed shapes obtained by parameterizing planar surfels with Fourier encoded descriptors. This formulation allows a single trained model to be rendered at varying levels of detail simply by truncating Fourier coefficients at runtime. To facilitate stable optimization, we employ a straight-through estimator for gradient extension beyond the primitive boundary, and introduce HYDRA, a densification strategy that decomposes complex primitives into simpler constituents within the MCMC framework. Our method achieves state-of-the-art rendering quality among planar-primitive frameworks and comparable perceptual metrics compared to leading volumetric representations on standard benchmarks, providing a versatile solution for bandwidth-constrained high-fidelity rendering.

Fourier Boundary Construction

Starting from a circle ($K\!=\!1$), each additional frequency component progressively deforms the boundary into complex shapes.

HYDRA Densification

A learned MLP detects lobes in the parent boundary, then predicts child primitives that together reconstruct the original shape.

Visual Comparisons

Drag the dividers to compare all four methods simultaneously.

Qualitative Results

Close-up comparisons on Tanks & Temples and Mip-NeRF 360 scenes.

Quantitative Results

Among planar primitives: best, second best.

Level-of-Detail Scaling

A single trained model rendered at varying levels of detail by truncating Fourier coefficients at runtime vs. Octree-GS pruning levels.

Mesh Reconstruction (DTU)

Interact with the reconstructed meshes. Drag to rotate, scroll to zoom.

Surface Normals (Mip-NeRF 360)

Qualitative surface alignment on outdoor Mip-NeRF 360 scenes.

Citation

@article{jurca2026fourier,
  title={Fourier Splatting: Generalized Fourier encoded primitives for scalable radiance fields},
  author={Jurca, Mihnea-Bogdan and Munteanu, Adrian and others},
  journal={arXiv preprint arXiv:2603.19834},
  year={2026}
}