Fourier Splatting: Generalized Fourier encoded primitives for scalable radiance fields

Novel view synthesis has recently been revolutionized by 3DGaussian Splatting (3DGS), which enables real-time rendering throughexplicit primitive rasterization. However, existing methods tie visual fi-delity strictly to the number of primitives: quality downscaling is achievedonly through pruning primitives. We propose the first inherently scal-able primitive for radiance field rendering. Fourier Splatting employsscalable primitives with arbitrary closed shapes obtained by parameter-izing planar surfels with Fourier encoded descriptors. This formulationallows a single trained model to be rendered at varying levels of de-tail simply by truncating Fourier coefficients at runtime. To facilitatestable optimization, we employ a straight-through estimator for gradi-ent extension beyond the primitive boundary, and introduce HYDRA,a densification strategy that decomposes complex primitives into sim-pler constituents within the MCMC framework. Our method achievesstate-of-the-art rendering quality among planar-primitive frameworksand comparable perceptual metrics compared to leading volumetric rep-resentations on standard benchmarks, providing a versatile solution forbandwidth-constrained high-fidelity rendering.