Fourier Splatting: Generalized Fourier encoded primitives for scalable radiance fields
Authors: Mihnea-Bogdan Jurca, Bert Van hauwermeiren, Adrian Munteanu
Organizations: Vrije Universiteit Brussel, Brussels, Belgium · Technical University of Cluj-Napoca, Cluj-Napoca, Romania
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.
We introduce a probabilistic splat-based radiance field framework that retains the fast rasterization and test-time efficiency of 3D Gaussian Splatting (3DGS) while replacing heuristic primitive manipulation with gradient-based optimization of a volumetric probability density. Rather than relocating, splitting, or culling Gaussians via hand-tuned densification (e.g., ADC), we treat primitive locations as samples drawn from a persistent, learnable density. We instantiate this density using a novel, memory-efficient multi-scale hierarchical grid that enables end-to-end gradient-based optimization. To stabilize the optimization, we derive an unbiased gradient estimator with control variates that markedly reduces variance. By allowing probability mass to flow to where the loss demands, our framework eliminates brittle priors and naturally explores the volume, achieving state-of-the-art reconstruction quality on mip-NeRF 360 while preserving 3DGS-level rendering speed.
Mia Gaia Polansky, George Kopanas, Stephan Garbin +2
Recent radiance field methods represent scenes with 2D primitives that offer surface alignment and efficient rasterization, from Gaussian disks to triangles, yet all rely on convex boundaries: curved and concave structures demand excessive primitives. We introduce Deformable Triangle Splatting, which augments each triangle with K control points per edge, each parameterized by a single learnable scalar displacement that shifts the boundary inward or outward, enabling non-convex shape representation while preserving the three base vertices that define the 3D plane. To render these non-convex primitives differentiably, we design a rasterization pipeline in the triangle's barycentric coordinate space, ensuring view-consistent rendering. A winding number test determines whether each pixel lies inside the deformed primitive, and a window function controlled by two learnable parameters, sharpness and corner smoothness, together with a per-primitive scalar opacity, produces the smooth opacity transition from interior to boundary. Validation is done in a variety of real-world scenes, outperforming recent works based on non-volumetric primitives in terms of visual quality and versatility while still achieving competitive rendering efficiency.
Recent extensions of 3D Gaussian Splatting (3DGS) capture fine color details using hash-grid-based appearance parameterization but incur high computational cost during fragment rendering. We introduce a decoupled radiance representation that models low-frequency geometry and view dependent appearance features with 2D surfels while representing high-frequency textures via a view-independent spatial hash grid that is baked into a compact texture atlas. By including sparsity-enhancing optimizations that penalize semi-transparency and per-primitive falloff, our method aggressively prunes insignificant surfels and achieves significantly faster and sparser reconstructions than prior work. Exploiting geometric sparsity and efficient GPU texture mapping, our approach achieves up to a fivefold speedup over 3DGS while preserving state-of-the-art visual fidelity, enabling real-time 4K rendering at 60 FPS on consumer hardware.