NURBS Splatting: A Unified Differentiable Rendering Framework for Vector Graphics
Authors: Jingye Qiu, Shizhe Zhou
Organizations: Hunan University, Changsha, China
Abstract
Differentiable rendering of planar rational splines remains largely underexplored, despite their widespread use in vector graphics and design. Existing differentiable vector renderers primarily focus on Bézier curves and rely on analytic rasterization, which can suffer from gradient instability and limited flexibility. We propose NURBS Splatting, a unified framework that represents planar rational curves as continuous Gaussian fields. By sampling Gaussians along the curve parameter domain and inside closed regions, rendering is reformulated as a smooth accumulation process with stable gradients. Our method naturally supports long splines, rational weights, non-uniform knots, and closed-region filling. We demonstrate its effectiveness in calligraphy reconstruction, vectorization frameworks, and long-spline image abstraction, showing improved stability and reconstruction quality over existing approaches.
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
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.
Mihnea-Bogdan Jurca, Bert Van hauwermeiren, Adrian Munteanu
3D Gaussian Splatting (3DGS) enables high-quality real-time 3D rendering but faces challenges in efficiently scaling to ultra-dense scenes and high-resolution due to computational bottlenecks that limit its use in latency-sensitive applications. Instead of optimizing the splatting pipeline itself, we propose \textbf{3DGS3}, a unified post-rendering framework that jointly performs super sampling and frame interpolation through differentiable processing of low-resolution outputs to achieve both high-resolution and high-frame-rate rendering. Our \textbf{Gradient- -Aware Super Sampling (GASS)} module leverages the continuous differentiability of 3DGS to extract image gradients that guide a GRU-based refinement network to enable high-fidelity super sampling. Furthermore, a \textbf{Lightweight Temporal Frame Interpolation (LTFI)} module based on a compact U-Net-like backbone fuses temporal and differentiable spatial cues from consecutive frames to synthesize temporally coherent intermediate frames. Experiments on public datasets demonstrate that 3DGS3 achieves superior rendering efficiency and visual quality when compared with state-of-the-art methods and remains compatible with existing 3DGS acceleration techniques. The code will be publicly released upon acceptance.