Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized Exponential Splatting), a novel representation that employs Generalized Exponential Function (GEF) to model 3D scenes, requiring far fewer particles to represent a scene and thus significantly outperforming Gaussian Splatting methods in efficiency with a plug-and-play replacement ability for Gaussian-based utilities. GES is validated theoretically and empirically in both principled 1D setup and realistic 3D scenes. It is shown to represent signals with sharp edges more accurately, which are typically challenging for Gaussians due to their inherent low-pass characteristics. Our empirical analysis demonstrates that GEF outperforms Gaussians in fitting natural-occurring signals (e.g. squares, triangles, and parabolic signals), thereby reducing the need for extensive splitting operations that increase the memory footprint of Gaussian Splatting. With the aid of a frequency-modulated loss, GES achieves competitive performance in novel-view synthesis benchmarks while requiring less than half the memory storage of Gaussian Splatting and increasing the rendering speed by up to 39%. The code is available on the project website https://abdullahamdi.com/ges .

翻译：三维高斯飞溅技术的进步显著加速了三维重建与生成任务。然而，该方法常需大量高斯函数，导致内存占用巨大。本文提出GES（广义指数飞溅法），一种采用广义指数函数（GEF）建模三维场景的全新表示方法，能以更少的粒子数量表示场景，在效率上显著优于高斯飞溅方法，并具备即插即用替换高斯基础工具的能力。本文在原理性一维实验与逼真三维场景中，从理论与实证两方面验证了GES的有效性。结果表明，GES能更精确表示包含尖锐边缘的信号——这类信号因高斯函数固有的低通特性而难以处理。我们的实证分析显示，GEF在拟合自然信号（如方波、三角波和抛物波）时优于高斯函数，从而减少了导致高斯飞溅内存占用的分裂操作。借助频率调制损失函数，GES在新视角合成基准测试中达到竞争性性能，同时内存存储需求不足高斯飞溅的一半，渲染速度提升高达39%。代码已发布在项目网站上：https://abdullahamdi.com/ges。