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：三维高斯泼溅技术的进展显著加速了三维重建与生成过程。然而，该方法可能需要大量高斯函数，导致内存占用巨大。本文提出GES（广义指数泼溅），这是一种采用广义指数函数对三维场景进行建模的新型表示方法，其所需粒子数量远少于场景表示需求，因此以即插即用的方式替代基于高斯的实用工具时，在效率上显著优于高斯泼溅方法。GES在理论一维场景与真实三维场景中均得到理论与实证验证。该方法被证明能更精确地表示具有尖锐边缘的信号——这类信号因高斯函数固有的低通特性通常难以处理。我们的实证分析表明，广义指数函数在拟合自然信号（如方波、三角波和抛物线信号）方面优于高斯函数，从而减少了对大量分裂操作的依赖，这些操作会增加高斯泼溅的内存占用。借助调频损失函数的辅助，GES在新视角合成基准测试中取得了具有竞争力的性能，同时所需内存存储不到高斯泼溅的一半，并将渲染速度提升最高达39%。代码已在项目网站https://abdullahamdi.com/ges 公开。