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%.
3D高斯喷溅的进步显著加速了3D重建和生成。然而，它可能需要大量的高斯函数，这将产生大量的内存占用。本文介绍了GES（广义指数喷溅），一种新颖的表示方法，采用广义指数函数（GEF）来模拟3D场景，需要远少于高斯喷溅方法的粒子来表示场景，因此在效率上显著超越高斯喷溅方法，并且具有替代基于高斯的工具的即插即用能力。GES在原理上和实证上都在一维设置和现实3D场景中得到了验证。它被证明能更准确地表示具有尖锐边缘的信号，这对于高斯函数来说通常是个挑战，因为它们固有的低通特性。我们的实证分析表明，GEF在拟合自然出现的信号（例如，正方形、三角形和抛物线信号）方面优于高斯函数，从而减少了需要增加高斯喷溅内存占用的广泛分割操作的需求。借助频率调制损失，GES在新视图合成基准测试中实现了竞争性能，同时所需的内存存储量不到高斯喷溅的一半，并将渲染速度提高了多达39%。