Splatting-based 3D reconstruction methods have gained popularity with the advent of 3D Gaussian Splatting, efficiently synthesizing high-quality novel views. These methods commonly resort to using exponential family functions, such as the Gaussian function, as reconstruction kernels due to their anisotropic nature, ease of projection, and differentiability in rasterization. However, the field remains restricted to variations within the exponential family, leaving generalized reconstruction kernels largely underexplored, partly due to the lack of easy integrability in 3D to 2D projections. In this light, we show that a class of decaying anisotropic radial basis functions (DARBFs), which are non-negative functions of the Mahalanobis distance, supports splatting by approximating the Gaussian function's closed-form integration advantage. With this fresh perspective, we demonstrate up to 34% faster convergence during training and a 15% reduction in memory consumption across various DARB reconstruction kernels, while maintaining comparable PSNR, SSIM, and LPIPS results. We will make the code available.

本研究解决了现有基于Splatting的3D重建方法在重建内核多样性方面的不足。通过引入衰减各向异性径向基函数（DARBFs），研究展示了这些函数在训练期间能够实现高达34%的收敛速度提升，并能将内存消耗降低15%，同时保持相似的重建质量。这一新方法使得3D到2D投影的整合变得更加高效，拓展了Splatting技术的应用潜力。

衰减各向异性径向基函数的泛化：DARB-Splatting方法