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.
基于 Splatting 的 3D 重建方法随着 3D Gaussian Splatting 的出现而广受欢迎，能够高效地合成高质量的新视角。这些方法通常使用指数族函数（如高斯函数）作为重建核，因其各向异性、易于投影以及在光栅化中的可微性。然而，该领域的研究主要局限于指数族函数的变体，对通用重建核的探索相对较少，部分原因是缺乏简单的 3D 到 2D 投影积分方法。在此背景下，我们表明，一类衰减的各向异性径向基函数（DARBFs），作为 Mahalanobis 距离的非负函数，通过近似高斯函数的闭式积分优势，能够支持 Splatting 操作。通过这种全新的视角，我们展示了在不同的 DARBF 重建核中，训练收敛速度提高了多达 34%，内存消耗减少了 15%，同时在 PSNR、SSIM 和 LPIPS 结果上保持了可比的表现。