DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions

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.