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 varying performances across selected DARB reconstruction kernels, achieving comparable training convergence and memory footprints, with on-par PSNR, SSIM, and LPIPS results.

翻译：随着3D高斯溅射技术的出现，基于溅射的三维重建方法因其能高效合成高质量新视角而广受欢迎。这类方法通常采用指数族函数（如高斯函数）作为重建核，因其具备各向异性、易于投影且在栅格化过程中可微的特性。然而，该领域目前仍局限于指数族函数内部的变体，广义重建核的研究尚未充分展开，部分原因在于三维到二维投影中缺乏易于积分的特性。有鉴于此，我们证明了一类衰减各向异性径向基函数——作为马氏距离的非负函数——能够通过近似高斯函数的闭式积分优势来支持溅射操作。基于这一新视角，我们展示了所选DARB重建核在不同性能指标上的表现，在训练收敛速度与内存占用方面达到可比水平，并在PSNR、SSIM和LPIPS指标上取得相当的结果。