DARB-Splatting: 通过衰减各向异性径向基函数实现通用的Splatting
DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions
AI总结：
DARB-Splatting通过衰减各向异性径向基函数实现通用的Splatting，实现了与高斯函数相近的重建性能和效率。
摘要：
基于Splatting的3D重建方法随着3D高斯Splatting的出现而变得流行，能够高效合成高质量的新型视角。这些方法通常依赖于指数族函数，如高斯函数，作为重建核，因为它们具有各向异性、易于投影和在光栅化中的可微性。然而，该领域仍局限于指数族的变种，通用的重建核大多未被探索，部分原因是3D到2D投影中缺乏简单的可积性。在此背景下，我们证明了一类衰减各向异性径向基函数（DARBFs），它们是Mahalanobis距离的非负函数，通过近似高斯函数的闭式积分优势来支持Splatting。从这一新的视角出发，我们展示了在选定的DARB重建核上表现各异，实现了与训练收敛性和内存占用相当的性能，PSNR、SSIM和LPIPS结果也相当。
英文摘要：
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.
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