用新型径向基函数提升3D点云渲染效果，突破传统高斯模型限制。
DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions
- 引入衰减各向异性径向基函数，实现更灵活的3D重建核设计。
- 在相同训练速度和内存下，性能接近高斯方法，保真度指标相当。
- 适合追求渲染多样性与可扩展性的3D视觉研究者使用。
基于点阵列的3D重建方法因3D高斯点阵技术的兴起而受到关注，能高效生成高质量的新视角图像。这类方法通常采用指数族函数（如高斯函数）作为重建核，因其各向异性、投影简便及可微性优势。然而，该领域仍局限于指数族内的变体，对更广义的重建核探索不足，部分原因在于3D到2D投影难以解析积分。本文提出一类衰减各向异性径向基函数（DARBFs），其为马哈拉诺比距离的非负函数，通过近似高斯函数的闭式积分特性支持点阵操作。实验表明，不同DARBF核在训练收敛速度、内存占用上与高斯方法相当，且在PSNR、SSIM和LPIPS指标上表现相当。
原文摘要 · Abstract (English)
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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