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

TL;DR

This paper introduces DARB-Splatting, a novel 3D reconstruction method using decaying anisotropic radial basis functions, expanding the kernel options beyond Gaussian functions while maintaining high-quality view synthesis.

Contribution

It proposes a new class of reconstruction kernels based on decaying anisotropic radial basis functions that support splatting with integrability advantages over traditional Gaussian kernels.

Findings

Comparable training convergence and memory footprint to Gaussian-based methods

Achieves similar PSNR, SSIM, and LPIPS metrics

Demonstrates the versatility of DARB kernels in 3D reconstruction

Abstract

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.