From ex(p) to poly: Gaussian Splatting with Polynomial Kernels

TL;DR

This paper introduces a polynomial kernel for Gaussian Splatting that improves computational efficiency and performance while maintaining dataset compatibility, enabling broader adoption and hardware benefits.

Contribution

It proposes a polynomial kernel with ReLU for Gaussian Splatting, enhancing efficiency and performance without dataset incompatibility issues.

Findings

Performance improved by 4-15%

Compatible with existing datasets

Negligible impact on image quality

Abstract

Recent advancements in Gaussian Splatting (3DGS) have introduced various modifications to the original kernel, resulting in significant performance improvements. However, many of these kernel changes are incompatible with existing datasets optimized for the original Gaussian kernel, presenting a challenge for widespread adoption. In this work, we address this challenge by proposing an alternative kernel that maintains compatibility with existing datasets while improving computational efficiency. Specifically, we replace the original exponential kernel with a polynomial approximation combined with a ReLU function. This modification allows for more aggressive culling of Gaussians, leading to enhanced performance across different 3DGS implementations. Our results show a notable performance improvement of 4 to 15% with negligible impact on image quality. We also provide a detailed mathematical analysis of the new kernel and discuss its potential benefits for 3DGS implementations on NPU hardware.