Reproduce “From ex(p) to poly: Gaussian Splatting with Polynomial Kernels” on OpenResearch

About this paper

Joerg H. Mueller, Martin Winter, Markus Steinberger

The method replaces the exponential contribution kernel in 3D Gaussian Splatting with a first-order polynomial clipped at zero, enabling tighter, opacity-aware culling without retraining existing Gaussian scenes. Across 13 evaluated scenes, Faster-GS frame time falls from 1.43 milliseconds to 1.30 milliseconds, a reported 10% improvement. Image-quality scores decline slightly, which the authors describe as perceptually negligible.

Key insights

• The primary driver of performance improvements in 3DGS, when using polynomial kernels, stems from the tighter culling strategies enabled by their finite support, rather than solely from the direct computational simplification of the kernel function.
• Lower-order polynomial approximations (first and second-order) can achieve perceptually negligible quality degradation, suggesting that the precise mathematical form of the kernel's activation function is less critical than efficient geometric representation and culling for perceived fidelity.
• The use of polynomial and ReLU functions aligns well with the architectural characteristics of Neural Processing Units (NPUs), indicating strong potential for further hardware acceleration on such platforms.

Summary by alphaXiv.