Revisiting 3D Reconstruction Kernels as Low-Pass Filters

TL;DR

This work reframes 3D reconstruction as a signal-processing task, identifying the periodic spectral extension from discrete sampling as the core aliasing challenge. It introduces the Jinc kernel, derived from the 3D ideal low-pass filter, to achieve ideal baseband filtering, and couples it with a frequency modulation strategy to recover practical spatial decay. The proposed Jinc Splatting and its modulated variants demonstrate superior performance in novel-view synthesis against Gaussian- and Student's-t-based kernels, reducing aliasing while maintaining rendering efficiency. The approach offers a principled path to anti-aliasing in explicit 3D representations and highlights trade-offs between spatial support and frequency fidelity, with potential extensions to dynamic scenes and feed-forward pipelines.

Abstract

3D reconstruction is to recover 3D signals from the sampled discrete 2D pixels, with the goal to converge continuous 3D spaces. In this paper, we revisit 3D reconstruction from the perspective of signal processing, identifying the periodic spectral extension induced by discrete sampling as the fundamental challenge. Previous 3D reconstruction kernels, such as Gaussians, Exponential functions, and Student's t distributions, serve as the low pass filters to isolate the baseband spectrum. However, their unideal low-pass property results in the overlap of high-frequency components with low-frequency components in the discrete-time signal's spectrum. To this end, we introduce Jinc kernel with an instantaneous drop to zero magnitude exactly at the cutoff frequency, which is corresponding to the ideal low pass filters. As Jinc kernel suffers from low decay speed in the spatial domain, we further propose modulated kernels to strick an effective balance, and achieves superior rendering performance by reconciling spatial efficiency and frequency-domain fidelity. Experimental results have demonstrated the effectiveness of our Jinc and modulated kernels.

Figures (5)

• Figure 1: Frequency analysis of 3D reconstruction kernels. The table systematically summarizes key aspects for five kernel, including point clouds, Gaussians kerbl20233dgaussiansplattingrealtime, exponential function GES2024CVPR, student's t distribution zhu20253dstudentsplattingscooping, Jinc function and modulated kernels. This comparison aims to provide a qualitative reference for evaluating the spectral behavior of different kernels in 3D reconstruction, facilitating the design of optimal kernels for anti-aliasing, high-frequency information preservation, and low-frequency structural integrity.
• Figure 2: The influence of spatial decay speed. Our Jinc-based method suffers from rectangular artifacts due to premature truncation, while Gaussians benefit from its rapid decay without such artifacts. Our Modulated Gaussian Splatting method strikes an effective balance, and achieves superior rendering performance by reconciling spatial efficiency and frequency-domain fidelity.
• Figure 3: Modulation of Gaussian kernels. A proper frequency shift allows the Gaussian kernel to approximate an ideal filter.
• Figure 4: Qualitative comparison. We visualize the rendering results of based kernels kerbl20233dgaussiansplattingrealtimezhu20253dstudentsplattingscooping and our modulated kernels.
• Figure 5: The sketch map of half of the ILPF.