Revisiting 3D Reconstruction Kernels as Low-Pass Filters

TL;DR

This paper introduces the Jinc kernel and modulated kernels for 3D reconstruction, addressing spectral overlap issues by providing ideal low-pass filtering to improve rendering accuracy.

Contribution

It proposes the Jinc kernel with an exact cutoff in the frequency domain and modulated kernels to balance spatial decay and spectral fidelity, advancing 3D reconstruction techniques.

Findings

Jinc kernel achieves ideal low-pass filtering with a sharp cutoff.

Modulated kernels improve spatial decay while maintaining spectral fidelity.

Experimental results show superior rendering performance with proposed kernels.

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.