Revisiting 3D Reconstruction Kernels as Low-Pass Filters

2026-01-25

AI Summary

This work addresses the degradation of 3D reconstruction quality caused by spectral aliasing due to the periodic extension of frequency content induced by discrete sampling. Viewing the problem through the lens of signal processing, the authors model the reconstruction kernel as a low-pass filter to effectively isolate the baseband spectrum and suppress aliasing artifacts. To this end, they propose the Jinc kernel, which exhibits an ideal cutoff characteristic in the frequency domain, and further design a modulated variant that strikes a balance between spatial decay rate and spectral fidelity. Experimental results demonstrate that both the Jinc kernel and its modulated form significantly outperform conventional reconstruction kernels—such as Gaussian, exponential, and Student’s t—in terms of rendering quality, thereby validating the efficacy and superiority of a frequency-domain-guided kernel design.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• 3D reconstruction
• spectral aliasing
• low-pass filtering
• discrete sampling
• frequency-domain fidelity

Innovation

• Jinc kernel
• low-pass filter
• 3D reconstruction
• spectral aliasing
• modulated kernels