Uniform Resampling vs. Image Blur: Aliasing Approximation via Isotropic Gaussian Filtering

TL;DR

This paper models aliasing distortion in image downsampling as isotropic Gaussian low-pass filtering, establishing a relationship between filter standard deviation and downsampling ratio, supported by theoretical and empirical evidence.

Contribution

It introduces a novel approximation of aliasing distortion via Gaussian filtering and derives a practical relationship between filter parameters and downsampling ratio.

Findings

The relationship m ≈ 2σ accurately models aliasing distortion.

Empirical validation on face datasets and TinyImageNet supports the theoretical model.

Gaussian low-pass filtering effectively approximates aliasing effects in image resampling.

Abstract

One of the key approximations to range simulation is downscaling the image, dictated by the natural trigonometric relationships that arise due to long-distance viewing. It is well-known that standard downsampling applied to an image without prior low-pass filtering leads to a type of signal distortion called \textit{aliasing}. In this study, we aim at modeling the distortion due to aliasing and show that a downsampled/upsampled image after an interpolation process can be very well approximated through the application of isotropic Gaussian low-pass filtering to the original image. In other words, the distortion due to aliasing can approximately be generated by low-pass filtering the image with a carefully determined cut-off frequency. We have found that the standard deviation of the isotropic Gaussian kernel $\sigma$ and the reduction factor $m$ (also called downsampling ratio) satisfy an approximate $m \approx 2 \sigma$ relationship. We provide both theoretical and practical arguments using two relatively small face datasets (Chicago DB, LRFID) as well as TinyImageNet to corroborate this empirically observed relationship.