Uniform Resampling vs. Image Blur: Aliasing Approximation via Isotropic Gaussian Filtering
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916727859707904 |
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| author | Arslan, Suayb S. Vogelsang, Lukas Fux, Michal Sinha, Pawan |
| author_facet | Arslan, Suayb S. Vogelsang, Lukas Fux, Michal Sinha, Pawan |
| contents | 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 $σ$ and the reduction factor $m$ (also called downsampling ratio) satisfy an approximate $m \approx 2 σ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform Resampling vs. Image Blur: Aliasing Approximation via Isotropic Gaussian Filtering Arslan, Suayb S. Vogelsang, Lukas Fux, Michal Sinha, Pawan Signal Processing 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 $σ$ and the reduction factor $m$ (also called downsampling ratio) satisfy an approximate $m \approx 2 σ$ 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. |
| title | Uniform Resampling vs. Image Blur: Aliasing Approximation via Isotropic Gaussian Filtering |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2502.11605 |