基于二维自适应Whittaker-Shannon的缩放

Carlo Ciulla, Blerta Shabani, Farouk Yahaya
{"title":"基于二维自适应Whittaker-Shannon的缩放","authors":"Carlo Ciulla,&nbsp;Blerta Shabani,&nbsp;Farouk Yahaya","doi":"10.1002/appl.202400018","DOIUrl":null,"url":null,"abstract":"<p>In this work, we introduce a novel image zooming methodology that transitions from a nonadaptive Sin-based approach to an adaptive Sinc-based zooming technique. The two techniques base their theoretical foundation on the Whittaker–Shannon interpolation formula and the Nyquist theorem. The evolution into adaptive Sinc-based zoom is accomplished through the use of two novel concepts: (1) the pixel-local scaled k-space and (2) the k-space filtering sigmoidal function. The pixel-local scaled k-space is the standardized and scaled k-space magnitude of the image to zoom. The k-space filtering sigmoidal function scales the pixel-local scaled k-space values into the numerical interval [0, 1]. Using these two novel concepts, the Whittaker–Shannon interpolation formula is elaborated and used to zoom images. Zooming is determined by the shape of the Sinc functions in the Whittaker–Shannon interpolation formula, which, in turn, depends on the combined effect of the pixel-local scaled k-space, the sampling rate, and the k-space filtering sigmoidal function. The primary outcome of this research demonstrates that the Whittaker–Shannon interpolation formula can achieve successful zooms for values of the sampling rate significantly greater than the bandwidth. Conversely, when the sampling rate is much greater than the bandwidth, the nonadaptive technique fails to perform the zoom correctly. The conclusion is that the k-space filtering sigmoidal function is identified as the crucial parameter in the adaptive Sinc-based zoom technique. The implications of this research extend to Sinc-based image zooming applications.</p>","PeriodicalId":100109,"journal":{"name":"Applied Research","volume":"3 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/appl.202400018","citationCount":"0","resultStr":"{\"title\":\"Two-dimensional adaptive Whittaker–Shannon Sinc-based zooming\",\"authors\":\"Carlo Ciulla,&nbsp;Blerta Shabani,&nbsp;Farouk Yahaya\",\"doi\":\"10.1002/appl.202400018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work, we introduce a novel image zooming methodology that transitions from a nonadaptive Sin-based approach to an adaptive Sinc-based zooming technique. The two techniques base their theoretical foundation on the Whittaker–Shannon interpolation formula and the Nyquist theorem. The evolution into adaptive Sinc-based zoom is accomplished through the use of two novel concepts: (1) the pixel-local scaled k-space and (2) the k-space filtering sigmoidal function. The pixel-local scaled k-space is the standardized and scaled k-space magnitude of the image to zoom. The k-space filtering sigmoidal function scales the pixel-local scaled k-space values into the numerical interval [0, 1]. Using these two novel concepts, the Whittaker–Shannon interpolation formula is elaborated and used to zoom images. Zooming is determined by the shape of the Sinc functions in the Whittaker–Shannon interpolation formula, which, in turn, depends on the combined effect of the pixel-local scaled k-space, the sampling rate, and the k-space filtering sigmoidal function. The primary outcome of this research demonstrates that the Whittaker–Shannon interpolation formula can achieve successful zooms for values of the sampling rate significantly greater than the bandwidth. Conversely, when the sampling rate is much greater than the bandwidth, the nonadaptive technique fails to perform the zoom correctly. The conclusion is that the k-space filtering sigmoidal function is identified as the crucial parameter in the adaptive Sinc-based zoom technique. The implications of this research extend to Sinc-based image zooming applications.</p>\",\"PeriodicalId\":100109,\"journal\":{\"name\":\"Applied Research\",\"volume\":\"3 6\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/appl.202400018\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/appl.202400018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Research","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/appl.202400018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在这项工作中,我们介绍了一种新的图像缩放方法,该方法从基于非自适应sin的方法过渡到基于自适应sin的缩放技术。这两种技术的理论基础是惠特克-香农插值公式和奈奎斯特定理。通过使用两个新概念(1)像素局部缩放k空间和(2)k空间滤波s型函数,实现了向基于自适应自适应的缩放。像素局部缩放的k空间是图像缩放的标准化和缩放的k空间大小。k空间滤波s型函数将像素局部缩放的k空间值缩放到数值区间[0,1]。利用这两个新概念,阐述了Whittaker-Shannon插值公式,并将其用于图像缩放。缩放是由Whittaker-Shannon插值公式中Sinc函数的形状决定的,而这又取决于像素局部缩放k空间、采样率和k空间滤波s型函数的综合作用。本研究的主要结果表明,Whittaker-Shannon插值公式可以在采样率显著大于带宽的值下成功地实现变焦。相反,当采样率远远大于带宽时,非自适应技术无法正确实现变焦。研究结果表明,k空间滤波s型函数是自适应自适应变焦技术的关键参数。本研究的意义延伸到基于c的图像缩放应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Two-dimensional adaptive Whittaker–Shannon Sinc-based zooming

Two-dimensional adaptive Whittaker–Shannon Sinc-based zooming

In this work, we introduce a novel image zooming methodology that transitions from a nonadaptive Sin-based approach to an adaptive Sinc-based zooming technique. The two techniques base their theoretical foundation on the Whittaker–Shannon interpolation formula and the Nyquist theorem. The evolution into adaptive Sinc-based zoom is accomplished through the use of two novel concepts: (1) the pixel-local scaled k-space and (2) the k-space filtering sigmoidal function. The pixel-local scaled k-space is the standardized and scaled k-space magnitude of the image to zoom. The k-space filtering sigmoidal function scales the pixel-local scaled k-space values into the numerical interval [0, 1]. Using these two novel concepts, the Whittaker–Shannon interpolation formula is elaborated and used to zoom images. Zooming is determined by the shape of the Sinc functions in the Whittaker–Shannon interpolation formula, which, in turn, depends on the combined effect of the pixel-local scaled k-space, the sampling rate, and the k-space filtering sigmoidal function. The primary outcome of this research demonstrates that the Whittaker–Shannon interpolation formula can achieve successful zooms for values of the sampling rate significantly greater than the bandwidth. Conversely, when the sampling rate is much greater than the bandwidth, the nonadaptive technique fails to perform the zoom correctly. The conclusion is that the k-space filtering sigmoidal function is identified as the crucial parameter in the adaptive Sinc-based zoom technique. The implications of this research extend to Sinc-based image zooming applications.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
0.70
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信