Trigonometric Polynomial Interpolation of Images

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Communicated by Pascal Monasse and Jean-Michel Morel
Demo edited by Thibaud Briand

Abstract

For 1D and 2D signals, the Shannon-Whittaker interpolation with periodic extension can be formulated as a trigonometric polynomial interpolation (TPI). In this work, we describe and discuss the theory of TPI of images and some of its applications. First, the trigonometric polynomial interpolators of an image are characterized and it is shown that there is an ambiguity as soon as one size of the image is even. Three classical choices of interpolator for real-valued images are presented and cases where they coincide are pointed out. Then, TPI is applied to the geometric transformation of images, to up-sampling and to down-sampling. General results are expressed for any choice of interpolator but more details are given for the three proposed ones. It is proven that the well-known DFT-based computations have to be slightly adapted.

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  Software Heritage Archive @softwareversion{sw-ipol.2019.273, title = {{Trigonometric Polynomial Interpolation of Images}}, author = {Thibaud Briand}, date = {2019-09-09}, license = {GPL-3.0-or-later}, version = {1.0}, swhid = {swh:1:dir:51569f62dda14407ef724196d187e189700506e5;origin=https://doi.org/10.5201/ipol.2019.273;visit=swh:1:snp:7c77761da696838f90b50c38438d25bcabd0e6bf;anchor=swh:1:rev:de3db806419d5f2770b17790328fe2d82baeebe3}, related = {ipol.2019.273}, relatedtype = "Reference article: https://doi.org/10.5201/ipol.2019.273" } % the biblatex-software style extension is recommended for software bibitems
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History

• Note from the editor: the manuscript of the article was modified on 2022-01-01 to include information about its editors. The original version of the manuscript is available here.