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                "url": "https://doi.org/10.5201/ipol.2019.273"
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                    "atom:title": "ipol_273",
                    "codemeta:applicationCategory": "Image Processing",
                    "codemeta:author": {
                        "codemeta:affiliation": "Universit\u00e9 Paris-Est, LIGM (UMR CNRS 8049), ENPC, Marne-la-Vall\u00e9e, France and Universit\u00e9 Paris-Saclay, CMLA (UMR CNRS 8536), France",
                        "codemeta:name": "Thibaud Briand"
                    },
                    "codemeta:dateCreated": "2019-09-09",
                    "codemeta:datePublished": "2019-10-02",
                    "codemeta:description": "Trigonometric Polynomial Interpolation of Images",
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                        "codemeta:identifier": "ISSN: 2105-1232 DOI: 10.5201/ipol",
                        "codemeta:name": "Image Processing On Line (IPOL)",
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                    },
                    "codemeta:keywords": [
                        "interpolation",
                        "trigonometric polynomial",
                        "trigonometric polynomial interpolation",
                        "discrete Fourier transform (DFT)",
                        "Non-equispaced fast Fourier transform (NFFT)"
                    ],
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                        "codemeta: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.",
                        "codemeta:identifier": "https://doi.org/10.5201/ipol.2019.273",
                        "codemeta:name": "Trigonometric Polynomial Interpolation of Images",
                        "codemeta:url": "http://www.ipol.im/pub/art/2019/273/article.pdf"
                    },
                    "codemeta:relatedLink": "http://ipolcore.ipol.im/demo/clientApp/demo.html?id=273",
                    "codemeta:releaseNotes": "This code implements the algorithm(s) published in the IPOL paper \"Trigonometric Polynomial Interpolation of Images\"",
                    "codemeta:url": "http://www.ipol.im/pub/art/2019/273/",
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