Trigonometric Polynomial Interpolation of Images

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. Source Code The ANSI C99 implementation of the code that we provide is the one which has been peer reviewed and accepted by IPOL. The source code, the code documentation, and the online demo are accessible at the IPOL web page of this article1. Compilation and usage instructions are included in the README.txt file of the archive.

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