[IPOL announce] new article: Trigonometric Polynomial Interpolation of Images

[announcements about the IPOL journal]

A new article is available in IPOL: http://www.ipol.im/pub/art/2019/273/


Thibaud Briand,
Trigonometric Polynomial Interpolation of Images,
Image Processing On Line, 9 (2019), pp. 291–316.
https://doi.org/10.5201/ipol.2019.273

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.