A Kernel Representation for Exponential Splines with Global Tension

Abstract

Interpolation is a key ingredient in many imaging routines. In this note, we present a thorough evaluation of an interpolation method based on exponential splines in tension. They are based on so-called tension parameters, which allow for a tuning of their properties. As it turns out, these interpolants have very many nice features, which are, however, not born out in the literature. We intend to close this gap. We present for the first time an analytic representation of their kernel which enables one to come up with a space and frequency domain analysis. It is shown that the exponential splines in tension, as a function of the tension parameter, bridging the gap between linear and cubic B-Spline interpolation. For example, with a certain tension parameter, one is able to suppress ringing artefacts in the interpolant. On the other hand, the analysis in the frequency domain shows that one derives a superior signal reconstruction quality as known from the cubic B-Spline interpolation, which, however, suffers from ringing artifacts. With the ability to offer a trade-off between opposing features of interpolation methods we advocate the use of the exponential spline in tension from a practical point of view and use the new kernel representation to qualify the trade-off.
Original languageEnglish
Title of host publicationProceedings of the SPIE 2009, Image Processing: Algorithms and Systems VII, San Jose
EditorsJaakko T. Astola, Karen O. Egiazarian, Nasser M. Nasrabadi, Syed A. Rizvi
Number of pages10
Volume7245
PublisherSPIE
Publication date10.02.2009
Article number72450I
ISBN (Print)978-081947495-7
DOIs
Publication statusPublished - 10.02.2009
EventImage Processing: Algorithms and Systems VII - San Jose, United States
Duration: 19.01.200922.01.2009
Conference number: 76102

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