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Preprint (Vorabdruck) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-47357
URL: http://scidok.sulb.uni-saarland.de/volltexte/2012/4735/


How to choose interpolation data in images

Belhachmi, Zakaria ; Bucur, Dorin ; Burgeth, Bernhard ; Weickert, Joachim

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Freie Schlagwörter (Englisch): shape analysis , image interpolation , image compression
Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer: 205
Sprache: Englisch
Erstellungsjahr: 2008
Publikationsdatum: 23.03.2012
Kurzfassung auf Englisch: We introduce and discuss shape based models for finding the best interpolation data when reconstructing missing regions in images by means of solving the Laplace equation. The shape analysis is done in the framework of \Gamma -convergence, from two different points of view. First, we propose a continuous PDE model and get pointwise information on the ”importance” of each pixel by a topological asymptotic method. Second, we introduce a finite dimensional setting into the continuous model based on fat pixels (balls with positive radius), and study by \Gamma -convergence the asymptotics when the radius vanishes. In this way, we obtain relevant information about the optimal distribution of the best interpolation pixels. We show that the resulting optimal data sets are identical to sets that can also be motivated using level set ideas and approximation theoretic considerations. Numerical computations are presented that confirm the usefulness of our theoretical findings for PDE-based image compression.
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