Please use this identifier to cite or link to this item: doi:10.22028/D291-26367
Title: How to choose interpolation data in images
Author(s): Belhachmi, Zakaria
Bucur, Dorin
Burgeth, Bernhard
Weickert, Joachim
Language: English
Year of Publication: 2008
Free key words: shape analysis
image interpolation
image compression
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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.
Link to this record: urn:nbn:de:bsz:291-scidok-47357
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 205
Date of registration: 23-Mar-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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