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 hdl:20.500.11880/26423 http://dx.doi.org/10.22028/D291-26367 |
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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preprint_205_08.pdf | 306,77 kB | Adobe PDF | View/Open |
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