TY  - GEN
T1  - How to choose interpolation data in images
A1  - Belhachmi,Zakaria
A1  - Bucur,Dorin
A1  - Burgeth,Bernhard
A1  - Weickert,Joachim
Y1  - 2012/03/23
N2  - 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.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4735
ER  -