Optimising spatial and tonal data for homogeneous diffusion inpainting

Authors:
Markus Mainberger;Sebastian Hoffmann;Joachim Weickert;Ching Hoo Tang;Daniel Johannsen;Frank Neumann;Benjamin Doerr
Affiliations:
Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Department 1: Algorithms and Complexity, Max Planck Institute for Informatics, Saarbrücken, Germany;School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel;School of Computer Science, University of Adelaide, Adelaide, SA, Australia;Department 1: Algorithms and Complexity, Max Planck Institute for Informatics, Saarbrücken, Germany
Venue:
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Year:
2011

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Abstract

Finding optimal inpainting data plays a key role in the field of image compression with partial differential equations (PDEs). In this paper, we optimise the spatial as well as the tonal data such that an image can be reconstructed with minimised error by means of discrete homogeneous diffusion inpainting. To optimise the spatial distribution of the inpainting data, we apply a probabilistic data sparsification followed by a nonlocal pixel exchange. Afterwards we optimise the grey values in these inpainting points in an exact way using a least squares approach. The resulting method allows almost perfect reconstructions with only 5% of all pixels. This demonstrates that a thorough data optimisation can compensate for most deficiencies of a suboptimal PDE interpolant.