Optimising spatial and tonal data for homogeneous diffusion inpainting

Markus Mainberger; Sebastian Hoffmann; Joachim Weickert; Ching Hoo Tang; Daniel Johannsen; Frank Neumann; Benjamin Doerr

doi:10.1007/978-3-642-24785-9_3

Optimising spatial and tonal data for homogeneous diffusion inpainting

Markus Mainberger
, Sebastian Hoffmann
, Joachim Weickert
, Ching Hoo Tang
, Daniel Johannsen
, Frank Neumann
, Benjamin Doerr

Universität des Saarlandes
Max-Planck-Institut fur Informatik
Tel Aviv University
The University of Adelaide

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers
Pages	26-37
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-24785-9_3
Publication status	Published - 16 Jan 2012
Externally published	Yes
Event	3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011 - Ein-Gedi, Israel Duration: 29 May 2011 → 2 Jun 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6667 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011
Country/Territory	Israel
City	Ein-Gedi
Period	29/05/11 → 2/06/11

Keywords

homogeneous diffusion
image compression
inpainting
optimisation
partial differential equations (PDEs)

Access to Document

10.1007/978-3-642-24785-9_3

Cite this

Mainberger, M., Hoffmann, S., Weickert, J., Tang, C. H., Johannsen, D., Neumann, F., & Doerr, B. (2012). Optimising spatial and tonal data for homogeneous diffusion inpainting. In Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers (pp. 26-37). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6667 LNCS). https://doi.org/10.1007/978-3-642-24785-9_3

Mainberger, Markus ; Hoffmann, Sebastian ; Weickert, Joachim et al. / Optimising spatial and tonal data for homogeneous diffusion inpainting. Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. 2012. pp. 26-37 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Optimising spatial and tonal data for homogeneous diffusion inpainting",

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.",

keywords = "homogeneous diffusion, image compression, inpainting, optimisation, partial differential equations (PDEs)",

author = "Markus Mainberger and Sebastian Hoffmann and Joachim Weickert and Tang, \{Ching Hoo\} and Daniel Johannsen and Frank Neumann and Benjamin Doerr",

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doi = "10.1007/978-3-642-24785-9\_3",

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booktitle = "Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers",

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Mainberger, M, Hoffmann, S, Weickert, J, Tang, CH, Johannsen, D, Neumann, F & Doerr, B 2012, Optimising spatial and tonal data for homogeneous diffusion inpainting. in Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6667 LNCS, pp. 26-37, 3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011, Ein-Gedi, Israel, 29/05/11. https://doi.org/10.1007/978-3-642-24785-9_3

Optimising spatial and tonal data for homogeneous diffusion inpainting. / Mainberger, Markus; Hoffmann, Sebastian; Weickert, Joachim et al.
Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. 2012. p. 26-37 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6667 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Hoffmann, Sebastian

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AU - Tang, Ching Hoo

AU - Johannsen, Daniel

AU - Neumann, Frank

AU - Doerr, Benjamin

PY - 2012/1/16

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N2 - 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.

AB - 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.

KW - homogeneous diffusion

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Mainberger M, Hoffmann S, Weickert J, Tang CH, Johannsen D, Neumann F et al. Optimising spatial and tonal data for homogeneous diffusion inpainting. In Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. 2012. p. 26-37. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-24785-9_3

Optimising spatial and tonal data for homogeneous diffusion inpainting

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Keywords

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