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A generic approach to diffusion filtering of matrix-fields

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Summary

Diffusion tensor magnetic resonance imaging, is a image acquisition method, that provides matrix- valued data, so-called matrix fields. Hence image processing tools for the filtering and analysis of these data types are in demand. In this article, we propose a generic framework that allows us to find the matrix-valued counterparts of the Perona–Malik PDEs with various diffusivity functions. To this end we extend the notion of derivatives and associated differential operators to matrix fields of symmetric matrices by adopting an operator-algebraic point of view. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our novel matrix-valued Perona–Malik diffusion filters.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Saarland University, 66041, Saarbrücken, Germany

    B. Burgeth, S. Didas & J. Weickert

  2. Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    L. Florack

Authors
  1. B. Burgeth
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  2. S. Didas
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  3. L. Florack
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  4. J. Weickert
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Corresponding author

Correspondence to B. Burgeth.

Additional information

The Dutch Organization NWO is gratefully acknowledged for financial support.

The German Organization DFG is gratefully acknowledged for financial support.

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Burgeth, B., Didas, S., Florack, L. et al. A generic approach to diffusion filtering of matrix-fields. Computing 81, 179–197 (2007). https://doi.org/10.1007/s00607-007-0248-9

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  • DOI: https://doi.org/10.1007/s00607-007-0248-9

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