Edge-Enhancing Diffusion Filtering for Matrix Fields

Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

The elimination of noise and small details from an image while simultaneously preserving or enhancing the edge structures in an image is a ever-lasting task in image processing. Edge-enhancing anisotropic diffusion is known to tackle this problem successfully. The problem of noise removal and edge enhancement is also a major concern in diffusion tensor magnetic resonance imaging (DT-MRI). This medical image acquisition technique outputs a 3D matrix field of symmetric 3 ×3-matrices, and it helps to visualise, for example, the nerve fibres in brain tissue. As any physical measurement DT-MRI is subjected to errors causing faulty representations of the tissue structure corrupted by noise. In this paper we address that problem by proposing a edge-enhancing diffusion filtering methodology for matrix fields. The approach is based on a generic structure tensor concept for matrix fields that relies on the operator-algebraic properties of symmetric matrices, rather than their channel-wise treatment of earlier proposals. Numerical experiments with artificial and real DT-MRI data confirm the noise-removing and edge-enhancing qualities of the technique presented.

Keywords

Fractional Anisotropy Structure Tensor Diffusion Tensor Magnetic Resonance Imaging Matrix Field Block Operator Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

We are grateful to Anna Vilanova i Bartrolí (Eindhoven Institute of Technology) and Carola van Pul (Maxima Medical Center, Eindhoven) for providing us with the DT-MRI data set and for discussing questions concerning data conversion. The original helix data set is by courtesy of Gordon Kindlmann (University of Chicago). The thank Thomas Schultz (University of Chicago) for providing the tractography results.

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Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrückenGermany
  2. 2.Department of ComputingImperial College LondonLondonUK
  3. 3.Abteilung BildverarbeitungFraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWMKaiserslauternGermany

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