3D-Coherence-Enhancing Diffusion Filtering for Matrix Fields

  • Bernhard Burgeth
  • Luis Pizarro
  • Stephan Didas
  • Joachim Weickert
Part of the Computational Imaging and Vision book series (CIVI, volume 41)


Coherence-enhancing diffusion filtering is a striking application of the structure tensor concept in image processing. The technique deals with the problem of completion of interrupted lines and enhancement of flow-like features in images. The completion of line-like structures 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 visualize, for example, the nerve fibers in brain tissue. As any physical measurement DT-MRI is subjected to errors causing faulty representations of the tissue corrupted by noise and with visually interrupted lines or fibers.

In this paper we address that problem by proposing a coherence-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 gap-closing and flow-enhancing qualities of the technique presented.


Diffusion Tensor Structure Tensor Diffusion Tensor Magnetic Resonance Imaging Diffusion Filter Matrix Field 
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.



We are grateful to Anna Vilanova i Bartrolí (Eindhoven University 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 is by courtesy of Gordon Kindlmann (University of Chicago).


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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Bernhard Burgeth
    • 1
  • Luis Pizarro
    • 2
  • Stephan Didas
    • 3
  • Joachim Weickert
    • 1
  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer ScienceSaarland UniversitySaarbrueckenGermany
  2. 2.Department of ComputingImperial College LondonLondonUK
  3. 3.Abteilung BildverarbeitungFraunhofer-Institut für Techno- und WirtschaftsmathematikKaiserslauternGermany

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