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International Conference on Scale Space and Variational Methods in Computer Vision

SSVM 2009: Scale Space and Variational Methods in Computer Vision pp 247–258Cite as

PDE-Driven Adaptive Morphology for Matrix Fields

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5567))

Abstract

Matrix fields are important in many applications since they are the adequate means to describe anisotropic behaviour in image processing models and physical measurements. A prominent example is diffusion tensor magnetic resonance imaging (DT-MRI) which is a medical imaging technique useful for analysing the fibre structure in the brain. Recently, morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images have been extended to three dimensional fields of symmetric positive definite matrices.

In this article we propose a novel method to incorporate adaptivity into the matrix-valued, PDE-driven dilation process. The approach uses a structure tensor concept for matrix data to steer anisotropic morphological evolution in a way that enhances and completes line-like structures in matrix fields. Numerical experiments performed on synthetic and real-world data confirm the gap-closing and line-completing qualities of the proposed method.

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Author information

Authors and Affiliations

  1. Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, 66041, Saarbrücken, Germany

    Bernhard Burgeth, Michael Breuß, Luis Pizarro & Joachim Weickert

Authors
  1. Bernhard Burgeth
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  2. Michael Breuß
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  3. Luis Pizarro
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  4. Joachim Weickert
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  3. Simula Research Laboratory, M. Linges v 17, Fornebu, P.O.Box 134, N-1325, Lysaker, Norway

    Marius Lysaker

  4. SINTEF ICT, Oslo, Norway

    Knut-Andreas Lie

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© 2009 Springer-Verlag Berlin Heidelberg

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Burgeth, B., Breuß, M., Pizarro, L., Weickert, J. (2009). PDE-Driven Adaptive Morphology for Matrix Fields. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_21

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

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