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International Conference Image Analysis and Recognition

ICIAR 2018: Image Analysis and Recognition pp 81–89Cite as

DTI Segmentation Using Anisotropy Preserving Quaternion Based Distance Measure

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10882))

Abstract

In brain research, the second order tensor model of the diffusion tensor imaging (DTI) encodes diffusion of water molecules in micro-structures of tissues. These tensors are real matrices lying in a non-linear space enjoying the Riemannian symmetric space structure. Thus, there are natural intrinsic metrics there, together with their extrinsic approximations. The effective implementations are based on the extrinsic ones employing their vector space structure. In processing DTI, the Log-Euclidean (LogE) metric is most popular, though very far from optimal. The spectral decomposition approach yields the distance measures which respect the anisotropy much better. In the present work, we propose to use the spherical linear interpolation (slerp-SQ) which performs much better than the LogE one and provides better interpolation of geodesics than the spectral-quaternion one. We have implemented the localized active contour segmentation method for these metrics, providing much better handling of the inhomogeneity of the data than global counterpart.

Sumit Kaushik has been supported by the grant MUNI/A/1138/2017 of Masaryk University, Jan Slovak gratefully acknowledges support from the Grant Agency of the Czech Republic, grant Nr. GA17-01171S.

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Notes

  1. 1.

    Brain Image Source: http://brainimaging.waisman.wisc.edu/~chung/DTI.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Sumit Kaushik & Jan Slovak

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  1. Sumit Kaushik
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  2. Jan Slovak
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Correspondence to Sumit Kaushik .

Editor information

Editors and Affiliations

  1. University of Porto, Porto, Portugal

    Aurélio Campilho

  2. University of Waterloo, Waterloo, Ontario, Canada

    Fakhri Karray

  3. Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Bart ter Haar Romeny

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Kaushik, S., Slovak, J. (2018). DTI Segmentation Using Anisotropy Preserving Quaternion Based Distance Measure. In: Campilho, A., Karray, F., ter Haar Romeny, B. (eds) Image Analysis and Recognition. ICIAR 2018. Lecture Notes in Computer Science(), vol 10882. Springer, Cham. https://doi.org/10.1007/978-3-319-93000-8_10

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  • DOI: https://doi.org/10.1007/978-3-319-93000-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92999-6

  • Online ISBN: 978-3-319-93000-8

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