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  • Conference proceedings
  • Open Access
  • © 2021

Anisotropy Across Fields and Scales

Part of the book series: Mathematics and Visualization (MATHVISUAL)

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Table of contents (13 papers)

  1. Front Matter

    Pages i-x
  2. Foundations

    1. Front Matter

      Pages 1-1
    2. Variance Measures for Symmetric Positive (Semi-) Definite Tensors in Two Dimensions

      • Magnus Herberthson, Evren Özarslan, Carl-Fredrik Westin
      Pages 3-22Open Access
    3. Degenerate Curve Bifurcations in 3D Linear Symmetric Tensor Fields

      • Yue Zhang, Hongyu Nie, Eugene Zhang
      Pages 23-38Open Access
  3. Image Processing and Visualization

    1. Front Matter

      Pages 71-71
    2. Tensor Approximation for Multidimensional and Multivariate Data

      • Renato Pajarola, Susanne K. Suter, Rafael Ballester-Ripoll, Haiyan Yang
      Pages 73-98Open Access
    3. Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression

      • Ikram Jumakulyyev, Thomas Schultz
      Pages 99-124Open Access
    4. Uncertainty in the DTI Visualization Pipeline

      • Faizan Siddiqui, Thomas Höllt, Anna Vilanova
      Pages 125-148Open Access
    5. Challenges for Tractogram Filtering

      • Daniel Jörgens, Maxime Descoteaux, Rodrigo Moreno
      Pages 149-168Open Access
  4. Modeling Anisotropy

    1. Front Matter

      Pages 169-169
    2. Single Encoding Diffusion MRI: A Probe to Brain Anisotropy

      • Maëliss Jallais, Demian Wassermann
      Pages 171-191Open Access
    3. Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI

      • Tom Dela Haije, Aasa Feragen
      Pages 193-202Open Access
    4. Magnetic Resonance Assessment of Effective Confinement Anisotropy with Orientationally-Averaged Single and Double Diffusion Encoding

      • Cem Yolcu, Magnus Herberthson, Carl-Fredrik Westin, Evren Özarslan
      Pages 203-223Open Access
    5. Riemann-DTI Geodesic Tractography Revisited

      • Luc Florack, Rick Sengers, Stephan Meesters, Lars Smolders, Andrea Fuster
      Pages 225-243Open Access
  5. Measuring Anisotropy

    1. Front Matter

      Pages 245-245
    2. Magnetic Resonance Imaging of \(T_2\)- and Diffusion Anisotropy Using a Tiltable Receive Coil

      • Chantal M. W. Tax, Elena Kleban, Muhamed Baraković, Maxime Chamberland, Derek K. Jones
      Pages 247-262Open Access
    3. Anisotropy in the Human Placenta in Pregnancies Complicated by Fetal Growth Restriction

      • Paddy J. Slator, Alison Ho, Spyros Bakalis, Laurence Jackson, Lucy C. Chappell, Daniel C. Alexander et al.
      Pages 263-276Open Access
  6. Back Matter

    Pages 277-280

About this book

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain.

The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas.

This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018.






Editors and Affiliations

  • Linköping University, Linköping, Sweden

    Evren Özarslan

  • University of Bonn, Bonn, Germany

    Thomas Schultz

  • Oregon State University, Corvallis, USA

    Eugene Zhang

  • Eindhoven University of Technology, Eindhoven, The Netherlands

    Andrea Fuster

Bibliographic Information

Buy it now

Buying options

Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access