Mathematics and Visualization

Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

Editors: Westin, Carl-Fredrik, Vilanova, Anna, Burgeth, Bernhard (Eds.)

  • Discusses challenges in both theoretical and practical issues related to analyzing and visualizing fields of tensors and higher order descriptors
  • Provides examples of tensors as applied to research in engineering and brain connectivity
  • Multidisciplinary approach is intended to inspire and advance new research on analyzing and visualizing fields of tensors and higher order descriptors
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About this book

Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties.

Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs.

The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI.

Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and analyze large and complex diffusion data such as High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Kurtosis Imaging (DKI).

A Part entitled Tensor Signal Processing presents new methods for processing tensor-valued data, including a novel perspective on performing voxel-wise morphometry of diffusion tensor data using kernel-based approach, explores the free-water diffusion model, and reviews proposed approaches for computing fabric tensors, emphasizing trabecular bone research.

The last Part, Applications of Tensor Processing, discusses metric and curvature tensors, two of the most studied tensors in geometry processing. Also covered is a technique for diagnostic prediction of first-episode schizophrenia patients based on brain diffusion MRI data. The last chapter presents an interactive system integrating the visual analysis of diffusion MRI tractography with data from electroencephalography.

Table of contents (15 chapters)

  • Top Challenges in the Visualization of Engineering Tensor Fields

    Hlawitschka, Mario (et al.)

    Pages 3-15

  • Tensor Invariants and Glyph Design

    Kratz, Andrea (et al.)

    Pages 17-34

  • Monomial Phase: A Matrix Representation of Local Phase

    Knutsson, Hans (et al.)

    Pages 37-73

  • Order Based Morphology for Color Images via Matrix Fields

    Burgeth, Bernhard (et al.)

    Pages 75-95

  • Sharpening Fibers in Diffusion Weighted MRI via Erosion

    Dela Haije, Thomas C. J. (et al.)

    Pages 97-126

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-642-54301-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-3-642-54300-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-3-662-51257-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
Editors
  • Carl-Fredrik Westin
  • Anna Vilanova
  • Bernhard Burgeth
Series Title
Mathematics and Visualization
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-54301-2
DOI
10.1007/978-3-642-54301-2
Hardcover ISBN
978-3-642-54300-5
Softcover ISBN
978-3-662-51257-9
Series ISSN
1612-3786
Edition Number
1
Number of Pages
XV, 343
Number of Illustrations and Tables
25 b/w illustrations, 85 illustrations in colour
Topics