Overview
- 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
Part of the book series: Mathematics and Visualization (MATHVISUAL)
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Table of contents (15 papers)
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Front Matter
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Tensor Data Visualization
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Front Matter
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Representation and Processing of Higher-Order Descriptors
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Front Matter
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Higher Order Tensors and Riemannian-Finsler Geometry
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Front Matter
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Tensor Signal Processing
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Front Matter
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Applications of Tensor Processing
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Front Matter
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Keywords
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.
Editors and Affiliations
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
DOI: https://doi.org/10.1007/978-3-642-54301-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Hardcover ISBN: 978-3-642-54300-5Published: 01 August 2014
Softcover ISBN: 978-3-662-51257-9Published: 23 August 2016
eBook ISBN: 978-3-642-54301-2Published: 17 July 2014
Series ISSN: 1612-3786
Series E-ISSN: 2197-666X
Edition Number: 1
Number of Pages: XV, 343
Number of Illustrations: 25 b/w illustrations, 85 illustrations in colour
Topics: Visualization, Partial Differential Equations, Differential Geometry, Computer Imaging, Vision, Pattern Recognition and Graphics, Computer Graphics, Theoretical, Mathematical and Computational Physics