Anisotropy Across Fields and Scales

• Published in: Mathematics and visualization
• Main Authors: Özarslan, Evren, Schultz, Thomas, Zhang, Eugene, Fuster, Andrea
• Format: eBook Book
• Language: English
• Published: Netherlands Springer Nature 2021; Springer International Publishing AG; Eindhoven University of Technology
• Edition: 1
• Series: Mathematics and Visualization
• Subjects: Algebra; Artificial intelligence; astrophysics; Combinatorics & graph theory; Combinatorics and graph theory; Computational Science and Engineering; Computer Imaging; Computer science; Computer vision; Computing and Information Technology; Data and Information Visualization; diffusion-weighted imaging (DWI); higher-order harmonics; image processing; Linear Algebra; Linear and Multilinear Algebras; Mathematical and Computational Physics; Mathematical physics; Mathematics; Mathematics and Science; Maths for scientists; Matrix Theory; medical imaging; Nonfiction; open access; Pattern Recognition and Graphics; Physics; Probabilities & applied mathematics; Science; Science: general issues; spherical harmonics; statistics; structural mechanics; tensor; tensor fields; Theoretical; Vision; Visualization; image processing; spherical harmonics; open access; visualization; diffusion-weighted imaging (DWI); higher-order harmonics; tensor fields; structural mechanics; astrophysics; tensor; medical imaging; statistics
• ISBN: 9783030562151; 3030562158; 303056214X; 9783030562144
• ISSN: 2197-666X; 1612-3786
• DOI: 10.1007/978-3-030-56215-1

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.