Modeling, Analysis, and Visualization of Anisotropy

Description

This book focuses on the modeling, processing and visualization of anisotropy, irrespective of the context in which it emerges, using state-of-the-art mathematical tools. As such, it differs substantially from conventional reference works, which are centered on a particular application. It covers the following topics: (i) the geometric structure of tensors, (ii) statistical methods for tensor field processing, (iii) challenges in mapping neural connectivity and structural mechanics, (iv) processing of uncertainty, and (v) visualizing higher-order representations. In addition to original research contributions, it provides insightful reviews. This multidisciplinary book is the sixth in a series that aims to foster scientific exchange between communities employing tensors and other higher-order representations of directionally dependent data. A significant number of the chapters were co-authored by the participants of the workshop titled Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis, which was held in Dagstuhl, Germany in April 2016. It offers a valuable resource for those working in the field of multi-directional data, vital inspirations for the development of new models, and essential analysis and visualization techniques, thus furthering the state-of-the-art in studies involving anisotropy. Front Matter ....Pages i-x Front Matter ....Pages 1-1 Robustness for 2D Symmetric Tensor Field Topology (Bei Wang, Ingrid Hotz)....Pages 3-27 Applying 2D Tensor Field Topology to Solid Mechanics Simulations (Yue Zhang, Xiaofei Gao, Eugene Zhang)....Pages 29-41 Moment Invariants for Multi-Dimensional Data (Roxana Bujack, Hans Hagen)....Pages 43-64 Visualizing Gradients of Stress Tensor Fields (Valentin Zobel, Markus Stommel, Gerik Scheuermann)....Pages 65-81 Front Matter ....Pages 83-83 Geometries and Interpolations for Symmetric Positive Definite Matrices (Aasa Feragen, Andrea Fuster)....Pages 85-113 Towards Processing Fields of General Real-Valued Square Matrices (Bernhard Burgeth, Andreas Kleefeld)....Pages 115-144 Towards Grey Scale-Based Tensor Voting for Blood Vessel Analysis (Daniel Jörgens, Rodrigo Moreno)....Pages 145-173 Local Geometric Descriptors for Multi-Scale Probabilistic Point Classification of Airborne LiDAR Point Clouds (Jaya Sreevalsan-Nair, Beena Kumari)....Pages 175-200 Front Matter ....Pages 201-201 Diffusion MRI Anisotropy: Modeling, Analysis and Interpretation (Rutger H. J. Fick, Marco Pizzolato, Demian Wassermann, Rachid Deriche)....Pages 203-228 Measuring Microscopic Anisotropy with Diffusion Magnetic Resonance: From Material Science to Biomedical Imaging (Andrada Ianuş, Noam Shemesh, Daniel C. Alexander, Ivana Drobnjak)....Pages 229-255 Bayesian Heteroscedastic Regression for Diffusion Tensor Imaging (Bertil Wegmann, Anders Eklund, Mattias Villani)....Pages 257-282 Multi-Fiber Reconstruction Using Probabilistic Mixture Models for Diffusion MRI Examinations of the Brain (Snehlata Shakya, Nazre Batool, Evren Özarslan, Hans Knutsson)....Pages 283-308 Front Matter ....Pages 309-309 Edge Detection in Diffusion Weighted MRI Using a Tangent Curve Similarity Metric (Zi’Ang Ding, Xavier Tricoche, Yaniv Gur)....Pages 311-330 Repeated Tractography of a Single Subject: How High Is the Variance? (Xuan Gu, Anders Eklund, Hans Knutsson)....Pages 331-354 Automatic Atlas-Based Segmentation of Brain White Matter in Neonates at Risk for Neurodevelopmental Disorders (L. Fonseca, C. van Pul, N. Lori, R. van den Boom, P. Andriessen, J. Buijs et al.)....Pages 355-372 Front Matter ....Pages 373-373 A Deep Learning Approach to Identifying Shock Locations in Turbulent Combustion Tensor Fields (Mathew Monfort, Timothy Luciani, Jonathan Komperda, Brian Ziebart, Farzad Mashayek, G. Elisabeta Marai)....Pages 375-392 Reconstruction of Diffusion Anisotropies Using 3D Deep Convolutional Neural Networks in Diffusion Imaging (Simon Koppers, Matthias Friedrichs, Dorit Merhof)....Pages 393-404 Back Matter ....Pages 405-407