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E-raamat: Modeling, Analysis, and Visualization of Anisotropy

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  • Formaat: EPUB+DRM
  • Sari: Mathematics and Visualization
  • Ilmumisaeg: 14-Oct-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319613581
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  • Formaat: EPUB+DRM
  • Sari: Mathematics and Visualization
  • Ilmumisaeg: 14-Oct-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319613581
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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.
Part I Features and Visualization
Robustness for 2D Symmetric Tensor Field Topology
3(26)
Bei Wang
Ingrid Hotz
Applying 2D Tensor Field Topology to Solid Mechanics Simulations
29(14)
Yue Zhang
Xiaofei Gao
Eugene Zhang
Moment Invariants for Multi-Dimensional Data
43(22)
Roxana Bujack
Hans Hagen
Visualizing Gradients of Stress Tensor Fields
65(20)
Valentin Zobel
Markus Stommel
Gerik Scheuermann
Part II Image Processing and Analysis
Geometries and Interpolations for Symmetric Positive Definite Matrices
85(30)
Aasa Feragen
Andrea Fuster
Towards Processing Fields of General Real-Valued Square Matrices
115(30)
Bernhard Burgeth
Andreas Kleefeld
Towards Grey Scale-Based Tensor Voting for Blood Vessel Analysis
145(30)
Daniel Jorgens
Rodrigo Moreno
Local Geometric Descriptors for Multi-Scale Probabilistic Point Classification of Airborne LiDAR Point Clouds
175(28)
Jaya Sreevalsan-Nair
Beena Kumari
Part III Diffusion Modeling and Microstructure
Diffusion MRI Anisotropy: Modeling, Analysis and Interpretation
203(26)
Rutger H.J. Fick
Marco Pizzolato
Demian Wassermann
Rachid Deriche
Measuring Microscopic Anisotropy with Diffusion Magnetic Resonance: From Material Science to Biomedical Imaging
229(28)
Andrada Ianus
Noam Shemesh
Daniel C. Alexander
Ivana Drobnjak
Bayesian Heteroscedastic Regression for Diffusion Tensor Imaging
257(26)
Bertil Wegmann
Anders Eklund
Mattias Villani
Multi-Fiber Reconstruction Using Probabilistic Mixture Models for Diffusion MRI Examinations of the Brain
283(28)
Snehlata Shakya
Nazre Batool
Evren Ozarslan
Hans Knutsson
Part IV Tractography
Edge Detection in Diffusion Weighted MRI Using a Tangent Curve Similarity Metric
311(20)
Zi'Ang Ding
Xavier Tricoche
Yaniv Gur
Repeated Tractography of a Single Subject: How High Is the Variance?
331(24)
Xuan Gu
Anders Eklund
Hans Knutsson
Automatic Atlas-Based Segmentation of Brain White Matter in Neonates at Risk for Neurodevelopmental Disorders
355(20)
L. Fonseca
C. van Pul
N. Lori
R. van den Boom
P. Andriessen
J. Buijs
A. Vilanova
Part V Machine Learning Approaches
A Deep Learning Approach to Identifying Shock Locations in Turbulent Combustion Tensor Fields
375(18)
Mathew Monfort
Timothy Luciani
Jonathan Komperda
Brian Ziebart
Farzad Mashayek
G. Elisabeta Marai
Reconstruction of Diffusion Anisotropics Using 3D Deep Convolutional Neural Networks in Diffusion Imaging
393(12)
Simon Koppers
Matthias Friedrichs
Dorit Merhof
Index 405