Cover Image

Anisotropy Across Fields and Scales.

Bibliographic Details
Main Author: Özarslan, Evren.
Other Authors: Schultz, Thomas., Zhang, Eugene., Fuster, Andrea.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2021.
Edition:1st ed.
Series:Mathematics and Visualization Series
Subjects:
Electronic books.
Online Access:Click to View
LEADER 08702nam a22004693i 4500
001 EBC6478284
003 MiAaPQ
005 20231204023215.0
006 m o d |
007 cr cnu||||||||
008 231204s2021 xx o ||||0 eng d
020 |a 9783030562151  |q (electronic bk.) 
020 |z 9783030562144 
035 |a (MiAaPQ)EBC6478284 
035 |a (Au-PeEL)EBL6478284 
035 |a (OCoLC)1240211601 
040 |a MiAaPQ  |b eng  |e rda  |e pn  |c MiAaPQ  |d MiAaPQ 
050 4 |a QA76.9.I52 
100 1 |a Özarslan, Evren. 
245 1 0 |a Anisotropy Across Fields and Scales. 
250 |a 1st ed. 
264 1 |a Cham :  |b Springer International Publishing AG,  |c 2021. 
264 4 |c {copy}2021. 
300 |a 1 online resource (284 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Mathematics and Visualization Series 
505 0 |a Intro -- Preface -- Contents -- Foundations -- Variance Measures for Symmetric Positive (Semi-) Definite Tensors in Two Dimensions -- 1 Introduction -- 1.1 Outline -- 2 Preliminaries -- 2.1 Tensor Notation and Representations -- 2.2 Invariants, Traces and Decompositions -- 3 Rabcd as a Quadratic Form on mathbbR3 -- 3.1 Representation of the Canonically Derived Parts of Rabcd -- 3.2 The Behaviour of Mij Under a Rotation of the Coordinate System in Va -- 4 The Equivalence Problem for Rabcd -- 4.1 Different Ways to Characterize the Equivalence of Rabcd and widetildeRabcd -- 5 Discussion -- References -- Degenerate Curve Bifurcations in 3D Linear Symmetric Tensor Fields -- 1 Introduction -- 2 Previous Work -- 3 Background on Tensors and Tensor Fields -- 3.1 Tensors -- 3.2 Tensor Field Topology -- 3.3 3D Linear Tensor Fields -- 4 Bifurcations -- 4.1 Degenerate Curve Removal and Generation -- 4.2 Degenerate Curve Reconnection -- 4.3 Transition Point Pair Cancellation and Generation -- 4.4 Transition Point Relocation -- 5 Conclusion -- References -- Continuous Histograms for Anisotropy of 2D Symmetric Piece-Wise Linear Tensor Fields -- 1 Introduction -- 2 Context and Related Work -- 2.1 Continuous Histograms -- 2.2 Notes on Tensor Field Interpolation -- 2.3 Contour Trees, a Topological Summary of Scalar Functions -- 3 Problem Statement and Solution Overview -- 4 Background and Notations -- 4.1 Second Order Symmetric Tensors and Anisotropy -- 4.2 Barycentric Coordinates and Piece-Wise Linear Interpolation -- 4.3 Bivariate Quadratic Functions and Their Critical Points -- 5 Anisotropy for 2D Piece-Wise Linear Tensor Fields -- 5.1 Field Normalization Using Coordinate Transformations -- 6 Subdivision in Monotonous Sub-triangles -- 7 Computation of the Histogram for ν -- 7.1 Implementation -- 8 Results -- 8.1 Synthetic Data -- 8.2 Simulation Data. 
505 8 |a 8.3 Measurement Data -- 9 Conclusions -- References -- Image Processing and Visualization -- Tensor Approximation for Multidimensional and Multivariate Data -- 1 Introduction -- 1.1 Higher-Order Data Decompositions -- 1.2 TA Applications in Graphics and Visualization -- 1.3 Motivation and Contributions -- 2 Singular Value Decomposition -- 3 Tensor Approximation Notation and Definitions -- 3.1 General Notation -- 3.2 Computing with Tensors -- 3.3 Rank of a Tensor -- 4 Tensor Decompositions -- 4.1 Tucker Model -- 5 Tensor Rank Reduction -- 5.1 Rank-R and Rank-(R1, R2, …, RN) Approximations -- 5.2 Truncated Tensor Decomposition -- 6 Tucker Decomposition Algorithms -- 7 Tensor Reconstruction -- 7.1 Element-Wise Reconstruction -- 7.2 Optimized Tucker Reconstruction -- 8 Useful TA Properties for Scientific Visualization -- 8.1 Spatial Selectivity and Subsampling -- 8.2 Approximation and Rank Reduction -- 9 Application to Multivariate Data -- 9.1 Dataset -- 9.2 Vector Field Magnitude and Angle -- 9.3 Vorticity and Divergence -- 10 Conclusions -- References -- Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression -- 1 Introduction -- 2 Background and Related Work -- 2.1 Diffusion-Based Inpainting -- 2.2 From Linear to Anisotropic Nonlinear Diffusion -- 2.3 From Second to Fourth Order Diffusion -- 2.4 Alternative Approaches to Image Compression -- 3 Method -- 3.1 Anisotropic Edge-Enhancing Fourth Order PDE -- 3.2 A Unifying Framework for Fourth-Order Diffusion -- 3.3 Discretization and Stability -- 4 Experimental Results -- 4.1 Reconstruction From a Sparse Set of Pixels -- 4.2 Scratch Removal -- 4.3 Effect of Diffusivity Function and Contrast Parameter -- 5 Conclusions -- References -- Uncertainty in the DTI Visualization Pipeline -- 1 Introduction -- 2 Background -- 2.1 Diffusion Tensor -- 2.2 Fiber Tracking -- 3 Sources of Uncertainty. 
505 8 |a 3.1 Image Acquisition -- 3.2 Diffusion Tensor Calculation -- 3.3 Fiber Tracking -- 3.4 Visualization -- 4 Uncertainty Modeling -- 4.1 Analytical Methods -- 4.2 Stochastic Methods -- 5 Uncertainty Visualization -- 5.1 Local Uncertainty Visualization -- 5.2 Global Uncertainty Visualization -- 6 Conclusion -- References -- Challenges for Tractogram Filtering -- 1 Introduction -- 2 Approaches for Tractogram Filtering -- 2.1 Explainability of the Diffusion Signal -- 2.2 Inclusion and Exclusion ROIs -- 2.3 Streamline Geometry or Shape -- 2.4 Streamline Similarity and Clustering -- 2.5 Multiapproaches -- 3 Challenges and Perspective -- 4 Conclusion -- References -- Modeling Anisotropy -- Single Encoding Diffusion MRI: A Probe to Brain Anisotropy -- 1 Accessing Brain Anisotropy Using Diffusion MRI -- 1.1 Introduction -- 1.2 Anisotropy as Reflected by Water Motion -- 1.3 Structural Brain Anisotropy -- 1.4 Measuring Anisotropy Using Diffusion MRI -- 2 Diffusion MRI: Introduction to a Non-Invasive Imaging Technique -- 2.1 Diffusion MRI Acquisition Sequence -- 2.2 Mathematical Foundations -- 2.3 Acquisition Strategies -- 2.4 Difficulties -- 3 Quantifying Anisotropy via Signal Representation -- 3.1 Cumulant Expansion -- 3.2 Other Representations -- 3.3 Limitations -- 4 Biophysical Modeling to Measure Anisotropy -- 4.1 Multi-compartmental Model -- 4.2 Neurites as Sticks -- 4.3 Standard Model of Diffusion in Neural Tissue -- 4.4 Standard Model Parameter Estimation Using Constraints -- 4.5 Lemonade -- 5 Summary and Above -- References -- Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI -- 1 Introduction -- 2 Specific Volumes and the Short-Time Limit -- 3 Stationarity and the Long-Time Limit -- 4 Directional Measures and the Strong-Gradient Limit -- 5 Perspectives -- References. 
505 8 |a Magnetic Resonance Assessment of Effective Confinement Anisotropy with Orientationally-Averaged Single and Double Diffusion Encoding -- 1 Introduction -- 2 Double Diffusion Encoding at the Compartment Level -- 3 Double Diffusion Encoding: Powder Average -- 3.1 Axisymmetric Confinement -- 3.2 Insights from Two Dimensions -- 3.3 One-Dimensional Diffusion Under High Gradient: g-2 Scaling -- 4 Single Diffusion Encoding -- 4.1 Axisymmetry and the Power-Laws for Confined diffusion -- 5 Discussion -- 6 Conclusion -- References -- Riemann-DTI Geodesic Tractography Revisited -- 1 Introduction -- 2 Theory -- 3 Experiments -- 4 Conclusion and Discussion -- References -- Measuring Anisotropy -- Magnetic Resonance Imaging of T2- and Diffusion Anisotropy Using a Tiltable Receive Coil -- 1 Introduction -- 1.1 Background -- 1.2 Scope of This Work -- 2 Methods -- 2.1 Data Acquisition -- 2.2 MRI Signal Processing -- 2.3 Estimation -- 3 Results -- 4 Discussion -- 4.1 Incorporating Tiltable Coil in -diffusion correlation experiments -- 4.2 Origin of -Contrast and -Anisotropy in WM -- 4.3 Considerations in Data Processing -- 5 Conclusion -- References -- Anisotropy in the Human Placenta in Pregnancies Complicated by Fetal Growth Restriction -- 1 Introduction -- 1.1 Placental Microstructure -- 1.2 Placental MRI -- 2 Methods -- 2.1 Recruitment -- 3 Results -- 4 Discussion and Conclusion -- References -- Index. 
588 |a Description based on publisher supplied metadata and other sources. 
590 |a Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.  
655 4 |a Electronic books. 
700 1 |a Schultz, Thomas. 
700 1 |a Zhang, Eugene. 
700 1 |a Fuster, Andrea. 
776 0 8 |i Print version:  |a Özarslan, Evren  |t Anisotropy Across Fields and Scales  |d Cham : Springer International Publishing AG,c2021  |z 9783030562144 
797 2 |a ProQuest (Firm) 
830 0 |a Mathematics and Visualization Series 
856 4 0 |u https://ebookcentral.proquest.com/lib/matrademy/detail.action?docID=6478284  |z Click to View 

Similar Items