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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.
Foundations
Variance Measures for Symmetric Positive (Semi-) Definite Tensors in Two Dimensions
Degenerate Curve Bifurcations in 3D Linear Symmetric Tensor Fields
Continuous Histograms for Anisotropy of 2D Symmetric Piece-Wise Linear Tensor Fields
Image Processing and Visualization
Tensor Approximation for Multidimensional and Multivariate Data
Fourth-Order Anisotropic Diffusion for Inpainting and Image Compression
Uncertainty in the DTI Visualization Pipeline
Challenges for Tractogram Filtering
Modeling Anisotropy
Single Encoding Diffusion MRI: A Probe to Brain Anisotropy
Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI
Magnetic Resonance Assessment of Effective Confinement Anisotropy with Orientationally-Averaged Single and Double Diffusion Encoding
Riemann-DTI Geodesic Tractography Revisited
Measuring Anisotropy
Magnetic Resonance Imaging of T2 - and Diffusion Anisotropy Using a Tiltable Receive Coil
Anisotropy in the Human Placenta in Pregnancies Complicated by Fetal Growth Restriction