Anisotropy Across Fields and Scales, 1st ed. 2021
Mathematics and Visualization Series

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.

Tensor approximation for multidimensional and multivariate data.- Tensor field topology without symmetrization using Hermitian tensors.- Continuous histograms for Anisotropy of 2D symmetric piece-wise linear tensor fields.- Riemann-DTI geodesic tractography revisited.- Fourth-order anisotropic diffusion for inpainting and image compression.- Advanced deep learning for processing orientation-dependent diffusion magnetic resonance imaging data - A review.- On the variance measure of diffusion tensors in two dimensions.- Magnetic resonance assessment of effective confinement anisotropy with powder-averaged single and double diffusion encoding.- Merge trees, neutral surfaces, and tensor field topology.- Asymmetric tensor analysis.- Anisotropy issues in shape-based object analysis.- Tractogram filtering.- Multispectral image processing in astronomy.- Anisotropy in the human placenta in pregnancies complicated by fetal growth restriction.- The case for spatially homogeneous models in high gradient strength diffusion-weighted MRI: A position paper on the potential applicability of stochastic geometry.