Hotz I., Schultz T. (eds.) Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Springer, 2015. — 383 p.Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors in specific applications and a glimpse of the next generation of diffusion MRI. To do so, it combines contributions on new developments, current challenges in this area and state-of-the-art surveys.
Compared to the increasing importance of higher-order descriptors in a range of applications, tools for analysis and processing are still relatively hard to come by. Even though application areas such as medical imaging, fluid dynamics and structural mechanics are very different in nature they face many shared challenges. This book provides an interdisciplinary perspective on this topic with contributions from key researchers in disciplines ranging from visualization and image processing to applications. It is based on the 5th Dagstuhl seminar on Visualization and Processing of Higher Order Descriptors for Multi-Valued Data.
This book will appeal to scientists who are working to develop new analysis methods in the areas of image processing and visualization, as well as those who work with applications that generate higher-order data or could benefit from higher-order models and are searching for novel analytical tools.Diffusion-Weighted Magnetic Resonance Signal for General Gradient Waveforms: Multiple Correlation Function Framework, Path Integrals, and Parallels Between ThemFinslerian Diffusion and the Bloch–Torrey Equation
Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries
Topology of 3D Linear Symmetric Tensor Fields
Random Projections for Low Multilinear Rank TensorsPath-Based Mathematical Morphology on Tensor Fields
Processing Multispectral Images via Mathematical Morphology
Direction-Controlled DTI Interpolation
Tensor Voting: Current State, Challenges and New Trends in the Context of Medical Image AnalysisVisualization of Diffusion Propagator and Multiple Parameter Diffusion Signal
Visual Knowledge Discovery for Diffusion Kurtosis Datasets of the Human Brain
A Survey of Illustrative Visualization Techniques for Diffusion-Weighted MRI Tractography
Visualizing Symmetric Indefinite 2D Tensor Fields Using the Heat Kernel SignatureA Framework for the Analysis of Diffusion Compartment Imaging (DCI)
Statistical and Machine Learning Methods for Neuroimaging: Examples, Challenges, and Extensions to Diffusion Imaging DataA Clustering Method for Identifying Regions of Interest in Turbulent Combustion Tensor Fields
Tensor Lines in Engineering: Success, Failure, and Open Questions
Contextual Diffusion Image Post-processing Aids Clinical Applications