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.
Author(s): Ingrid Hotz, Thomas Schultz (eds.)
Series: Mathematics and Visualization
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 383
Tags: Visualization; Linear and Multilinear Algebras, Matrix Theory; Computational Science and Engineering; Image Processing and Computer Vision
Front Matter....Pages i-x
Front Matter....Pages 1-1
Diffusion-Weighted Magnetic Resonance Signal for General Gradient Waveforms: Multiple Correlation Function Framework, Path Integrals, and Parallels Between Them....Pages 3-19
Finslerian Diffusion and the Bloch–Torrey Equation....Pages 21-35
Fiber Orientation Distribution Functions and Orientation Tensors for Different Material Symmetries....Pages 37-71
Topology of 3D Linear Symmetric Tensor Fields....Pages 73-91
Random Projections for Low Multilinear Rank Tensors....Pages 93-106
Front Matter....Pages 107-107
Path-Based Mathematical Morphology on Tensor Fields....Pages 109-127
Processing Multispectral Images via Mathematical Morphology....Pages 129-148
Direction-Controlled DTI Interpolation....Pages 149-162
Tensor Voting: Current State, Challenges and New Trends in the Context of Medical Image Analysis....Pages 163-187
Front Matter....Pages 189-189
Visualization of Diffusion Propagator and Multiple Parameter Diffusion Signal....Pages 191-212
Visual Knowledge Discovery for Diffusion Kurtosis Datasets of the Human Brain....Pages 213-234
A Survey of Illustrative Visualization Techniques for Diffusion-Weighted MRI Tractography....Pages 235-256
Visualizing Symmetric Indefinite 2D Tensor Fields Using the Heat Kernel Signature....Pages 257-267
Front Matter....Pages 269-269
A Framework for the Analysis of Diffusion Compartment Imaging (DCI)....Pages 271-297
Statistical and Machine Learning Methods for Neuroimaging: Examples, Challenges, and Extensions to Diffusion Imaging Data....Pages 299-319
Front Matter....Pages 321-321
A Clustering Method for Identifying Regions of Interest in Turbulent Combustion Tensor Fields....Pages 323-338
Tensor Lines in Engineering: Success, Failure, and Open Questions....Pages 339-351
Contextual Diffusion Image Post-processing Aids Clinical Applications....Pages 353-377
Back Matter....Pages 379-383
