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Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and analyze large and complex diffusion data such as High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Kurtosis Imaging (DKI). A Part entitled Tensor Signal Processing presents new methods for processing tensor-valued data, including a novel perspective on performing voxel-wise morphometry of diffusion tensor data using kernel-based approach, explores the free-water diffusion model, and reviews proposed approaches for computing fabric tensors, emphasizing trabecular bone research. The last Part, Applications of Tensor Processing, discusses metric and curvature tensors, two of the most studied tensors in geometry processing. Also covered is a technique for diagnostic prediction of first-episode schizophrenia patients based on brain diffusion MRI data. The last chapter presents an interactive system integrating the visual analysis of diffusion MRI tractography with data from electroencephalography.

Calculus of tensors. --- Calculus of tensors --- Information visualization. --- Data processing. --- Data visualization --- Visualization of information --- Information science --- Visual analytics --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Visualization. --- Differential equations, partial. --- Global differential geometry. --- Computer vision. --- Computer graphics. --- Partial Differential Equations. --- Differential Geometry. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Computer Graphics. --- Theoretical, Mathematical and Computational Physics. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Partial differential equations --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Digital techniques --- Mathematics. --- Partial differential equations. --- Differential geometry. --- Optical data processing. --- Mathematical physics. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Differential geometry --- Physical mathematics --- Physics --- Math --- Science --- Optical equipment --- Mathematics

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This book contains the refereed proceedings of the 14th International Symposium on Mathematical Morphology, ISMM 2019, held in Saarbrücken, Germany, in July 2019. The 40 revised full papers presented together with one invited talk were carefully reviewed and selected from 54 submissions. The papers are organized in topical sections on Theory, Discrete Topology and Tomography, Trees and Hierarchies, Multivariate Morphology, Computational Morphology, Machine Learning, Segmentation, Applications in Engineering, and Applications in (Bio)medical Imaging.

Computer vision. --- Computer science. --- Information Systems. --- Software engineering. --- Artificial intelligence. --- Image Processing and Computer Vision. --- Math Applications in Computer Science. --- Management of Computing and Information Systems. --- Software Engineering. --- Artificial Intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Computer software engineering --- Engineering --- Informatics --- Science --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Mathematics. --- Optical data processing. --- Computer science—Mathematics. --- Management information systems. --- Computer-based information systems --- EIS (Information systems) --- Executive information systems --- MIS (Information systems) --- Sociotechnical systems --- Information resources management --- Management --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Communication systems --- Optical equipment