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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.

Mathematics. --- Visualization. --- Linear and Multilinear Algebras, Matrix Theory. --- Computational Science and Engineering. --- Image Processing and Computer Vision. --- Computer vision. --- Matrix theory. --- Computer science. --- Mathématiques --- Vision par ordinateur --- Informatique --- Visualisation --- Calculus of tensors -- Data processing. --- Information visualization. --- Engineering & Applied Sciences --- Computer Science --- Calculus of tensors --- Data processing. --- Data visualization --- Visualization of information --- Absolute differential calculus --- Analysis, Tensor --- Calculus, Absolute differential --- Calculus, Tensor --- Tensor analysis --- Tensor calculus --- Image processing. --- Algebra. --- Computer mathematics. --- Information science --- Visual analytics --- Geometry, Differential --- Geometry, Infinitesimal --- Vector analysis --- Spinor analysis --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Informatics --- Science --- Imagination --- Visual perception --- Imagery (Psychology) --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Computer mathematics --- Mathematics --- Mathematical analysis --- Math --- Optical equipment

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This book focuses on the modeling, processing and visualization of anisotropy, irrespective of the context in which it emerges, using state-of-the-art mathematical tools. As such, it differs substantially from conventional reference works, which are centered on a particular application. It covers the following topics: (i) the geometric structure of tensors, (ii) statistical methods for tensor field processing, (iii) challenges in mapping neural connectivity and structural mechanics, (iv) processing of uncertainty, and (v) visualizing higher-order representations. In addition to original research contributions, it provides insightful reviews. This multidisciplinary book is the sixth in a series that aims to foster scientific exchange between communities employing tensors and other higher-order representations of directionally dependent data. A significant number of the chapters were co-authored by the participants of the workshop titled Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis, which was held in Dagstuhl, Germany in April 2016. It offers a valuable resource for those working in the field of multi-directional data, vital inspirations for the development of new models, and essential analysis and visualization techniques, thus furthering the state-of-the-art in studies involving anisotropy.

Mathematics. --- Image processing. --- Matrix theory. --- Algebra. --- Computer mathematics. --- Visualization. --- Linear and Multilinear Algebras, Matrix Theory. --- Computational Science and Engineering. --- Image Processing and Computer Vision. --- Anisotropy. --- Anisotropy --- Mathematical models. --- Anisotropic crystals --- Crystallography --- Matter --- Properties --- Computer science. --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Informatics --- Science --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Math --- Computer mathematics --- Mathematics --- Mathematical analysis --- Optical equipment

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This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world’s leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.

Information visualization. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Data visualization --- Visualization of information --- Information science --- Visual analytics --- Visualization. --- Global analysis (Mathematics). --- Topology. --- Geometry. --- Computer vision. --- Optical pattern recognition. --- Analysis. --- Image Processing and Computer Vision. --- Pattern Recognition. --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Mathematics --- Euclid's Elements --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Mathematics. --- Analysis (Mathematics). --- Optical data processing. --- Pattern recognition. --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Math --- Science --- Optical equipment --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal

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Topology --- Geometry --- Mathematical control systems --- Computer science --- Computer architecture. Operating systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- bedrijfssoftware --- computers --- grafische vormgeving --- informatica --- wiskunde --- algoritmen --- computerkunde --- geometrie --- topologie