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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 provides a broad and vivid view of current work on this rising topic. Topics coated differ from functions of the analysis of tensor fields to evaluation on their mathematical and analytical properties.
Half I, Tensor Data Visualization, surveys strategies for visualization of tensors and tensor fields in engineering, discusses the current state of the paintings and challenges, and examines tensor invariants and glyph design, along with an abstract of widespread glyphs.
The second Half, Illustration and Processing of Higher-order Descriptors, describes a matrix illustration of local half, outlines mathematical morphological operations strategies, extended for use in vector footage, and generalizes erosion to the world of diffusion weighted MRI.
Half III, Higher Order Tensors and Riemannian-Finsler Geometry, presents extremely efficient mathematical language to model and analyze big and difficult diffusion data resembling Extreme Angular Choice Diffusion Imaging (HARDI) and Diffusion Kurtosis Imaging (DKI).
A Half entitled Tensor Signal Processing presents new methods for processing tensor-valued data, along with a novel perspective on performing voxel-intelligent morphometry of diffusion tensor data using kernel-based technique, explores the free-water diffusion model, and critiques proposed approaches for computing materials tensors, emphasizing trabecular bone evaluation.
The ultimate Half, Functions of Tensor Processing, discusses metric and curvature tensors, two of in all probability probably the most studied tensors in geometry processing. Moreover coated is a method for diagnostic prediction of first-episode schizophrenia victims based mostly totally on thoughts diffusion MRI data. The ultimate chapter presents an interactive system integrating the seen analysis of diffusion MRI tractography with data from electroencephalography.
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