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Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

2014-07-17 Mathematics
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Release : 2014-07-17
Genre : Mathematics
Kind : eBook
Book Rating : 014/5 ( reviews)

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Book Synopsis Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data by : Carl-Fredrik Westin

Download or read book Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data written by Carl-Fredrik Westin. This book was released on 2014-07-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

2015-07-03 Mathematics
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Release : 2015-07-03
Genre : Mathematics
Kind : eBook
Book Rating : 901/5 ( reviews)

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Book Synopsis Visualization and Processing of Higher Order Descriptors for Multi-Valued Data by : Ingrid Hotz

Download or read book Visualization and Processing of Higher Order Descriptors for Multi-Valued Data written by Ingrid Hotz. This book was released on 2015-07-03. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Visualization and Processing of Tensor Fields

2007-06-25 Mathematics
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Release : 2007-06-25
Genre : Mathematics
Kind : eBook
Book Rating : 722/5 ( reviews)

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Book Synopsis Visualization and Processing of Tensor Fields by : Joachim Weickert

Download or read book Visualization and Processing of Tensor Fields written by Joachim Weickert. This book was released on 2007-06-25. Available in PDF, EPUB and Kindle. Book excerpt: Matrix-valued data sets – so-called second order tensor fields – have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Modeling, Analysis, and Visualization of Anisotropy

2017-10-14 Mathematics
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Release : 2017-10-14
Genre : Mathematics
Kind : eBook
Book Rating : 588/5 ( reviews)

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Book Synopsis Modeling, Analysis, and Visualization of Anisotropy by : Thomas Schultz

Download or read book Modeling, Analysis, and Visualization of Anisotropy written by Thomas Schultz. This book was released on 2017-10-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Information Processing in Medical Imaging

2021-06-20 Computers
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Release : 2021-06-20
Genre : Computers
Kind : eBook
Book Rating : 917/5 ( reviews)

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Book Synopsis Information Processing in Medical Imaging by : Aasa Feragen

Download or read book Information Processing in Medical Imaging written by Aasa Feragen. This book was released on 2021-06-20. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 27th International Conference on Information Processing in Medical Imaging, IPMI 2021, which was held online during June 28-30, 2021. The conference was originally planned to take place in Bornholm, Denmark, but changed to a virtual format due to the COVID-19 pandemic. The 59 full papers presented in this volume were carefully reviewed and selected from 200 submissions. They were organized in topical sections as follows: registration; causal models and interpretability; generative modelling; shape; brain connectivity; representation learning; segmentation; sequential modelling; learning with few or low quality labels; uncertainty quantification and generative modelling; and deep learning.

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