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Author: Joachim Weickert
Publisher: Springer Science & Business Media
ISBN: 3540312722
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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.
Author: Joachim Weickert
Publisher: Springer Science & Business Media
ISBN: 3540312722
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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.
Author: David H. Laidlaw
Publisher: Springer Science & Business Media
ISBN: 3540883789
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book provides researchers an inspirational look at how to process and visualize complicated 2D and 3D images known as tensor fields. With numerous color figures, it details both the underlying mathematics and the applications of tensor fields.
Author: David H. Laidlaw
Publisher: Springer Science & Business Media
ISBN: 3642273432
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address. Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.
Author: David H. Laidlaw
Publisher: Springer
ISBN: 9783642273445
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address. Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.
Author: Carl-Fredrik Westin
Publisher: Springer
ISBN: 3642543014
Category : Mathematics
Languages : en
Pages : 343
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Book Description
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.
Author: David H. Laidlaw
Publisher: Springer Science & Business Media
ISBN: 3642273424
Category : Mathematics
Languages : en
Pages : 389
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Book Description
Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address. Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.
Author: Evren Özarslan
Publisher: Springer Nature
ISBN: 3030562158
Category : Algebra
Languages : en
Pages : 284
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Book Description
This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28-November 2, 2018.
Author: Santiago Aja-Fernández
Publisher: Springer Science & Business Media
ISBN: 1848822995
Category : Computers
Languages : en
Pages : 468
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Book Description
Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing. This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.
Author: Alexandru C. Telea
Publisher: CRC Press
ISBN: 1466585269
Category : Computers
Languages : en
Pages : 619
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Book Description
Designing a complete visualization system involves many subtle decisions. When designing a complex, real-world visualization system, such decisions involve many types of constraints, such as performance, platform (in)dependence, available programming languages and styles, user-interface toolkits, input/output data format constraints, integration with third-party code, and more. Focusing on those techniques and methods with the broadest applicability across fields, the second edition of Data Visualization: Principles and Practice provides a streamlined introduction to various visualization techniques. The book illustrates a wide variety of applications of data visualizations, illustrating the range of problems that can be tackled by such methods, and emphasizes the strong connections between visualization and related disciplines such as imaging and computer graphics. It covers a wide range of sub-topics in data visualization: data representation; visualization of scalar, vector, tensor, and volumetric data; image processing and domain modeling techniques; and information visualization. See What’s New in the Second Edition: Additional visualization algorithms and techniques New examples of combined techniques for diffusion tensor imaging (DTI) visualization, illustrative fiber track rendering, and fiber bundling techniques Additional techniques for point-cloud reconstruction Additional advanced image segmentation algorithms Several important software systems and libraries Algorithmic and software design issues are illustrated throughout by (pseudo)code fragments written in the C++ programming language. Exercises covering the topics discussed in the book, as well as datasets and source code, are also provided as additional online resources.
Author: Thierry Delmarcelle
Publisher:
ISBN:
Category : Vector fields
Languages : en
Pages : 456
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Book Description
