Books in the Mathematics and Visualization series

This book is the outcome of the second workshop on Topological Methods in Visualization, which was held March 4-6, 2007 in Kloster Nimbschen near Leipzig,Germany.Theworkshopbroughttogethermorethan40international researchers to present and discuss the state of the art and new trends in the ?eld of topology-based visualization.

This volume gathers papers presented at the Workshop on Computational Diffusion MRI (CDMRI 2019), held under the auspices of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), which took place in Shenzhen, China on October 17, 2019. This book presents the latest advances in the rapidly expanding field of diffusion MRI. It shares new perspectives on the latest research challenges for those currently working in the field, but also offers a valuable starting point for anyone interested in learning about computational techniques in diffusion MRI. The book includes rigorous mathematical derivations, a wealth of rich, full-colour visualisations and extensive clinically relevant results. As such, it will be of interest to researchers and practitioners in the fields of computer science, MRI physics and applied mathematics. Readers will find contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in vivo recovery of microstructural and connectivity features, as well as diffusion-relaxometry and frontline applications in research and clinical practice. This edition includes invited works from high-profile researchers with a specific focus on three new and important topics that are gaining momentum within the diffusion MRI community, including diffusion MRI signal acquisition and processing strategies, machine learning for diffusion MRI, and diffusion MRI outside the brain and clinical applications.

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.

This volume offers a valuable starting point for anyone interested in learning computational diffusion MRI and mathematical methods for brain connectivity, while also sharing new perspectives and insights on the latest research challenges for those currently working in the field.Over the last decade, interest in diffusion MRI has virtually exploded. The technique provides unique insights into the microstructure of living tissue and enables in-vivo connectivity mapping of the brain. Computational techniques are key to the continued success and development of diffusion MRI and to its widespread transfer into the clinic, while new processing methods are essential to addressing issues at each stage of the diffusion MRI pipeline: acquisition, reconstruction, modeling and model fitting, image processing, fiber tracking, connectivity mapping, visualization, group studies and inference.These papers from the 2016 MICCAI Workshop "Computational Diffusion MRI" - which was intended to provide a snapshot of the latest developments within the highly active and growing field of diffusion MR - cover a wide range of topics, from fundamental theoretical work on mathematical modeling, to the development and evaluation of robust algorithms and applications in neuroscientific studies and clinical practice. The contributions include rigorous mathematical derivations, a wealth of rich, full-color visualizations, and biologically or clinically relevant results. As such, they will be of interest to researchers and practitioners in the fields of computer science, MR physics, and applied mathematics.

This book discusses research, methods, and recent developments in the interdisciplinary field that spans research in visualization, eye tracking, human-computer interaction, and psychology.

The book discusses novel visualization techniques driven by the needs in medicine and life sciences as well as new application areas and challenges for visualization within these fields.

Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine.

This volume gathers papers presented at the Workshop on Computational Diffusion MRI (CDMRI'18), which was held under the auspices of the International Conference on Medical Image Computing and Computer Assisted Intervention in Granada, Spain on September 20, 2018.

For some time, medicine has been an important driver for the development of data processing and visualization techniques. The workshop and the book addressed questions of whether medical data visualization approaches can be devised or improved to meet these challenges, with the promise of ultimately being adopted by medical experts.

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.

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.

This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013.

This book provides a solid and uniform derivation of the various properties Bezier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure.

Based on the seminar that took place in Dagstuhl, Germany in June 2011, this contributed volume studies the four important topics within the scientific visualization field: uncertainty visualization, multifield visualization, biomedical visualization and scalable visualization.

This volume offers a valuable starting point for anyone interested in learning computational diffusion MRI and mathematical methods for brain connectivity, while also sharing new perspectives and insights on the latest research challenges for those currently working in the field.Over the last decade, interest in diffusion MRI has virtually exploded. The technique provides unique insights into the microstructure of living tissue and enables in-vivo connectivity mapping of the brain. Computational techniques are key to the continued success and development of diffusion MRI and to its widespread transfer into the clinic, while new processing methods are essential to addressing issues at each stage of the diffusion MRI pipeline: acquisition, reconstruction, modeling and model fitting, image processing, fiber tracking, connectivity mapping, visualization, group studies and inference.These papers from the 2016 MICCAI Workshop ¿Computational Diffusion MRI¿ ¿ which was intended to provide a snapshot of the latest developments within the highly active and growing field of diffusion MR ¿ cover a wide range of topics, from fundamental theoretical work on mathematical modeling, to the development and evaluation of robust algorithms and applications in neuroscientific studies and clinical practice. The contributions include rigorous mathematical derivations, a wealth of rich, full-color visualizations, and biologically or clinically relevant results. As such, they will be of interest to researchers and practitioners in the fields of computer science, MR physics, and applied mathematics.

After an introduction to the subject area and a concise treatment of the technical foundations for the subsequent chapters, this book features 14 chapters on state-of-the-art graph drawing software systems, ranging from general "tool boxes'' to customized software for various applications.

From the reviews: " A unique and fascinating blend, which is shown to be useful for a variety of applications, including robotics, geometrical optics, computer animation, and geometric design.

This volume presents the latest developments in the highly active and rapidly growing field of diffusion MRI. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as frontline applications in neuroscience research and clinical practice.These proceedings contain the papers presented at the 2017 MICCAI Workshop on Computational Diffusion MRI (CDMRI'17) held in Québec, Canada on September 10, 2017, sharing new perspectives on the most recent research challenges for those currently working in the field, but also offering a valuable starting point for anyone interested in learning computational techniques in diffusion MRI. This book includes rigorous mathematical derivations, a large number of rich, full-colour visualisations and clinically relevant results. As such, it will be of interest to researchers and practitioners in the fields of computer science, MRI physics and applied mathematics.

This volume presents the latest developments in the highly active and rapidly growing field of diffusion MRI. The reader will find numerous contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in-vivo recovery of microstructural and connectivity features, as well as frontline applications in neuroscience research and clinical practice.These proceedings contain the papers presented at the 2017 MICCAI Workshop on Computational Diffusion MRI (CDMRI¿17) held in Québec, Canada on September 10, 2017, sharing new perspectives on the most recent research challenges for those currently working in the field, but also offering a valuable starting point for anyone interested in learning computational techniques in diffusion MRI. This book includes rigorous mathematical derivations, a large number of rich, full-colour visualisations and clinically relevant results. As such, it will be of interest to researchers and practitioners in the fields of computer science, MRI physics and applied mathematics.