Bücher der Reihe Mathematics and Visualization

This book provides an overview of the emerging field of in situ visualization, i.e. visualizing simulation data as it is generated. In situ visualization is a processing paradigm in response to recent trends in the development of high-performance computers. It has great promise in its ability to access increased temporal resolution and leverage extensive computational power. However, the paradigm also is widely viewed as limiting when it comes to exploration-oriented use cases. Furthermore, it will require visualization systems to become increasingly complex and constrained in usage. As research efforts on in situ visualization are growing, the state of the art and best practices are rapidly maturing.Specifically, this book contains chapters that reflect state-of-the-art research results and best practices in the area of in situ visualization. Our target audience are researchers and practitioners from the areas of mathematics computational science, high-performance computing, and computer science that work on or with in situ techniques, or desire to do so in future. 

Geometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap; this observation led to the idea of composing a book on Geometric Modeling for Scientific Visualization.

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.

Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.

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 reference text presents some of the tools and algorithms currently being used to create new ways of making enhanced interactive presentations and multimedia courses. The accompanying CD-ROM enables readers to get a hands on experience of the material in the book.

The nature of the physical Universe has been increasingly better understood in recent years, and cosmological concepts have undergone a rapid evolution (see, e.g., [11], [2],or [5]).

With a lot of recent developments in the field, this much-needed book has come at just the right time. The contributors also cover subjects that are relevant to effectively capturing the structure of a shape by identifying relevant shape components and their mutual relationships.

Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.

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.

Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail.

This book will serve as a valuable source of information about triangulations for the graduate student and researcher. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues.

With a lot of recent developments in the field, this much-needed book has come at just the right time. The contributors also cover subjects that are relevant to effectively capturing the structure of a shape by identifying relevant shape components and their mutual relationships.

Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail.

TheseProceedings of the 2015 MICCAI Workshop ¿Computational Diffusion MRI¿ offer asnapshot of the current state of the art on a broad range of topics within thehighly active and growing field of diffusion MRI. The topics vary fromfundamental theoretical work on mathematical modeling, to the development andevaluation of robust algorithms, new computational methods applied to diffusionmagnetic resonance imaging data, and applications in neuroscientific studiesand clinical practice.Over thelast decade interest in diffusion MRI has exploded. The technique providesunique insights into the microstructure of living tissue and enables in-vivoconnectivity mapping of the brain. Computational techniques are key to thecontinued success and development of diffusion MRI and to its widespreadtransfer into clinical practice. New processing methods are essential for addressingissues at each stage of the diffusion MRI pipeline: acquisition, reconstruction,modeling and model fitting, image processing, fiber tracking, connectivitymapping, visualization, group studies and inference.Thisvolume, which includes both careful mathematical derivations and a wealth ofrich, full-color visualizations and biologically or clinically relevantresults, offers a valuable starting point for anyone interested in learningabout computational diffusion MRI and mathematical methods for mapping brainconnectivity, as well as new perspectives and insights on current researchchallenges for those currently working in the field. It will be of interest toresearchers and practitioners in the fields of computer science, MR physics,and applied mathematics.¿

This book presents recent advances in the field of shape analysis. Written by experts in the fields of continuous-scale shape analysis, discrete shape analysis and sparsity, and numerical computing who hail from different communities, it provides a unique view of the topic from a broad range of perspectives.Over the last decade, it has become increasingly affordable to digitize shape information at high resolution. Yet analyzing and processing this data remains challenging because of the large amount of data involved, and because modern applications such as human-computer interaction require real-time processing. Meeting these challenges requires interdisciplinary approaches that combine concepts from a variety of research areas, including numerical computing, differential geometry, deformable shape modeling, sparse data representation, and machine learning. On the algorithmic side, many shape analysis tasks are modeled using partial differential equations, which can be solved using tools from the field of numerical computing. The fields of differential geometry and deformable shape modeling have recently begun to influence shape analysis methods. Furthermore, tools from the field of sparse representations, which aim to describe input data using a compressible representation with respect to a set of carefully selected basic elements, have the potential to significantly reduce the amount of data that needs to be processed in shape analysis tasks. The related field of machine learning offers similar potential.The goal of the Dagstuhl Seminar on New Perspectives in Shape Analysis held in February 2014 was to address these challenges with the help of the latest tools related to geometric, algorithmic and numerical concepts and to bring together researchers at the forefront of shape analysis who can work together to identify open problems and novel solutions. The book resulting from this seminar will appeal to researchers in the field of shape analysis, image and vision, from those who want to become more familiar with the field, to experts interested in learning about the latest advances.¿

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

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.

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.

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 covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

Visualization has become increasingly important for many types of biomedical applications and this book collects the latest results in the development of visualization methods in this field.

It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics.

This is the only textbook available on multiresolution methods in geometric modeling, a central topic in visualization, which is of great importance for industrial applications. Other supplementary material and software can be downloaded from the website www.ma.tum.de/primus 2001/.

This book presents 13 peer-reviewed papers as written results from the 2005 workshop "Topology-Based Methods in Visualization" that was initiated to enable additional stimulation in this field. It captures key concepts and novel ideas and serves as an overview of current trends in its subject.