Visualization And Processing Of Tensors And Higher Order Descriptors For Multi Valued Data
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Visualization And Processing Of Higher Order Descriptors For Multi Valued Data
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Author : Ingrid Hotz
language : en
Publisher: Springer
Release Date : 2015-07-03
Visualization And Processing Of Higher Order Descriptors For Multi Valued Data written by Ingrid Hotz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-03 with Mathematics categories.
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 Tensors And Higher Order Descriptors For Multi Valued Data
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Author : Carl-Fredrik Westin
language : en
Publisher: Springer
Release Date : 2014-07-17
Visualization And Processing Of Tensors And Higher Order Descriptors For Multi Valued Data written by Carl-Fredrik Westin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-17 with Mathematics categories.
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.
Modeling Analysis And Visualization Of Anisotropy
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Author : Thomas Schultz
language : en
Publisher: Springer
Release Date : 2017-10-14
Modeling Analysis And Visualization Of Anisotropy written by Thomas Schultz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-14 with Mathematics categories.
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.
See Through
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Author : Jochen Jankowai
language : en
Publisher: Linköping University Electronic Press
Release Date : 2024-12-13
See Through written by Jochen Jankowai and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-13 with categories.
The problem of visualising multivariate data and tensor fields inherits its complexity from the data it targets. By definition, complex data is "hard to separate, analyse, or solve"1. This becomes evident through the fact that methods for "simple" data such as scalars and vectors do not trivially extend to multivariate data and tensors. In the light of increasing number of output variables from simulation models and measurements, this lack of methods leads to a limited choice in the analysis and to a lower fidelity of the analysis. In addition, split application of established methods to a subset of the data, for example the separate rendering of isosurfaces for the different scalar fields contained in multivariate data, brings about a number of challenges and pitfalls. In this work I present several approaches to extending existing methods for scalar field visualisation and analysis to multivariate data and, in some cases by extension, tensor fields. Specifically, I have investigated the extraction of isosurfaces from multivariate data, the topological analysis of multivariate data and tensor fields, and the design of transfer functions for tensor fields. Isosurfaces (contours) are a widely used visualisation modality. They can be used to intuitively highlight regions of interest and are the goto choice for taking snapshots during large-scale in-situ simulations to verify results. In domains such as meteorology where simulations yield a number of output variables for pressure, temperature, precipitation, etc., methods for visualising multivariate isosurfaces are needed. Feature level sets offer such a method by interpreting an isosurface as the result of an intersection of the isovalue with the data in the domain. From this, we expand the notion of isovalues, in this context called traits, and isosurfaces to arbitrary dimensionality. An intermediate product of the calculation of feature level sets is the distance field defining every data point’s distance towards the trait. Given this distance field, we compute the merge tree for it and thereby enable topological analysis of multivariate data. The choice of merge trees comes naturally as minima in the distance field correspond to regions closest to the trait. The concept of derived fields as input is also used in our approach to topological analysis of tensor fields. Special attention needs to be paid to the non-linear behaviour of derived vector and scalar fields. We use the field of eigenvectors derived from the tensor field to determine cells containing degenerate points in tensor fields and insert zero-valued points in the corresponding anisotropy field. This process yields a scalar field which can subsequently be used as input for further topological analysis.Another challenge when it comes to the visualisation of tensor fields is the design of transfer functions in the context of volume rendering. This is because of the high dimensional entity that is a tensor and its non-linear derivatives. We span a shape space which is populated by representatives which visually encode the tensor. This allows the user to steer the rendering by selecting the desired "shape" of the tensor rather than adjusting a slider for a derived scalar value. 1 Merriam-Webster. Complex. In Merriam-Webster dictionary (Merriam-Webster.com). Retrieved December 1st, 2024, from https://www.merriam-webster.com/dictionary/complex Problemet med att visualisera multivariat data och tensorfält beror på komplexiteten hos själva datan. Enligt definitionen består komplexa data av "många delar som hänger samman på ett svåröverskådligt sätt"2. Detta blir uppenbart genom det faktum att metoder för 'enkla' data, såsom skalärer och vektorer, inte på ett trivialt sätt går att utvidga till multivariat data och tensorer. På grund av det ökande antalet outputvariabler från simuleringsmodeller och mätningar leder denna brist till ett begränsat val av metoder i analysen och till en lägre analystrohet. Dessutom medför en uppdelad tillämpning av etablerade metoder på en delmängd av data, till exempel separat rendering av isoytor för de olika skalära fälten som ingår i multivariat data, ett antal utmaningar och fallgropar. I detta arbete presenterar jag flera tillvägagångssätt för att utvidga befintliga metoder för skalärfältsvisualisering och analys till multivariat data och, i vissa fall, i förlängningen, tensorfält. Specifikt har jag undersökt extraktion av isoytor från multivariat data, den topologiska analysen av multivariat data och tensorfält samt designen av överföringsfunktioner för tensorfält. Isoytor (konturer) är en välkänd visualiseringsteknik. De kan användas för att intuitivt lyfta fram områden av intresse och är det naturliga valet för att ta ögonblicksbilder under storskaliga simuleringar på plats för att verifiera resultat. Inom områden som meteorologi där simuleringar ger ett antal utdatavariabler för tryck, temperatur, nederbörd etc. behövs metoder för att visualisera multivariata isoytor. Feature level sets erbjuder en sådan metod genom att tolka en isoyta som resultatet av en skärning av isovärdet med data i domänen. Genom detta utökar vi begreppet isovärden, i detta sammanhang kallade traits, och isoytor till godtycklig dimensionalitet. En mellanprodukt av beräkningen av feature level sets är avståndsfältet som definierar varje datapunkts avstånd till trait:en. Med tanke på detta avståndsfält beräknar vi merge trees för det och möjliggör därigenom topologisk analys av multivariata data. Valet av merge trees kommer naturligt då minima i avståndsfältet motsvarar regioner närmast trait:en. Konceptet med beräknade fält som input används också i vårt förhållningssätt till topologisk analys av tensorfält. Det icke-linjära beteendet hos härledda/uträknade vektor- och skalära fält bör här ägnas särskild uppmärksamhet. Vi använder fältet av egenvektorer som härleds från tensorfältet för att bestämma celler som innehåller degenererade punkter i tensorfält och infogar nollvärdespunkter i motsvarande anisotropifält. Denna process ger ett skalärt fält som sedan kan användas som input för ytterligare topologisk analys. En annan utmaning när det kommer till visualisering av tensorfält är utformningen av överföringsfunktioner i samband med volymrendering. Detta beror på den högdimensionella enheten som är en tensor och dess icke-linjära derivator. Vi erbjuder ett bredd designutrymme för att visuellt koda tensorn. Detta gör att användaren kan styra renderingen genom att välja önskad "form" av tensorn istället för att justera en skjutreglage för ett härlett skalärt värde. 2 Svensk ordbok. Komplex. I Svenska Akademiens ordbok (svenska.se). Hämtad den 1:a december 2024 från https://svenska.se/so/?id=140703_ 1&pz=3
Handbook Of Diffusion Mr Tractography
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Author : Flavio Dell'Acqua
language : en
Publisher: Academic Press
Release Date : 2024-11-19
Handbook Of Diffusion Mr Tractography written by Flavio Dell'Acqua and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-19 with Computers categories.
Handbook of Tractography presents methods and applications of MR diffusion tractography, providing deep insights into the theory and implementation of existing tractography techniques and offering practical advice on how to apply diffusion tractography to research projects and clinical applications. Starting from the design of MR acquisition protocols optimized for tractography, the book follows a pipeline approach to explain the main methods behind diffusion modelling and tractography, including advanced analysis of tractography data and connectomics. An extensive section of the book is devoted to the description of tractography applications in research and clinical settings to give a complete picture of tractography practice today. By focusing on technology, models and applications, this handbook will be an indispensable reference for researchers and students with backgrounds in computer science, mathematics, physics, neuroscience and medical science. - Provides a unique reference covering the whole field of MRI diffusion tractography - Includes in-depth descriptions of the latest research and current state-of-the-art of methods available in the field of diffusion tractography - Present a step-by-step pipeline approach, from setting up MRI data acquisition to the analysis of large-scale tractography datasets
Information Processing In Medical Imaging
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Author : Aasa Feragen
language : en
Publisher: Springer Nature
Release Date : 2021-06-20
Information Processing In Medical Imaging written by Aasa Feragen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-20 with Computers categories.
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.
Computer Analysis Of Images And Patterns
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Author : George Azzopardi
language : en
Publisher: Springer
Release Date : 2015-08-25
Computer Analysis Of Images And Patterns written by George Azzopardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-25 with Computers categories.
The two volume set LNCS 9256 and 9257 constitutes the refereed proceedings of the 16th International Conference on Computer Analysis of Images and Patterns, CAIP 2015, held in Valletta, Malta, in September 2015. The 138 papers presented were carefully reviewed and selected from numerous submissions. CAIP 2015 is the sixteenth in the CAIP series of biennial international conferences devoted to all aspects of computer vision, image analysis and processing, pattern recognition, and related fields.
Mathematical Morphology And Its Applications To Signal And Image Processing
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Author : Jón Atli Benediktsson
language : en
Publisher: Springer
Release Date : 2015-05-15
Mathematical Morphology And Its Applications To Signal And Image Processing written by Jón Atli Benediktsson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-15 with Computers categories.
This book contains the thoroughly refereed proceedings of the 12th International Symposium on Mathematical Morphology, ISMM 2015 held in Reykjavik, Iceland, in May 2015. The 62 revised full papers were carefully reviewed and selected from 72 submissions. The papers are organized in topical sections on evaluations and applications; hierarchies; color, multivalued and orientation fields; optimization, differential calculus and probabilities; topology and discrete geometry; and algorithms and implementation.
Mathematical Morphology And Its Applications To Signal And Image Processing
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Author : Bernhard Burgeth
language : en
Publisher: Springer
Release Date : 2019-06-19
Mathematical Morphology And Its Applications To Signal And Image Processing written by Bernhard Burgeth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Computers categories.
This book contains the refereed proceedings of the 14th International Symposium on Mathematical Morphology, ISMM 2019, held in Saarbrücken, Germany, in July 2019. The 40 revised full papers presented together with one invited talk were carefully reviewed and selected from 54 submissions. The papers are organized in topical sections on Theory, Discrete Topology and Tomography, Trees and Hierarchies, Multivariate Morphology, Computational Morphology, Machine Learning, Segmentation, Applications in Engineering, and Applications in (Bio)medical Imaging.
Foundations Of Data Visualization
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Author : Min Chen
language : en
Publisher: Springer Nature
Release Date : 2020-08-11
Foundations Of Data Visualization written by Min Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-11 with Computers categories.
This is the first book that focuses entirely on the fundamental questions in visualization. Unlike other existing books in the field, it contains discussions that go far beyond individual visual representations and individual visualization algorithms. It offers a collection of investigative discourses that probe these questions from different perspectives, including concepts that help frame these questions and their potential answers, mathematical methods that underpin the scientific reasoning of these questions, empirical methods that facilitate the validation and falsification of potential answers, and case studies that stimulate hypotheses about potential answers while providing practical evidence for such hypotheses. Readers are not instructed to follow a specific theory, but their attention is brought to a broad range of schools of thoughts and different ways of investigating fundamental questions. As such, the book represents the by now most significant collective effort for gathering a large collection of discourses on the foundation of data visualization. Data visualization is a relatively young scientific discipline. Over the last three decades, a large collection of computer-supported visualization techniques have been developed, and the merits and benefits of using these techniques have been evidenced by numerous applications in practice. These technical advancements have given rise to the scientific curiosity about some fundamental questions such as why and how visualization works, when it is useful or effective and when it is not, what are the primary factors affecting its usefulness and effectiveness, and so on. This book signifies timely and exciting opportunities to answer such fundamental questions by building on the wealth of knowledge and experience accumulated in developing and deploying visualization technology in practice.