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Topological Modeling For Visualization
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Book Synopsis Topological Modeling for Visualization by : Anatolij T. Fomenko
Download or read book Topological Modeling for Visualization written by Anatolij T. Fomenko and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The flood of information through various computer networks such as the In ternet characterizes the world situation in which we live. Information worlds, often called virtual spaces and cyberspaces, have been formed on computer networks. The complexity of information worlds has been increasing almost exponentially through the exponential growth of computer networks. Such nonlinearity in growth and in scope characterizes information worlds. In other words, the characterization of nonlinearity is the key to understanding, utiliz ing and living with the flood of information. The characterization approach is by characteristic points such as peaks, pits, and passes, according to the Morse theory. Another approach is by singularity signs such as folds and cusps. Atoms and molecules are the other fundamental characterization ap proach. Topology and geometry, including differential topology, serve as the framework for the characterization. Topological Modeling for Visualization is a textbook for those interested in this characterization, to understand what it is and how to do it. Understanding is the key to utilizing information worlds and to living with the changes in the real world. Writing this textbook required careful preparation by the authors. There are complex mathematical concepts that require designing a writing style that facilitates understanding and appeals to the reader. To evolve a style, we set as a main goal of this book the establishment of a link between the theoretical aspects of modern geometry and topology, on the one hand, and experimental computer geometry, on the other.
Book Synopsis Topological Data Analysis for Scientific Visualization by : Julien Tierny
Download or read book Topological Data Analysis for Scientific Visualization written by Julien Tierny and published by Springer. This book was released on 2018-01-16 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining theoretical and practical aspects of topology, this book provides a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a painstaking but intuitive manner, with numerous high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in detail, and their application is carefully demonstrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis for lecturers, students and researchers.
Book Synopsis Topological Methods in Data Analysis and Visualization by : Valerio Pascucci
Download or read book Topological Methods in Data Analysis and Visualization written by Valerio Pascucci and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . The editors have brought together the most prominent and best recognized researchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Snowbird, Utah, US. The 2009 "TopoInVis" workshop follows the two successful workshops in 2005 (Slovakia) and 2007 (Germany).
Book Synopsis Topological Methods in Data Analysis and Visualization III by : Peer-Timo Bremer
Download or read book Topological Methods in Data Analysis and Visualization III written by Peer-Timo Bremer and published by Springer Science & Business. This book was released on 2014-04-22 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world’s leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.
Book Synopsis Topological Methods in Data Analysis and Visualization IV by : Hamish Carr
Download or read book Topological Methods in Data Analysis and Visualization IV written by Hamish Carr and published by Springer. This book was released on 2017-06-01 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.
Book Synopsis Topological Methods in Data Analysis and Visualization V by : Hamish Carr
Download or read book Topological Methods in Data Analysis and Visualization V written by Hamish Carr and published by Springer Nature. This book was released on 2020-12-10 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world’s leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.
Book Synopsis Topological Methods in Data Analysis and Visualization VI by : Ingrid Hotz
Download or read book Topological Methods in Data Analysis and Visualization VI written by Ingrid Hotz and published by Springer. This book was released on 2022-09-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.
Book Synopsis Topological Methods in Data Analysis and Visualization II by : Ronald Peikert
Download or read book Topological Methods in Data Analysis and Visualization II written by Ronald Peikert and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine. Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysis—theory, algorithms and applications.
Book Synopsis Topology-based Methods in Visualization by : Helwig Hauser
Download or read book Topology-based Methods in Visualization written by Helwig Hauser and published by Springer Science & Business Media. This book was released on 2007-05-24 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 contains a survey of the state-of-the-art, as well original work by leading experts that has not been published before, spanning both theory and applications. It captures key concepts and novel ideas and serves as an overview of current trends in its subject.
Book Synopsis Establishing Topological Data Analysis by : Tanmay J. Kotha
Download or read book Establishing Topological Data Analysis written by Tanmay J. Kotha and published by . This book was released on 2020 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: When visualizing data, we would like to convey both the data and the uncertainty associated with it. There are many incentives to do this, ranging from hurricane path projection to geographical surveys. Important decision making tasks rely upon humans perceiving a clear picture of the data and having confidence in their decisions. Topological Data Analysis has the potential to visualize the data as features or hierarchies in ways that are familiar to human intuition, and thus could help us convey the variation associated with uncertainty. In this thesis, we evaluate four visualization techniques: color maps, isocontours, Reeb graphs, and persistence diagrams, that each demonstrate some level of topological representation of the data. We build and run a user study evaluating the perception of various Gaussian signals applied on 3D models using each of the visualization techniques, and measure how effectively they each portray positional and amplitude variations. We show that for positional variation, the topology-based Reeb graph visualization shows higher accuracy than the other types of visualizations. For amplitude variation, the least topologically-oriented technique, color maps, demonstrated the highest accuracy. In terms of confidence, we show high levels of confidence in decision making for all techniques, except for color maps. These results take an important step towards understanding what topology-based tools are best to use under various data configuration scenarios.
Book Synopsis Visualization and Mathematics by : H.-C. Hege
Download or read book Visualization and Mathematics written by H.-C. Hege and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts. Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.
Book Synopsis Computational Topology for Data Analysis by : Tamal Krishna Dey
Download or read book Computational Topology for Data Analysis written by Tamal Krishna Dey and published by Cambridge University Press. This book was released on 2022-03-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Book Synopsis Data-Driven Modeling Using Spherical Self-Organizing Feature Maps by : Archana Sangole
Download or read book Data-Driven Modeling Using Spherical Self-Organizing Feature Maps written by Archana Sangole and published by Universal-Publishers. This book was released on 2006-04-28 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Researchers and data analysts are increasingly relying on graphical tools to assist them in modeling their data, generating their hypotheses, and gaining deeper insights on their experimentally acquired data. Recent advances in technology have made available more improved and novel modeling and analysis media that facilitate intuitive, task-driven exploratory analysis and manipulation of the displayed graphical representations. In order to utilize these emerging technologies researchers must be able to transform experimentally acquired data vectors into a visual form or secondary representation that has a simple structure and, is easily transferable into the media. As well, it is essential that it can be modified or manipulated within the display environment. This thesis presents a data-driven modeling technique that utilizes the basic learning strategy of an unsupervised clustering algorithm, called the self-organizing feature map, to adaptively learn topological associations inherent in the data and preserve them within the topology imposed by its predefined spherical lattice, thereby transforming the data into a 3D tessellated form. The tessellated graphical forms originate from a sphere thereby simplifying the process of computing its transformation parameters on re-orientation within an interactive, task-driven, graphical display medium. A variety of data sets including six sets of scattered 3D coordinate data, chaotic attractor data, the more commonly used Fisher s Iris flower data, medical numeric data, geographic and environmental data are used to illustrate the data-driven modeling and visualization mechanism. The modeling algorithm is first applied to scattered 3D coordinate data to understand the influence of the spherical topology on data organization. Two cases are examined, one in which the integrity of the spherical lattice is maintained during learning and, the second, in which the inter-node connections in the spherical lattice are adaptively changed during learning. In the analysis, scattered coordinate data of freeform objects with topology equivalent to a sphere and those whose topology is not equivalent to a sphere are used. Experiments demonstrate that it is possible to get reasonably good results with the degree of resemblance, determined by an average of the total normalized error measure, ranging from 6.2x10-5 1.1x10-3. The experimental analysis using scattered coordinate data facilitates an understanding of the algorithm and provides evidence of the topology-preserving capability of the spherical self-organizing feature map. The algorithm is later implemented using abstract, seemingly random, numeric data. Unlike in the case of 3D coordinate data, wherein the SOFM lattice is in the same coordinate frame (domain) as the input vectors, the numeric data is abstract. The criterion for deforming the spherical lattice is determined using mathematical and statistical functions as measures-of information that are tailored to reflect some aspect of meaningful, tangible, inter-vector relationships or associations embedded in the spatial data that reveal some physical aspect of the data. These measures are largely application-dependent and need to be defined by the data analyst or an expert. Interpretation of the resulting 3D tessellated graphical representation or form (glyph) is more complex and task dependent as compared to that of scattered coordinate data. Very simple measures are used in this analysis in order to facilitate discussion of the underlying mechanism to transform abstract numeric data into 3D graphical forms or glyphs. Several data sets are used in the analysis to illustrate how novel characteristics hidden in the data, and not easily apparent in the string of numbers, can be reflected via 3D graphical forms. The proposed data-driven modeling approach provides a viable mechanism to generate 3D tessellated representations of data that can be easily transferred to a graphical modeling and ana
Book Synopsis Topological Methods in Data Analysis and Visualization VI by : Ingrid Hotz
Download or read book Topological Methods in Data Analysis and Visualization VI written by Ingrid Hotz and published by Springer Nature. This book was released on 2021-09-28 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.
Book Synopsis Gaining Insights Into Volumetric Data Visualization by : Jianlong Zhou
Download or read book Gaining Insights Into Volumetric Data Visualization written by Jianlong Zhou and published by LAP Lambert Academic Publishing. This book was released on 2012-05 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, topology based techniques have begun to emerge as a general framework in visualization with the increase of scientific data in size and complexity. Topology could be used to capture significant features of the data at an abstract level, enabling and facilitating data understanding in visualization. This book focuses on investigating effective uses of the contour tree, one of topological abstractions of the scalar field, in improving efficiency of volumetric data analysis. It achieves the goals by increasing the presentation of topology information in order to explore various relationships of geometrical structures. In particular, the book plays emphasis on a novel approach for automating transfer function generations in volume visualization using topology-controlled residue flow model and harmonic colors. The generated transfer functions reveal structural relationships automatically. To make this work practical, this book also deals with topology simplification. The analysis should help shed some light on the research of topology-controlled visualization. It should be especially useful to professionals in volumetric visualization and medical image analysis.
Book Synopsis Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration by : Torsten Möller
Download or read book Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration written by Torsten Möller and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. 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.
Book Synopsis Mathematical Modeling Through Topological Surgery and Applications by : Stathis Antoniou
Download or read book Mathematical Modeling Through Topological Surgery and Applications written by Stathis Antoniou and published by Springer. This book was released on 2018-08-23 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological surgery is a mathematical technique used for creating new manifolds out of known ones. In this book the authors observe that it also occurs in natural phenomena of all scales: 1-dimensional surgery happens during DNA recombination and when cosmic magnetic lines reconnect; 2-dimensional surgery happens during tornado formation and cell mitosis; and they conjecture that 3-dimensional surgery happens during the formation of black holes from cosmic strings, offering an explanation for the existence of a black hole’s singularity. Inspired by such phenomena, the authors present a new topological model that extends the formal definition to a continuous process caused by local forces. Lastly, they describe an intrinsic connection between topological surgery and a chaotic dynamical system exhibiting a “hole drilling” behavior. The authors’ model indicates where to look for the forces causing surgery and what deformations should be observed in the local submanifolds involved. These predictions are significant for the study of phenomena exhibiting surgery and they also open new research directions. This novel study enables readers to gain a better understanding of the topology and dynamics of various natural phenomena, as well as topological surgery itself and serves as a basis for many more insightful observations and new physical implications.
