Topological Methods in Data Analysis and Visualization

Theory, Algorithms, and Applications
Author: Valerio Pascucci,Xavier Tricoche,Hans Hagen,Julien Tierny
Publisher: Springer Science & Business Media
ISBN: 9783642150142
Category: Mathematics
Page: 260
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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).

Topological Methods in Data Analysis and Visualization III

Theory, Algorithms, and Applications
Author: Peer-Timo Bremer,Ingrid Hotz,Valerio Pascucci,Ronald Peikert
Publisher: Springer Science & Business
ISBN: 3319040995
Category: Mathematics
Page: 279
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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.

Topological Methods in Data Analysis and Visualization II

Theory, Algorithms, and Applications
Author: Ronald Peikert,Helwig Hauser,Hamish Carr,Raphael Fuchs
Publisher: Springer Science & Business Media
ISBN: 3642231756
Category: Mathematics
Page: 299
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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.

Topological Methods in Data Analysis and Visualization IV

Theory, Algorithms, and Applications
Author: Hamish Carr,Christoph Garth,Tino Weinkauf
Publisher: Springer
ISBN: 3319446843
Category: Mathematics
Page: 363
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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.

Handbook of Discrete and Computational Geometry, Third Edition

Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher: CRC Press
ISBN: 1351645919
Category: Computers
Page: 1928
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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Mathematical Morphology and Its Applications to Signal and Image Processing

11th International Symposium, ISMM 2013, Uppsala, Sweden, May 27-29, 2013, Proceedings
Author: Cris L. Luengo Hendriks,Gunilla Borgefors,Robin Strand
Publisher: Springer
ISBN: 3642382940
Category: Computers
Page: 532
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This book contains the refereed proceedings of the 11th International Symposium on Mathematical Morphology, ISMM 2013 held in Uppsala, Sweden, in May 2013. The 41 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 52 submissions. The papers are organized in topical sections on theory; trees and hierarchies; adaptive morphology; colour; manifolds and metrics; filtering; detectors and descriptors; and applications.

Topological Data Analysis for Scientific Visualization

Author: Julien Tierny
Publisher: Springer
ISBN: 3319715070
Category: Mathematics
Page: 150
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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.

Topological and Statistical Methods for Complex Data

Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces
Author: Janine Bennett,Fabien Vivodtzev,Valerio Pascucci
Publisher: Springer
ISBN: 3662449005
Category: Mathematics
Page: 297
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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. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.

Mathematical Visualization

Algorithms, Applications and Numerics
Author: H.-C. Hege,K. Polthier
Publisher: Springer Science & Business Media
ISBN: 3662035677
Category: Mathematics
Page: 393
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Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications. The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.

Topologie I

Erster Band. Grundbegriffe der Mengentheoretischen Topologie Topologie der Komplexe · Topologische Invarianzsätze und Anschliessende Begriffsbildungen · Verschlingungen im n-Dimensionalen Euklidischen Raum Stetige Abbildungen von Polyedern
Author: Paul Alexandroff,H. Hopf
Publisher: Springer-Verlag
ISBN: 3662020211
Category: Mathematics
Page: 638
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Principal Manifolds for Data Visualization and Dimension Reduction

Author: Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev
Publisher: Springer Science & Business Media
ISBN: 3540737502
Category: Technology & Engineering
Page: 340
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The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described. Presentation of algorithms is supplemented by case studies. The volume ends with a tutorial PCA deciphers genome.

Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration

Author: Torsten Möller,Bernd Hamann,Robert D. Russell
Publisher: Springer Science & Business Media
ISBN: 3540499261
Category: Computers
Page: 350
View: 7568

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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.

Visualize This!

Author: Nathan Yau
Publisher: John Wiley & Sons
ISBN: 3527760229
Category: Statistics / Graphic methods / Data processing
Page: 422
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A guide on how to visualise and tell stories with data, providing practical design tips complemented with step-by-step tutorials.

Graph-Based Clustering and Data Visualization Algorithms

Author: Ágnes Vathy-Fogarassy,János Abonyi
Publisher: Springer Science & Business Media
ISBN: 1447151585
Category: Computers
Page: 110
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This work presents a data visualization technique that combines graph-based topology representation and dimensionality reduction methods to visualize the intrinsic data structure in a low-dimensional vector space. The application of graphs in clustering and visualization has several advantages. A graph of important edges (where edges characterize relations and weights represent similarities or distances) provides a compact representation of the entire complex data set. This text describes clustering and visualization methods that are able to utilize information hidden in these graphs, based on the synergistic combination of clustering, graph-theory, neural networks, data visualization, dimensionality reduction, fuzzy methods, and topology learning. The work contains numerous examples to aid in the understanding and implementation of the proposed algorithms, supported by a MATLAB toolbox available at an associated website.

Graduate Programs in Engineering & Applied Sciences 2008

Author: Peterson's
Publisher: Peterson's
ISBN: 9780768924039
Category: Education
Page: 1224
View: 1577

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Peterson's six-volume Graduate and Professional Programs is the trusted source for accurate, up-to-date graduate program information. With complete details on more than 44,000 master, doctoral, and first-professional degree programs in 476 disciplines at more than 2,000 accredited colleges and universities in the U.S. and Canada, this series is the perfect for students, acadmic advisors, administrators, researchers, scholars, professionals, and librarians.

Triangulations and Applications

Author: Øyvind Hjelle,Morten Dæhlen
Publisher: Springer Science & Business Media
ISBN: 3540332618
Category: Mathematics
Page: 229
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This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.

Digital Geometry

Geometric Methods for Digital Picture Analysis
Author: Reinhard Klette,Azriel Rosenfeld
Publisher: Morgan Kaufmann
ISBN: 9781558608610
Category: Computers
Page: 656
View: 3944

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Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures. *A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision *Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data *Includes exercises, examples, and references to related or more advanced work

Handbook of Graph Drawing and Visualization

Author: Roberto Tamassia
Publisher: Discrete Mathematics and its Applications
ISBN: 9781138034242
Category: Graph theory
Page: 862
View: 8036

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Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications The Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references. The first several chapters of the book deal with fundamental topological and geometric concepts and techniques used in graph drawing, such as planarity testing and embedding, crossings and planarization, symmetric drawings, and proximity drawings. The following chapters present a large collection of algorithms for constructing drawings of graphs, including tree, planar straight-line, planar orthogonal and polyline, spine and radial, circular, rectangular, hierarchical, and three-dimensional drawings as well as labeling algorithms, simultaneous embeddings, and force-directed methods. The book then introduces the GraphML language for representing graphs and their drawings and describes three software systems for constructing drawings of graphs: OGDF, GDToolkit, and PIGALE. The final chapters illustrate the use of graph drawing methods in visualization applications for biological networks, computer security, data analytics, education, computer networks, and social networks. Edited by a pioneer in graph drawing and with contributions from leaders in the graph drawing research community, this handbook shows how graph drawing and visualization can be applied in the physical, life, and social sciences. Whether you are a mathematics researcher, IT practitioner, or software developer, the book will help you understand graph drawing methods and graph visualization systems, use graph drawing techniques in your research, and incorporate graph drawing solutions in your products.