Topological Methods in Data Analysis and Visualization Theory, Algor
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 ma
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Series Editors Gerald Farin Hans-Christian Hege David Hoffman Christopher R. Johnson Konrad Polthier Martin Rumpf
For further volumes: http://www.springer.com/series/4562
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Valerio Pascucci Xavier Tricoche Hans Hagen Julien Tierny Editors
Topological Methods in Data Analysis and Visualization Theory, Algorithms, and Applications With 146 Figures, 122 in Color
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Editors Valerio Pascucci University of Utah – School of Computing Scientific Computing and Imaging Institute (SCI) S. Central Campus Dr. 50 Salt Lake City, UT 84132 USA [email protected] Xavier Tricoche Purdue University Department of Computer Science N. University Street 305 West Lafayette, IN 47907-2107 USA [email protected]
Hans Hagen Universität Kaiserslautern Fachbereich Informatik 67653 Kaiserslautern Germany [email protected]
Julien Tierny CNRS LTCI - Telecom ParisTech 46 rue Barrault Paris Cedex 13 France [email protected]
ISBN 978-3-642-15013-5 e-ISBN 978-3-642-15014-2 DOI 10.1007/978-3-642-15014-2 Springer Heidelberg Dordrecht London New York
Mathematics Subject Classification (2010): 57Q05, 68U05, 68U20, 76M27 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The deluge of data observed throughout research and industry has turned the analysis of the resulting information into the primary limiting factor for the rapid progress of science, engineering, and medicine. The field of visualization strives to tackle this data analysis challenge by devising visual representations that afford users an effective interface with their datasets. Driven by the explosion in data size and complexity experienced over the last decade, a prominent trend in today’s visualization research applies a data abstraction approach to yield high-level depictions emphasizing various salient properties of the phenomenon considered. Topology-based methods have proved especially compelling in this regard, as the topological abstraction provides a common mathematical language to identify remarkable structures in a broad range of applications and semantic contexts. Topological concep
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