Topological Methods in Data Analysis and Visualization II Theory, Al
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
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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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Ronald Peikert Helwig Hauser Hamish Carr Raphael Fuchs Editors
Topological Methods in Data Analysis and Visualization II Theory, Algorithms, and Applications
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Editors Ronald Peikert ETH Z¨urich Computational Science Z¨urich Switzerland [email protected]
Hamish Carr University of Leeds School of Computing Leeds United Kingdom [email protected]
Helwig Hauser University of Bergen Dept. of Informatics Bergen Norway [email protected]
Raphael Fuchs ETH Z¨urich Computational Science Z¨urich Switzerland [email protected]
ISBN 978-3-642-23174-2 e-ISBN 978-3-642-23175-9 DOI 10.1007/978-3-642-23175-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011944972 Mathematical Subject Classification (2010): 37C10, 57Q05, 58K45, 68U05, 68U20, 76M27 c Springer-Verlag Berlin Heidelberg 2012 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Over the past few decades, scientific research became increasingly dependent on large-scale numerical simulations to assist the analysis and comprehension of physical phenomena. This in turn has led to an increasing dependence on scientific visualization, i.e., computational methods for converting masses of numerical data to meaningful images for human interpretation. In recent years, the size of these data sets has increased to scales which vastly exceed the ability of the human visual system to absorb information, and the phenomena being studied have become increasingly complex. As a result, scientific visualization, and scientific simulation which it assists, have given rise to systematic approaches to recognizing physical and mathematical features in the data. Of these systematic approaches, one of the most effective has been the use of a topological analysis, in particular computational topology, i.e., the topological analysis of discretely sampled and combinatorially represented data sets. As topological analysis has become more important in scientific visualization, a ne
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