Discrete Images, Objects, and Functions in Zn
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Algorithms and Combinatorics 11
Editorial Board
R. L. Graham, Murray Hill B. Korte, Bonn L. Lovasz, Budapest
Klaus Voss
Discrete Images, Objects, and Functions in Zn With 100 Figures
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Klaus Voss Friedrich-Schiller-Universitat Jena Mathematische Fakultat Lehrstuhl Digitale Bildverarbeitung UHH, 17. OG
0-6900 Jena, Deutschland
Mathematics Subject Classification (1991): 68T10, 68U10, 68RlO
ISBN-13: 978-3-642-46781-3 DOl: 10.1007/978-3-642-46779-0
e-ISBN-13: 978-3-642-46779-0
Library of Congress Cataloging-in-Publication Data Voss. K. (Klaus): Discrete images. objects, and functions in Z" 1 Klaus Voss. p. cm. (Algorithms and combinatorics ; 11) Includes bibliographical references and index. ISBN-l3: 978-3-642-46781-3 I. Image processing-Mathematics. 2. Topology. I. Title. II. Series. TA1632.V6714 621.36'1'OI51-dc20 92-45827
1993
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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. Typesetting: Camera-ready by author 41/3140 - 5 4 3 2 I 0 - Printed on acid-free paper
Preface Man wird dem einzelnen nicht gerecht, wenn man es gesondert ins Auge jaftt, ohne seinen Zusammenhang mit dem Ganzen zu beachten und dem Beziehungssystem Rechnung zu tragen, in dem es steht. Thomas Mann
Science in general, as well as in each of its individual fields, is a part of human culture. In that sense, this book aims to contribute to uncovering a small part of the connections and relationships which bind image processing, categorized in informatics and technology, with the knowledge accumulated over the years on discrete structures. How does one consider problems, models, mathematical methods and practical applications? How does the search for ideas and the endeavour for knowledge in the original work of scientists find expression? Is there something to be learnt from science to date for future developments? Such questions have shaped the content and style of this book. Substantial impetus to the discrete theory of image processing was afforded by the work of Rosenfeld and colleagues. Other fruitful sources of ideas considered here are number theoretical
