Local Features in Natural Images via Singularity Theory
This monograph considers a basic problem in the computer analysis of natural images, which are images of scenes involving multiple objects that are obtained by a camera lens or a viewer’s eye. The goal is to detect geometric features of objects in the ima
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James Damon Peter Giblin Gareth Haslinger
Local Features in Natural Images via Singularity Theory
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zürich Mario di Bernardo, Bristol Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and New York Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
James Damon • Peter Giblin • Gareth Haslinger
Local Features in Natural Images via Singularity Theory
123
Peter Giblin Dept. of Mathematical Sciences University of Liverpool Liverpool, United Kingdom
James Damon Department of Mathematics University of North Carolina Chapel Hill, NC USA Gareth Haslinger Ainsdale, United Kingdom
Partially supported by (1) Insight 2+ grant from the European Commission and (2) the Simons Foundation grant 230298, National Science Foundation grants DMS-0706941 and DMS-1105470, and DARPA Grant HR0011-05-1-0057
ISSN 0075-8434 Lecture Notes in Mathematics ISBN 978-3-319-41470-6 DOI 10.1007/978-3-319-41471-3
ISSN 1617-9692 (electronic) ISBN 978-3-319-41471-3 (eBook)
Library of Congress Control Number: 2016947050 Mathematics Subject Classification (2010): Applications to computer imaging: 97R60, 65D18, 68U10, 58E50 Mathematics: 58C25, 58A35, 14P15, 53A05, 58Kxx, 58K40, 58K50, 58K60, 58K25, 58K15 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
To our families Joanne and Jimi Rachel, Stephen and Charlotte Mike and Sandy
Contents
Part I
Preliminaries
1
Introduction .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .
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