Geometric Description of Images as Topographic Maps
This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent i
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1984
Vicent Caselles · Pascal Monasse
Geometric Description of Images as Topographic Maps
ABC
Vicent Caselles
Pascal Monasse
Departament de Tecnologies de la Informació i les Comunicacions Universitat Pompeu Fabra C/Roc Boronat 138 08018 Barcelona Spain [email protected]
IMAGINE École des Ponts ParisTech 19 rue Alfred Nobel 77455 Champs-sur-Marne France [email protected]
ISBN: 978-3-642-04610-0 e-ISBN: 978-3-642-04611-7 DOI: 10.1007/978-3-642-04611-7 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2009938947 Mathematics Subject Classification (2000): 68U10, 94A08, 05C05 c Springer-Verlag Berlin Heidelberg 2010 ° 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: SPi Publisher Services Printed on acid-free paper springer.com
Preface
This book discusses the basic geometric contents of an image and presents a tree data structure to handle it efficiently. It analyzes also some morphological operators that simplify this geometric contents and their implementation in terms of the data structures introduced. It finally reviews several applications to image comparison and registration, to edge and corner computation, and the selection of features associated to a given scale in images. Let us first say that, to avoid a long list, we shall not give references in this summary; they are obviously contained in this monograph. A gray level image is usually modeled as a function defined in a bounded domain D ⊆ RN (typically N = 2 for usual snapshots, N = 3 for medical images or movies) with values in R. The sensors of a camera or a CCD array transform the continuum of light energies to a finite interval of values by means of a nonlinear function g. The contrast change g depends on the properties of the sensors, but also on the illumination conditions and the reflection properties of the objects, and those conditions are generally unknown. Images are thus observed modulo an arbitrary and unknown contrast change. Mathematical morphology recognizes contrast invariance as a basic requirement and proposes that image analysis operators take into account this invariance principle. An image u is
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