Gaussian Scale-Space Theory
Gaussian scale-space is one of the best understood multi-resolution techniques available to the computer vision and image analysis community. It is the purpose of this book to guide the reader through some of its main aspects. During an intensive weekend
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Computational Imaging and Vision
Managing Editor MAX A. VIERGEVER Utrecht University, Utrecht, The Netherlands
Editorial Board OLIVIER D. FAUGERAS, INRIA, Sophia-Antipolis, France
JAN J. KOENDERINK, Utrecht University, Utrecht. The Netherlands STEPHEN M. PIZER. University ofNorth Carolina. Chapel Hill. USA SABURO TSUn, Osaka University, Osaka, Japan
STEVEN W. ZUCKER, McGill University. Montreal, Canada
Volume 8
Gaussian Scale-Space Theory Edited by
Jon Sparring DIKU. Department of Computer Science. University of Copenhagen. Copenhagen.De~rk
Mads Nielsen 3D-Laboratory. School of Dentistry. University of Copenhagen. Copenhagen. De~k
LucFlorack Department of Computer Science. Faculty of Mathematics and Computer Science. University of Utrecht. Utrecht. The Netherlands
and
Peter Johansen DlKU. Department of Computer Science. University of Copenhagen. Copenhagen. De~k
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-4852-3 ISBN 978-94-015-8802-7 (eBook) DOI 10.1007/978-94-015-8802-7
Printed on acid-free paper
All Rights Reserved © 1997 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1997 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
Contents Preface Contributors Scale in Perspective Jan J. Koenderink
I 1
Applications Applications of Scale-Space Theory Bart ter Haar Romeny 1.1 Introduction... 1.2 Feature detection 1.3 Shape Properties 1.4 Higher Order Invariants 1.5 Deblurring........ 1.6 Ridges and Multimodality Matching 1. 7 Deep Structure and the Hyperstack . 1.8 Denoising and Edge-Preserving Smoothing. 1.9 Discussion...................
xi xiii xv
1 3 3 4 6 8 9 11 12 13 14
2
Enhancement of Fingerprint Images using Shape-Adapted ScaleSpace Operators Andres Almansa and Tony Lindeberg 21 2.1 Introduction.................. 21 2.2 Shape-adapted smoothing . . . . . . . . . . 23 2.3 Enhancement of ridges by shape adaptation 24 2.4 Automatic scale selection 26 2.5 Summary and discussion. 29
3
Optic Flow and Stereo Wiro J. Niessen and Robert Maas 3.1 Introduction.................. 3.2 Generalized Brightness Constraint Equation
31 31 32
vi 3.3 3.4 3.5 3.6 3.7 3.8
II
Optic flow . . . . Binocular stereo Scale selection. . Optic flow results . Stereo results Summary . . . . .
The Foundation
34 35 37 39 40 41
43
4 On the History of Gaussian Scale-Space Axiomatics Joachim Weickert, Seiji Ishikawa, and Atsushi Imiya 4.1 Introduction . . . . . . . . . . 4.2 Iijima's 1-D Axiomatic (1962) 4.2.1 Motivation . 4.2.2 Axioms .. . . . 4.2.3 Consequences.. 4.2.4 Further Results . 4.3 Otsu's 2-D Axiomatic (1981) 4.3.1 Derivation of the Gaussian 4.3.2 Further Results . 4.4 Relation to Other Work 4.5 Discussion........
45 45 47 47 47 48 50 51
