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A Theory of Shape Identification
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A Theory of Shape Identification A Theory of Shape Identification A Theory of Shape IdentificationA Theory of Shape Identification
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Lecture Notes in Mathematics 1948
Editors:
J.-M. Morel, Cachan
F. Takens, Groningen
B. Teissier, Paris
Frédéric Cao · José-Luis Lisani
Jean-Michel Morel · Pablo Musé
Frédéric Sur
A Theory of Shape
Identification
123
Frédéric Cao
DxO Labs
3 rue Nationale
92100 Boulogne Billancourt, France
fcao@dxo.com
José-Luis Lisani
Dep. Matemàtiques i Informàtica
University Balearic Islands
ctra. Valldemossa km.7,5
07122 Palma de Mallorca, Balears
Spain
joseluis.lisani@uib.es
Jean-Michel Morel
CMLA, Ecole Normale
Supérieure de Cachan
61 av. du Président Wilson
94235 Cachan Cédex, France
morel@cmla.ens-cachan.fr
Pablo Musé
Instituto de Ingeniería Eléctrica
Facultad de Ingeniería
Julio Herrera y Reissig 565
11300 Montevideo, Uruguay
pmuse@fing.edu.uy
Frédéric Sur
Loria Bat. C - projet Magrit
Campus Scientifique - BP 239
54506 Vandoeuvre-lès-Nancy Cédex
France
sur@loria.fr
ISBN 978-3-540-68480-0 e-ISBN 978-3-540-68481-7
DOI 10.1007/978-3-540-68481-7
Lecture Notes in Mathematics ISSN print edition: 0075-8434
ISSN electronic edition: 1617-9692
Library of Congress Control Number: 2008927359
Mathematics Subject Classification (2000): 62C05, 62G10, 62G32, 62H11, 62H15, 62H30, 62H35,
68T10, 68T45, 68U10, 91E30, 94A08, 94A13, 94B70
c
° 2008 Springer-Verlag Berlin Heidelberg
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: WMX Design Bender
Printed on acid-free paper
9 8 7 6 5 4 3 2 1
springer.com
Preface
Recent years have seen dramatic progress in shape recognition algorithms applied
to ever-growing image databases. They have been applied to image stitching, stereo
vision, image retrieval, image mosaics, solid object recognition and video and web
shape retrieval. More fundamentally, the ability of humans and animals to detect and
recognize shapes is one of the enigmas of perception. Digital images and computer
vision methods open new ways to address this enigma.
Given a dictionary of digitized shapes and a previously unobserved digital image,
the aim of shape recognition algorithms is to know whether some of the shapes in
the dictionary are present in the image. This book describes a complete method that
starts from a query image and an image database and yields a list of the images in
the database containing the query shapes.
Technically speaking there are two main issues. The first is extracting invariant
shape descriptors from digital images. Indeed, a shape can be seen from various
angles and distances and in various lights. A shape can even be partially occluded
by other shapes and still be identifiable. Because the extraction step is so crucial,
three acknowledged shape descriptors, SIFT (Scale-Invariant Feature Transform),
MSER (Maximally Stable Extremal Regions) and LLD (Level Line Descriptor) will
be introduced.
1
The second issue is deciding whether two shape descriptors are identifiable as
the same shape or not. This decision process will derive from a unique paradigm,
called the Helmholtz principle. For each decision a background model is introduced.
Then one decides whether an event of interest (such as the presence of a shape in
the image) has occurred if it has a very low probability of occurring by chance in
the background model. Thus from the statistical viewpoint shape identification goes
back to multiple hypothesis testing.
A shape descriptor is recognized if it is not likely to appear by chance in the back-
ground model. At a higher complexity level, a group of shape descriptors is recog-
nized if its spatial arrangement could not occur just by chance. These two decisions
1
In a recent review paper on affine invariant recognition written by a pool of experts, SIFT and
MSER were actually acclaimed as the best shape descriptors [122].
v
vi Preface
rely on simple stochastic geometry and eventually compute a false alarm number
for each shape descriptor. The lower this number, the more secure the identification.
In that way most familiar simple shapes or images can be reliably identified. Many
realistic experiments show false alarm rates ranging from 10
−5
to less than 10
−300
.
All in all these lecture notes prove that many shapes can indeed be identified.
For these shapes one needs no a priori model and no training, just one sample of
the shape and what statisticians call a background model, or a null model. In the
case of shape recognition, the term background is to be taken to the letter. By the
Helmholtz principle a shape is conspicuous if and only if it cannot be generated by
the image background on which it is perceived. The background model is therefore
easily learnt from the image database itself.
The above description should not be taken to suggest that the shape recognition
problem is solved. The methods described only apply to solid shapes and not to
deformable shapes. They only deal with individual shapes and images such as logos
or paintings, and not with wide classes of objects such as all humans, all cats or
all cars. This latter problem is known as categorization and is still widely open to
research.
The authors are indebted to their collaborators for many important comments
and corrections, particularly to Andrés Almansa, Yann Gousseau and Guoshen Yu.
David Mumford and another anonymous referee made valuable comments which
reshaped the book. All experiments were done using the public software MegaWave
(authors: Jacques Froment and Lionel Moisan). The SIFT method is also public and
downloadable.
The present theory was mainly developed at the Centre de Mathématiques et
Leurs Applications, at ENS Cachan, at the Universitat de les Illes Balears and
at IRISA, Rennes. It was partially financed for the past eight years by the Cen-
tre National d’Etudes Spatiales, the Centre National de la Recherche Scientifique,
the Office of Naval research (grant N00014-97-1-0839) and the Ministère de la
Recherche (project ISII-RNRT), and the Ministerio de Educación y Cultura (project
MTM2005-08567). Special thanks to Bernard Rougé and Wen Masters for their
great interest and support. We are indebted to Nick Chriss for numerous stylistic
corrections.
Frédéric Cao
José Luis Lisani
Jean-Michel Morel
Pablo Musé
Frédéric Sur
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