Morphological Image Analysis: Principles and Applications

400 Pages·2004·14.699 MB·English

by  Dr. Pierre Soille (auth.)

Pierre Soille
Morphological Image Analysis
Springer-Verlag Berlin Heidelberg GmbH
Pierre Soille
Morphological
Image Analysis
Principles and Applications
Second Edition
Corrected second printing
With 260 Figures
, Springer
Dr. Pierre Soille
EC Joint Research Centre
Via Enrico Fermi 1, T.P.262
21020 Ispra (Va)
ltaly
e-mail: [email protected]
Library of Congress Cataloging-in-Publication Data
SoiIle, Pierre.
(Morphologische Bildverarbeitung. English)
Morphological image analysis: principles and applications 1 Pierre SoiIle.--md ed
ISBN 978-3-642-07696-1 ISBN 978-3-662-05088-0 (eBook)
DOI 10.1007/978-3-662-05088-0
1. Image analysis. 2. Image processing--Mathematics. 3. Morphisms (Mathematics) I. Title
TA1637.S6513 2002
621.36'7--dc21 2002030513
ISBN 978-3-642-07696-1
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To the memory of my father,
Andre Soille (1923-2002)
Preface to the second edition
Following the success of the first edition, recent developments in the field of
morphological image analysis called for an extended second edition. This was
not an easy task because any single modification and extension had to be care
fully evaluated for preserving a coherent structure. The text has been fully
revised with the goal of improving its clarity while introducing new concepts
of interest to real image analysis applications. The skeleton of the book en
joys one additional bone in the form of a chapter devoted to texture analysis.
Flesh around the initial bones has grown by more than 20 percent leading to
a total of 391 pages (including 39 additional figures, 3 new tables, 93 extra
bibliographical references, as well as 1 supplementary index). This increase
has been distributed more or less evenly across all chapters. Main extensions
include: discussion about multichannel images and their morphological pro
cessing, ordering relations on image partitions, connected operators and level
lings, homotopy for grey tone images, translation-invariant implementations
of erosions and dilations by line segments, reinforced emphasis on rank-based
morphological operators, grey tone hit-or-miss, ordered independent homoto
pic thinnings and anchored skeletons, self-dual geodesic transformation and
reconstruction, area based self-dual filters, anti-centre, watershed-based tex
ture segmentation, texture models, and a series of new scientific and industrial
applications. Chapters on erosions/dilations and openings/closings have been
made more concise by moving notions such as the morphological covariance
and granulometries to the texture analysis chapter.
The first edition in English has been published in 1999 while I was with
the Silsoe Research Institute (SRI) located in Silsoe, England. I am indebted
to all members of the image analysis group led by Robin Tillett for intro
ducing me to the captivating world of computer vision applied to agri-food
industries. John Marchant from this group deserves special thanks for sug
gestions he made on a draft of the revised 'background notions' chapter. In
December 1999, I joined the Space Applications Institute of the EC Joint
Research Centre (JRC) established in Ispra, Italy. This opened an avenue for
the application of mathematical morphology (MM) to Pan-European geospa
tial data sets. I am very grateful to all JRC staff I have been in contact with
since my arrival and especially to all members of the advanced methods sec
tor led by Joannis Kanellopoulos. Martino Pesaresi deserves a special thank
Vlll
for sparkling ideas and great enthusiasm for applying MM to earth obser
vation imagery. I have also the pleasure to acknowledge Philippe Caperan,
Daniele Ehrlich, and Jurgen Vogt for their interest in the application of MM
to their projects. Beyond my colleagues at work, I wish to thank all people
interested in image analysis I have been in touch with since the last edition of
this book. Their encouragements, suggestions, or simply eager to learn and
apply morphological image analysis to real problems have been a constant
source of motivation and inspiration for the completion of this second edition.
Feedback from readers has always been very much appreciated. In particular,
I would like to credit Michel Kocher for regular correspondence and sugges
tions. Special thanks to Dietrich Stoyan for his interest to the first edition of
this book including his comments on the first edition in German. The chapter
on texture analysis is based on a paper published in a volume of the Lecture
Notes in Physics co-edited by Dietrich Stoyan and Klaus Mecke. I am thank
ful to them for their comments and suggestions on the early version of the
paper. Many thanks also to Robert Magerle for his openness and interest
in applying morphology to atomic force microscopy images, Henk Heijmans
for many fruitful discussions at the JRC and CWI, Christian Ronse for his
advices, Hugues Talbot for his visit to SRI and the collaborative work we did
on directional morphology, Vincent Ranwez for the joint work on order in
dependent thinnings, Laurent Misson for the tree ring project, Paul Whelan
for the watermark project, Gunilla Borgefors, Vito Di Gesu, Joachim Ohser,
Pramod Rastogi, Gerald Sommer, Michela Spagnuolo, Cesare Valenti, and
Rein van den Boomgaard for inviting me to give lectures in conjunction with
seminars, conferences, or postgraduate courses.
Finally, the greatest change since the last edition is the arrival of my son
Simon in March 2000. He and my wife Sabine motivated me to speed up
the production of this second edition during the many sacrificed evenings
and holidays. I am enormously thankful to them for their understanding and
support. I hope you will appreciate this new edition and find it useful. In
any case, I will be very grateful to hear from you for further comments and
suggestions.
Preface to the first edition
In 1992, by the time I was finishing my doctorate thesis jointly at the Ecole
des Mines de Paris and the Universite catholique de Louvain, my former
colleague Jean-Franc;ois Rivest and I have had the opportunity to organise
a tutorial course about morphological image processing during an interna
tional conference held in The Hague. The success of this course as well as
others organised later in Sydney, Delft, Quebec City, and Brisbane rapidly
convinced me that there was a need for an application-oriented book present
ing the principles and latest developments of morphological image analysis.
The intent of the present book is to fulfil this need.
The book is self-contained in the sense that it is accessible to engineers,
scientists, and practitioners having no prior experience with morphology. In
addition, most necessary background notions about digital image processing
are covered. The emphasis being put on the techniques useful for solving prac
tical problems rather than the theory underlying mathematical morphology,
no special knowledge about set theory and topology is required. Neverthe
less, the book goes well beyond an introduction to mathematical morpho
logy. Indeed, starting from the fundamental transformations, more elaborate
methods which have proved their practical usefulness are explained. This is
achieved through a step by step process pursued until the most recent ad
vances.
The successful completion of this book has been very challenging because
there are now many teams around the world participating to the fruitful de
velopment of morphology and working on a wide variety of topics ranging
from the definition of new filters to the design of novel algorithmic tech
niques. Inevitably, some subjects are more detailed than others due to my
own experience and research activities. Bibliographical notes and references
are included at the end of each chapter to help the reader finding further
readings on a specific theme. The total number of distinct references equals
364. Each chapter dealing with a well defined topic, only 30 of references
appear on more than one chapter.
Acknowledgements are due to all people involved with image analysis and
whom I met since 1988 when I begun my research activities in this fascinating
field. Their dedication to both applied and theoretical research has been a
constant source of inspiration for the writing of this book. Naming all these
x
people would be a very difficult and dangerous exercise since I would surely
forget some of them. Nevertheless, I wish to express my deep acknowledge
ments to Jean Serra's group of the Centre de Morphologie Mathematique of
the Ecole des Mines de Paris which I worked with during four years. This
book would never have been published without the very fruitful discussions
and joint research projects I have had with the group members and the many
people who visited the Centre during my stay. Mark Berman's image analysis
group of the Commonwealth Scientific and Industrial Research Organisation,
Mathematical and Information Sciences (Sydney) which I visited in 1992-
1993 and September 1997 also deserves special thanks. The comments and
suggestions of all group members concerning preliminary versions of this book
helped me a lot. Moreover, their constant interest in my book project motiv
ated me to pursue it. The pattern recognition department of the Fraunhofer
Institut fur Produktionsanlagen und Konstruktionstechnik (Berlin) which I
visited in 1993 and 1995 has been a real chance for me to be confronted with
the many technical aspects regarding the application of image analysis to
industrial applications. Thanks a lot to Bertram Nickolay and all members
of his department. I am also indebted to Tilman Jochems for many advises
and helpful discussions following the reading of a draft copy of this book.
Piero Zamperoni from the Technische Universitiit Braunschweig deserves my
deep gratitude for its kind encouragements, the very careful reading of the
German version of this book, and the many discussions and thorough sugges
tions. Thanks are also due to Bernd Jiihne from the Universitiit Heidelberg
and Paul Whelan from the Dublin City University for their interest in my
book project. In addition, I wish to acknowledge the Ecole des Mines d'Ales
and its Laboratoire de Genie Informatique et d'Ingenierie de la Production,
site EERIE (Nimes) where I have been lecturing and pursuing my research
activities during the period 1995-1998.
I would like to conclude in gratitude to Sabine Miiller who shared with me
the necessary motivation for successfully achieving this book. In addition, the
former German version of this book would never have been written without
her help. For comments and suggestions aiming at improving and extending
the present book, I would like to thank all readers in advance.
Contents
1. Introduction.............................................. 1
1.1 Origin of mathematical morphology. . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scope of morphological image analysis .................... 4
1.2.1 Image filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Image segmentation .............................. 6
1.2.3 Image measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.4 Some other tasks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Book organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
1.4 Bibliographical notes and references ...................... 12
2. Background Notions.. . . . . . .. .. .. . . .. . . .. . . .. .. .... .. . .. .. 15
2.1 From continuous to discrete spaces ....................... 15
2.2 Discrete images ........................................ 17
2.2.1 Binary image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
2.2.2 Grey tone image ................................. 18
2.2.3 Multichannel image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21
2.3 Image to image transformations . . . . . . . . . . . . . . . . . . . . . . . . .. 22
2.3.1 Point image transformations. . . . . . . . . . . . . . . . . . . . . .. 23
2.3.2 Neighbourhood image transformations. . . . . . . . . . . . .. 24
2.4 Set operators applied to images .......................... 26
2.5 Ordering relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
2.5.1 On pixel intensity values .......................... 29
2.5.2 On images and image transformations.. . . . . . . . . . . . .. 30
2.5.3 On set partitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
2.5.4 Links to lattice theory ............................ 32
2.6 Discrete geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32
2.6.1 Graphs.......................................... 32
2.6.2 Grids and connectivity. . . . . . . . . . . . . . . . . . . . . . . . . . .. 35
2.6.3 Discrete boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 38
2.6.4 Discrete lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40
2.6.5 Convexity....................................... 43
2.7 Discrete distances and distance functions. . . . . . . . . . . . . . . . .. 45
2.7.1 Definitions ...................................... 45
2.7.2 Computation.................................... 47
2.8 Image transformation properties. . . . . . . . . . . . . . . . . . . . . . . . .. 49
2.9 Bibliographical notes and references ...................... 57