9781402034428

Mathematical Morphology is a speciality in Image Processing and Analysis, which considers images as geometrical objects, to be analyzed through their interactions with other geometrical objects. It relies on several branches of mathematics, such as discrete geometry, topology, lattice theory, partial differential equations, integral geometry and geometrical probability. It has produced fast and efficient algorithms for computer analysis of images, and has found applications in bio-medical imaging, materials science, geoscience, remote sensing, quality control, document processing and data analysis. This book contains the 43 papers presented at the 7th International Symposium on Mathematical Morphology, held in Paris on April 18-20, 2005. It gives a lively state of the art of current research topics in this field. It also marks a milestone, the 40 years of uninterrupted development of this ever-expanding domain.

Dedication

v

Foreword

xi

Preface

xiii

Acknowledgments

xvii

Part I Morphological operators

Binary Decision Diagrams as a New Paradigm for Morphological Machines

3

(10)

Junior Barrera

Ronaldo Fumio Hashimoto

Image filtering using morphological amoebas

13

(10)

Romain Lerallut

Etienne Decenciere

Fernand Meyer

Numerical Residues

23

(10)

Serge Beucher

Efficient path openings and closings

33

(10)

Ben Appleton

Hugues Talbot

Structuring Elements following the Optical Flow

43

(10)

Nicolas Laveau

Christophe Bernard

Recursive Interpolation Technique For Binary Images Based on Morphological Median Sets

53

(12)

Javier Vidal

Jose Crespo

Victor Maojo

Part II Connected filters and reconstruction

Second-Order Connected Attribute Filters Using Max-Trees

65

(10)

Georgios K. Ouzounis

Michael H. F. Wilkinson

Transformations with Reconstruction Criteria: Image Segmentation and Filtering

75

(10)

Ivan R. Terol-Villalobos

Jorge D. Mendiola-Santibanez

Attribute-Space Connected Filters

85

(10)

Michael H.F. Wilkinson

Vector-attribute Filters

95

(10)

Erik R. Urbach

Niek J. Boersma

Michael H.F. Wilkinson

Ruminations on Tarjan's Union-Find Algorithm and Connected Operators

105

(12)

Thierry Geraud

Labelled Reconstruction of Binary Objects: A Vector Propagation Algorithm

117

(12)

Michael Buckley

Ryan Lagerstrom

Grayscale Level Multiconnectivity

129

(10)

Ulisses Braga-Neto

Shape-Tree Semilattices

139

(12)

Renato Keshet

Part III Segmentation

Morphological Segmentations of Colour Images

151

(26)

Jean Serra

Fast Implementation of Waterfall based on Graphs

177

(10)

Beatriz Marcotegui

Serge Beucher

Mosaics and Watersheds

187

(10)

Laurent Najman

Michel Couprie

Gilles Bertrand

A new definition for the dynamics

197

(10)

Gilles Bertrand

Watershed-driven region-based image retrieval

207

(10)

I. Pratikakis

I. Vanhamel

H. Sahli

B. Gatos

S. Perantonis

Efficient implementation of the locally constrained watershed transform and seeded region growing

217

(12)

Richard Beare

Part IV Geometry and topology

Optimal shape and inclusion

229

(20)

Jean-Marc Chassery

David Coeurjolly

Regular Metric: Definition and Characterization in the Discrete Plane

249

(10)

Gerald Jean Francis Banon

Euclidean skeletons of 3D data sets in linear time by the integer medial axis transform

259

(10)

Wim H. Hesselink

Menno Visser

Jos B.T.M. Roerdink

Digitization of Non-regular Shapes

269

(10)

Peer Stelldinger

Downsampling of binary images using adaptive crossing numbers

279

(10)

Etienne Decenciere

Michel Bilodeau

Grey-weighted, ultrametric and lexicographic distances

289

(10)

Fernand Meyer

Mathematical modeling of the relationship ``between'' based on morphological operators

299

(12)

Isabelle Bloch

Olivier Colliot

Roberto M. Cesar

Part V Partial differential equations and evolutionary models

Semidiscrete and Discrete Well-Posedness of Shock Filtering

311

(10)

Martin Welk

Joachim Weickert

A Variational Formulation of PDE's for Dilations and Levelings

321

(12)

Petros Maragos

Stochastic Shape Optimisation

333

(10)

Costin Alin Caciu

Etienne Decenciere

Dominique Jeulin

On the local connectivity number of stationary random closed sets

343

(14)

Evgueni Spodarev

Volker Schmidt

Part VI Texture, colour and multivalued images

Intersize correlation of grain occurrences in textures and its application to texture regeneration

357

(10)

Akira Asano

Yasushi Kobayashi

Chie Muraki

Texture Segmentation Using Area Morphology Local Granulometries

367

(10)

Neil D. Fletcher

Adrian N. Evans

Illumination-invariant Morphological Texture Classification

377

(10)

Allan Hanbury

Umasankar Kandaswamy

Donald A. Adjeroh

Unified morphological color processing framework in a lum/sat/hue representation

387

(10)

Jesus Angulo

Iterative area seeded region growing for multichannel image simplification

397

(10)

Dominik Brunner

Pierre Soille

Morphology for Higher-Dimensional Tensor Data via Loewner Ordering

407

(12)

B. Burgeth

N. Papenberg

A. Bruhn

M. Welk

C. Feddern

J. Weickert

Part VII Applications in imaging sciences

Using Watershed and Multimodal Data for Vessel Segmentation: Application to the Superior Sagittal Sinus

419

(10)

N. Passat

C. Ronse

J. Baruthio

J.-P. Armspach

J. Foucher

Using grey scale hit-or-miss transform for segmenting the portal network of the liver

429

(12)

Benoit Naegel

Christian Ronse

Luc Soler

Blood Cell Segmentation Using Minimum Area Watershed and Circle Radon Transformations

441

(14)

F. Boray Tek

Andrew G. Dempster

Izzet Kale

Quantifying mean shape and variability of footprints using mean sets

455

(10)

J. Domingo

B. Nacher

E. de Ves

E. Alcantara

E. Diaz

G. Ayala

A. Page

Exploiting and Evolving Rn Mathematical Morphology Feature Spaces

465

(10)

Vitorino Ramos

Pedro Pina

Morphological Segmentation Applied To 3D Seismic Data

475

(10)

Timothee Faucon

Etienne Decenciere

Cedric Magneron

Index

485

(4)

Author Index

489

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Mathematical Morphology

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