Proceedings of the International Symposium on ADVANCES IN THEORY AND APPLICATIONS OF RANDOM SETS

Editor D. Jeulin - World Scientific

1997

Twenty years after the publication of the book ''Random Sets and Integral Geometry'' written by Professor Georges Matheron, an international symposium was organized to focus on the Advances in the Theory and Applications of Random Sets (Fontainebleau, France, 9-11 October 1996).

This volume contains the invited lectures given by leading scientists in this field. It shows the applications of the theory of random sets to many practical domains: models issued from this theory, by means of image simulation and analysis by computer, are applied in various fields such as biology or materials. On a different scale, they are used to simulate mineral ore deposits, oil reservoirs, or even astronomical data. Finally they provide sources of textures to encode or to generate artificial images.

It is of interest to mathematicians, engineers and scientists who need to relate the physical behavior and the texture of heterogeneous media and also to users of image analysis and synthesis for its applications (materials, biology, artificial vision, CAD, teledetection, geophysics, biometry and image coding etc.)

CONTENTS

Foreword p.V

PART I.

GENERAL PROPERTIES OF RANDOM SETS

On the Expected Measure of a Random Set

A. J. Baddeley gif & I.S. Molchanov p.3

The Mean Normal Distribution of Stationary Random Sets and Particle Processes

W. Weil p.21

Unions of Random Sets and their Applications gif

I. Molchanov p.35

Morphologically Constrained Discrete Random Sets

K. Sivakumar and J. Goutsias p.49

Equicontinuous Random Functions

J. Serra p.67

PART II.

MODELS OF RANDOM TESSELLATIONS AND OF RANDOM SETS

Models of Random Sets and Figures

D. Stoyan p.87

On some Weighted Boolean Models

W.S. Kendall p.105

On Likelihoods for Markov Random Sets and Boolean Models

M.N.M. van Lieshout p.121

Dead Leaves Models: from Space Tessellation to Random Functions

D. Jeulin p.137

The Covariance of the Stienen Model

M. Schlather & D. Stoyan p.157

Size Distributions for Excursion Sets

D. J. Nott & R.J. Wilson p.175

Applications of Random Models in Solid State Research and Materials Science

H. Hermann, J. Collazo, F. Fugaciu, P. Uebele p.195

PART III.

STATISTICS OF RANDOM SETS

Recursive Decomposition in Discrete Coverage Processes gif

Ed. R. Dougherty & J.C. Handley p.215

Approach of Liquid Phase Sintering Process by Probabilistic Models

J. L. Quenec'h, D. Jeulin, M. Coster , J.L. Chermant p.231

Estimation of Intensity and Shape in a Non-Stationary Boolean Model

M. Schmitt p.251

PART IV.

SIMULATIONS

Conditional Simulation of Object-Based Models

Ch. Lantuéjoul p.271

Simulation des Modèles de Gibbs Spatiaux par Chaine de Markov

Carlo Gaetan & X. Guyon p.289

Author Index p.321

Subject Index p.323

List of Participants p.325



Etienne Decenciere
Mon Nov 4 14:35:58 WET 1996