Geometrical Probability and Biological Structures: Buffon’s 200th Anniversary: Proceedings of the Buffon Bicentenary Symposium on Geometrical Probability, Image Analysis, Mathematical Stereology, and Their Relevance to the Determination of Biological Stru

337 Pages·1978·11.57 MB·English

by  Jean Dry (auth.)

Lecture Notes in Biomathematics
Vol. 1: P. Waltman, Deterministic Threshold Models in the Theory of Epidemics. \
101 pages. 1974.
Vol. 2: Mathematical Problems in Biology, Victoria Conference 1973. Edited by P. va
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Vol. 10: J. J. Tyson, The Belousov-Zhabotinskii Reaktion. IX, 128 pages. 1976.
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Vol. 22: F. M. Scudo and J. R. Ziegler, The Golden Age of Theoretical Ecology: 1923-194
1
XII, 490 pages. 1978.
Vol. 23: Geometrical Probability and Biological Structures: Buffon's 200th Anniversar
Proceedings 1977. Edited by R. E. Miles and J. Serra. XII, 338 pages. 1978.
Lectu re Notes in
Biomathematics
Managing Editor: S. Levin
23
Geometrical Probability
and Biological Structures:
Buffon's 200th Anniversary
Proceedings of the Buffon Bicentenary Symposium
on Geometrical Probability, Image Analysis,
Mathematical Stereology, and Their Relevance
to the Determination of Biological Structures,
Held in Paris, June 1977
Edited by R. E. Miles and J. Serra
Springer-Verlag
Berlin HeidelberQ New York 1978
Editorial Board
w. Bossert· H. J. Bremermann . J. D. Cowan· W. Hirsch
S. Karlin· J. B. Keller· M. Kimura· S. Levin (Managing Editor)
R. C. Lewontin . R. May· G. F. Oster· AS. Perelson . L. A Segel
Editors
Roger E. Miles
Department of Statistics
Institute of Advanced Studies
Australian National University
P.O. Box 4
Canberra, AC.T. 2600/A ustralia
Jean Serra
Centre de Morphologie Mathematique
Ecole des Mines de Paris
35 rue St. Honore
77305 Fontainebleau/France
Library of Congress Cataloging in Publication Data
Buffon Bicentenary Symposium on Geometrical Probability,
Image Analysis, Mathematical Stereology, and Their
Relevance to the Determination of Biological Struc
tures, Paris, 1977.
Geometrical probabilities and biological struct-ures,
Buffon's 200th anniversary.
(Lecture notes in biomathematics ; 23)
Bibliography: p.
Includes index.
L Morpho10gy--Ma.thematics--Congresses. 2. Geo
metric probabilities--Congresses. 3. Stereo10gy-
Ma.thematics--Congresses. I. Buffon, Georges Louis
Leclerc, comte de, 1707-1788. II. Miles, Roger
Edmund, 1935- III. Serra, Jean, 1940- IV. Title.
V. Series.
QH351.B83 1977 519.2 78-18234
AMS Subject Classifications (1970): 60D05, 01A50, 53C65, 92-00
ISBN-13: 978-3-540-08856-1 e-ISBN-13: 978-3-642-93089-8
001:10.1007/978-3-642-93089-8
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© by Springer-Verlag Berlin Heidelberg 1978
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PRE F ACE
The idea for this Buffon bicentenary Symposium was due to E. Weibel, and
realized by an organizing committee, made up of H. Haug, G. Matheron, J.L. Binet,
R. Miles (programme chairman) and J. Serra (organization chairman). In the year
1777, Buffon published the famous study of a needle dropped at random on a grid
of lines, which we could consider as the starting point of geometric probability.
This publication is all the more remarkable because it comes from one of the
founders of the natural sciences. We wanted to celebrate this, two hundred years
later, by gathering together in the same Symposium, about thirty biologists and
the same number of mathematicians, in particular specialists in integral geometry
and geometric probability.
VI
The Symposium was held in June 1977, in the buildings of the Jardin des
Plantes de Paris, the very gardens that Buffon created, and where he spent much
of the last years of his life. This memorial aspect of the Symposium appears
in the introduction which follows, where we survey the germination of the basic
idea of "Buffon's needle", from Buffon to the beginning of the twentieth century.
During the Symposium itself, the homage to Buffon was manifested also by an
exhibition of paintings in the Salpetriere organized by J.L. Binet, and by the
publication of a book where J. Roger and J.L. Binet collected together the major
works of Buffon.
In these proceedings, we have not changed the chronological order of the
papers and we have respected the alternation between mathematical and biologi
cal presentations. Both are written in a deliberate everyday manner, avoiding
difficult technicalities.
We would like to acknowledge the Museum d'Histoire Naturelle, the Centre
of Mathematical Morphology of the Paris School of Mines, The Anatomy Institute
of Berne, the Hospital of La Salpetriere, the International Association for
Stereology, and the University of Paris VI, for their moral and financial help.
R.E. MILES, Canberra
J. SERRA, Fontainebleau
LIST OF THE PARTICIPANTS
-=-=-=-=-=-=-=-=-=-=-=-=-
* R. AMBARTZUMIAN Armenian Academy of Science EREVAN (S.U.)
A. BADDELEY 18 Price Avenue MONTMORENCY Victoria 3094 (Australia)
* G. BERNROIDER UNIVERSITAT SALZBURG ZOOLOGISCHES INSTITUT
AKADEMIESTRASSE 26 A-5020 SALZBURG
* S. BEUCHER CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
S. BIDIKHOF Bolcho! Vouzovski per. 3/12 M/I/E/MI Chaire de
Cybernetique MOSCOU
* + J.L. BINET PITIE SALPETRIERE 91 Bld de 1 'Hopital 75013 PARIS
* J.C.BISCONTE C.H.U. DE BOBIGNY Dept de Biologie Av. Marcel Cachin
93000 BOBIGNY
H. BOLEY Department of Histochemistry and Cytochemistry
University of LEIDEN Wassenaarserveg 72 LEIDEN
H. BRAUN STATISTICS Princeton University PRINCETON NJ 08540
G. BRUGAL Laboratoire de Zoologie et Biologie Animale U.S.M.
B.P. 33 CENTRE DE TRI 38041 GRENOBLE CEDEX
J.M. CHASSERY Laboratoire de Zoologie et Biologie Animale U.S.M.
B.P. 33 CENTRE DE TRI 38041 GRENOBLE CEDEX
* R. COLEMAN Department of Mathematics Imperial College Queen's Gate
LONDON SW7 2BZ
F. CORELLA CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
M. COSTER UNIVERSITE DE CAEN Labo. Chimie Minerale Industrielle
14032 CAEN CEDEX
M. COURTOIS Laboratoire de Microscopie Quantitative
U.E.R. de Medecine 93000 BOBIGNY
L. M. CRUZ ORIVE UNIVERSITAT BERN ANATOMISCHES INSTITUT
Postfach 139, BUhlstrasse 26 3000 BERN 9
* P. D'ATHIS PITIE SALPETRIERE 47 Bld de l'Hopital
75634 PARIS CEDEX 13
P. DEBRE PITIE SALPETRIERE 47 Bld de 1 'Hopital
75634 PARIS CEDEX 13
* R. DEHOFF College of Engineering Department of Materials Science
and Engineering, University of Florida
GAINESVILLE Florida 32611
VIII
P. DELFINER CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
* H. DIGABEL CENTRE DE MORPHOLOGIE MATHE~ATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
G. DIGIERO PITIE SALPETRIERE 47 Bld de 1 'Hopital
75634 PARIS CEDEX 13
* A. FELLOUS 39 Rue Lamarck 75018 PARIS
W.M. FISCHER Laboratorium fUr Elektronen mikroskopie der Theoretisch
Medirinischen Institute der Universitat InnsbrUck
Fritz Pregl Strasse 3 A-6020 INNSBRUCK
M. GAUTHIER CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
G. GIRAUT PITIE SALPETRIERE 47 Bld de 1 'Hopi tal
75634 PARIS CEDEX 13
* J. GRANARA 153 Fbg St-Denis 75010 PARIS
* H.J. GUNDERSEN Arhus Kommunehospital 2nd University Clinic of Internal Me.
DK-8000 ARHUS C
E. HARDING UNIYERSITE DE CAMBRIDGE STATISTICAL LABORATORY
16 Mill Lane CAMBRIDGE CB2 ISB
* + H. HAUG Abteilung fUr Anatomie der Medizinischen Hochschule LUbeck
Ratzeburger Allee 160 D-2400 LUEBECK
D. JEULIN I.R.S.I.D. 57210 MAIZIERES LES METZ
H. KELLER Anatomisches Institut BUhlstrasse 26 CH-3012 BERN
J.C. KLEIN CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue Saint-Honore 77305 FONTAINEBLEAU
* K. KRICKEBERG U.E.R. de Mathematique. Logique Formelle et Informatique
Sorbonne 12 Rue Cujas 75005 PARIS
* Ch. LANTUEJOUL CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
H. MAITRE ECOLE DES TELECOMMUNICATIONS 45 Rue Barrault 75013 PARIS
* B. MANDELBROT P.O. Box 218 Yorktown Heights NEW YORK 10598
* J.C. MARIANNA I.N.R.A. NOUZILLY 37380 MONNAIE
B. MATERN SKOGSCHOGSCKOLAN Royal College of Forestry S-104 05 STOCKHOU1
* + G. MATHERON CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
IX
* F. MEYER CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
* J. MIGNOT HOPITAL AMBROISE 9 Av. du Gal de Gaulle 92100 BOULOGNE
* + R. MILES THE AUSTRALIAN NATIONAL UNIVERSITY THE RESEARCH SCHOOL OF
SOCIAL SCIENCES Box 4 P.O. CANBERRA ACT 2600
F. De MONTAUX PITIE SALPETRIERE 47 Bld de 1 'Hopi tal 75634 PARIS CEDEX 13
R. OSTERBY Arhus Kommunehospital 2nd University Clinic of Internal Med.
*
DK-8000 ARHUS
W. PFALLER Institut fUr Physiologie der Universitat Innsbruck
Fritz Pregl Strasse 3 A-6020 INNSBRUCK
F. PIEFKE Institut B fUr Mathematik Technische Universitat
Pokelstrasse 14 - Forum 0-330 BRAUNSCHEWEIG
J. PIRET CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
Y. POULIGUEN PITIE SALPETRIERE 47 Bld de 1 'Hopital 75634 PARIS CEDEX 13
J.P. RASSON Facultes Universitaires Departement de Mathematiques
8 Rempart de la Vierge 5000 NAMUR Belgique
* A. REITH Norsk Hydro's Institute for Cancer Research
The Norwegian Radium Hospital Montebello OSLO 3
* J. ROGER 13 Rue de Mezieres 75006 PARIS
* H. RUBEN Department of Mathematics Mc Gill University
P.O. Box 6070, Station A MONTREAL Quebec H3C 3GI
* L.A. SANTALO Cochabamba 780 1150 BUENOS AIRES
H.E. SCHROEDER Zahnarztliches Institut der Universitat
Plattenstrasse 11 8000·ZURICH
* + J. SERRA CENTRE DE MORPHOLOGIE MATHEMATIQUE E.M.P.
35 Rue St-Honore 77305 FONTAINEBLEAU
B.W. SILVERMAN UNIVERSITY OF CAMBRIDGE STATISTICAL LABORATORY
16 Mill Lane CAMBRIDGE CB2 1SB
A. SOLARI I.N.R.A. 78350 JOUY EN JOSAS
* F. STREIT Section de Mathematique Universite de Geneve
2-4 Rue du Lievre Case Postale 124 1211 GENEVE 24
x
* T. TAKAHASKI Department of Pathology Tohoku University School of Medecine
Seiryomachi, SENDAI
J.F. THERY ECOLE DES TELECOMMUNICATIONS 45 Rue Barrault 75013 PARIS
H. VROL YK Department of Histochemistry and Cytochemistry
University of Leiden Wassenaarserveg 72 LEIDEN
* G.S. WATSON Department of Statistics Fine Hall Princeton University
PRINCETON, New Jersey
* + E.R. WEIBEL lIniversitat Bern Anatomisches Institut
BUhlstrasse 26 3000 BERN 9
* Speakers
+ Scientific Committee