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 PDF
Preview 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
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 den Driessche. VI, 280 pages. 1974. Vol. 3: D. ludwig, Stochastic Population Theories. VI, 108 pages. 1974. Vol. 4: Physics and Mathematics of the Nervous System. Edited by M. Conrad, W. GO! tinger, and M. Dal Cin. XI, 584 pages. 1974. Vol. 5: Mathematical Analysis of Decision Problems in Ecology. Proceedings 197~ Edited by A. Charnes and W. R. lynn. VIII, 421 pages. 1975. Vol. 6: H. T. Banks, Modeling and Control in the Biomedical Sciences. V, 114 pages.197E Vol. 7: M. C. Mackey, Ion Transport through Biological Membranes, An Integratef Theoretical Approach. IX, 240 pages. 1975. Vol. 8: C. Delisi, Antigen Antibody Interactions. IV, 142 pages. 1976. Vol. 9: N. Dubin, A Stochastic Model for Immunological Feedback in Carcinogenesi~ Analysis and Approximations. XIII, 163 pages. 1976. Vol. 10: J. J. Tyson, The Belousov-Zhabotinskii Reaktion. IX, 128 pages. 1976. Vol. 11: Mathematical Models in Medicine. Workshop 1976. Edited by J. Berger, W. BO~ ler, R. Repges, and P. Tautu. XII, 281 pages. 1976. Vol. 12: A. V. Holden, Models of the Stochastic Activity of Neurones. VII, 368 pages. 197E Vol. 13: Mathematical Models in Biological Discovery. Edited by D. L. Solomon an C. Walter. VI, 240 pages. 1977. Vol. 14: L. M. Ricciardi, Diffusion Processes and Related Topics in Biology. VI, 200 page~ 1977. Vol. 15: Th. Nagylaki, Selection in One- and Two-locus Systems. VIII, 208 pages. 197, Vol. 16: G. Sampath, S. K. Srinivasan, Stochastic Models for Spike Trains of Singl Neurons. VIII, 188 pages. 1977. Vol. 17: T. Maruyama, Stochastic Problems in Population Genetics. VIII, 245 pages. 197' Vol. 18: Mathematics and the life Sciences. Proceedings 1975. Edited by D. E. Matthew: • VII, 385 pages. 1977. Vol. 19: Measuring Selection in Natural Populations. Edited by F. B. Christiansen an T. M. Fenchel. XXXI, 564 pages. 1977. Vol. 20: J. M. Cushing, Integrodifferential Equations and Delay Models in Populatio Dynamics. VI, 196 pages. 1977. Vol. 21: Theoretical Approaches to Complex Systems. Proceedings 1977. Edited t R. Heim and G. Palm. VI, 244 pages. 1978. 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 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, re printing, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1978 'r Al~2I.r17 .A "& .. J ~ ,. 7- ? xll . • .s c P 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
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