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SPATIAL STATISTICS AND DIGITAL IMAGE ANALYSIS Panel on Spatial Statistics and image Processing Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C. :199:1

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NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distin- guished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Frank Press is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the Na- tional Academy of Sciences, as a parallel orgaruzation of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages ed- ucation and research, and recognizes the superior achievements of engineers. Dr. Robert A/I. White is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Samuel O. Thier is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Franl; Press and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council. The National Research Council established the Board on Mathematical Sciences in 1984. The objectives of the Board are to maintain awareness and active concern for the health of the mathematical sciences and serve as the focal point in the National Research Council for issues connected with the mathematical sciences. In addition, the Board is designed to conduct studies for federal agencies and maintain liaison with the mathematical sciences communities and academia, professional societies, and industry. Support for this project was provided by the Office of Naval Research under grant number N00014-89-J-1641. Library of Congress Catalog Card No. 9~63215 International Standard Book Number 0-309-04376-X Available from National Academy Press, 2101 Constitution Avenue, NW Washington, DC 20418 S237 Printed in the United States of America

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CONTRIBUTORS ADRIAN BADDELEY, Centre for Mathematics and Computer Science JULIAN BESAG*, University of Washington HERMAN CHERNOFF*, Harvard University PETER CLIFFORD, Oxforc! University NOEL A. CRESSIE, Iowa State University DONALD J. GEMAN, University of Massachusetts BASTETS GTDAS*, Brown University LAWRENCE S. GTELICK*, Dragon Systems' Inc. N [CHOLAS GREEN, Oxford University PETER M. GUTTORP, University of Washington TED KADOTA, AT&T Bell Laboratories ALAN LIPPMAN, University of Washington JAMES SIMPSON*, Scripps Institution of Oceanography Stag SCOTT T. WETDMAN, Senior Staff Officer *Member of Panel on Spatial Statistics and Image Processing, Julian Besag and James Simpson, cmchairs ~

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BOARD ON MATHEMATICAL SCIENCES PHILLIP A. GRTFFITHS, Duke University, Chair LAWRENCE D. BROWN, Cornell University SUN-YUNG CHANG, University of California at Los Angeles RONALD DOUGLAS, State University of New York-Stony Brook DAVID EDDY, Duke University AVNER FRIEDMAN, University of Minnesota FREDERICK W. GEARING, University of Michigan JAMES GRIMM, State University of New York-Stony Brook JOSEPH KADANE, Carnegie-Mellon University DIANE LAMBERT, AT&T Bell Laboratories GERALD J. LlEBERMAN, Stanford University JEROME SACKS, University of Illinois SHMUEL WINOGRAD, IBM T. J. Watson Research Center Ex Officio Member WlI`~lAM EDDY, Carnegie-Mellon University Stay LAWRENCE H. COX, Director JO SEVILLE, Administrative Secretary RUTH E. O'BRIEN, Staff Associate HANS OSER, Staff Officer JOHN TUCKER, Staff Officer SCOTT T. WElDMAN, Senior Staff Officer . 1V

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COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS* NORMAN HACKERMAN, Robert A. Welch Foundation, Chair PETER B[CKEL, University of California at Berkeley GEORGE F. CARRIER, Harvard University HERBERT D. DOAN, The Dow Chemical Company (retired) DEAN E. EASTMAN, IBM T. J. Watson Research Center MARYE ANNE FOX, University of Texas PHILLTP A. GRTFFITHS, Duke University NEAL F. LANE, Rice University ROBERT W. LUCKY, AT&T Bell Laboratories CHRISTOPHER F. MCKEE, University of California at Berkeley RICHARD S. NICHOLSON, American Association for the Advancement of Science JEREMIAH P. OSTRIKER, Princeton University Observatory ALAN SCHRIESHETM, Argonne National Laboratory ROY F. SCHWITTERS, Superconducting Supercollider Laboratory KENNETH G. \VTESON, Ohio State University NORMAN METZGER, Executive Director * The project that is the subject of this report was initiated under the predecessor group of the Commission on Physical Sciences, Mathematics, and Applications, which was the Commission on Physical Sciences, Mathematics, and Resources, whose members are listed on the following page. v

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COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND RESOURCES NORMAN HACKERMAN, Robert A. Welch Foundation' Chair ROBERT C. BEARDSLEY, Woods Hole Oceanographic Institution B. CLARK BURCHFIEL, Massachusetts Institute of Technology GEORGE F. CARRIER, Harvard University RALPH J. CICERONE, University of California at Irvine HERBERT D. DOAN, The Dow Chemical Company (retired) PETER S. EAGLESON, Massachusetts Institute of Technology DEAN E. EASTMAN, IBM T. J. Watson Research Center MARYE ANNE FOX, University of Texas GERHART FRIEDEANDER, Brookhaven National Laboratory LAWRENCE W. FUNKHOUSER, Chevron Corporation (retired) PHTLETP A. GRIFFITHS, Duke University NEAL F. LANE, Rice University CHRISTOPHER F. MCKEE, University of California at Berkeley RICHARD S. NICHOLSON, American Association for the Advancement of Science JACK E. OLIVER, Corned University JEREMIAH P. OSTRIKER, Princeton University Observatory PHILIP A. PALMER, E. I. du Pont de Nemours & Company FRANK L. PARKER, Vanderbilt University DENTS J. PRAGER, MacArthur Foundation DAVID M. RAUP, University of Chicago ROY F. SCHWITTERS, Superconducting SupercoHider Laboratory LARRY L. SMARR, University of Illinois at Urbana-Champaign KARL K. TUREKlAN, Yale University V1 .

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PREFACE Spatial statistics is one of the most rapidly growing areas of statistics, rife with fascinating research opportunities. Yet, many statisticians are unaware of those opportunities, and most students in the United States are never ex- posed to any course work in spatial statistics. This report aims at illustrating the wide scope of spatial statistics to provide an introductory snapshot of the field to researchers and graduate students in both statistics and related areas. It is hoped that these readers will go on to explore the many research opportunities in the subject, or bring appropriate problems to the attention of practicing spatial statisticians. This pane} was specifically charged to prepare a cross-disciplinary report on spatial statistics and image analysis that would (1) describe the contri- butions of the mathematical sciences, (2) summarize the current state of knowledge and open problems, and (3) identify likely future fruitful direc- tions for research. ~ V11

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CONTENTS 1 INTRODUCTION IMAGE ANALYSIS AND COMPUTER VISION Donald Geman and Basins Gidas 3 OCEANOGRAPHIC AND ATMOSPHERIC APPLICATIONS OF SPATIAL STATISTICS AND DIGITAL IMAGE ANALYSIS James ]. Simpson 4 SPATIAL STATISTICS IN ENVIRONMENTAL SCIENCE Peter Guttorp GEOSTATISTICAL ANALYSIS OF SPATIAL DATA Noel Cressie SPATIAL STATISTICS IN THE ANALYSIS OF AGRICULTURAL FIELD EXPERIMENTS Julian Besag SPATIAL STATISTICS IN ECOLOGY Peter Guttorp SPATIAL SIGNAL-PROCESSING IN RADARS AND SONARS T. T. Kadota 9 STOCHASTIC MODELING IN PHYSICAL CHEMISTRY Peter C]i~ord and N. ]. B. Green 10 STEREOLOGY Adrian BaddeJey 11 MARKOV MODELS FOR SPEECH RECOGNITION Alan F. I,ippman Plates for chapters 2, 3, and 10 precede page 71. 1X 1 9 37 71 87 109 129 147 159 181 217

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