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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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