# Donald E. McClureProfessor Emeritus of Applied Mathematics

Don McClure is a transplanted Oregonian who has been on the faculty of
the Division of Applied Mathematics since 1969. He received his A.B.
in Mathematics from UC Berkeley and his Ph.D. in Applied Mathematics
from Brown. He served as Chair of the Division from 1985 to 1988 and
from 1994 to 1996. During the period 1986-2000, he was Associate
Director of the Brown-Harvard-MIT Center for Intelligent Control
Systems. He has served as Associate Treasurer and Trustee of the
American Mathematical Society (AMS). In 2009, he became Executive
Director of the AMS and Professor Emeritus at Brown.

## Brown Affiliations

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### scholarly work

Geman, Stuart; McClure, Donald E.; Geman, Donald. A nonlinear filter for film restoration and other problems in image processing. (pdf file) CVGIP: Graphical Models and Image Processing 54 (1992), no. 4, 281-289.

Geman, Stuart; Manbeck, Kevin M.; McClure, Donald E. A comprehensive statistical model for single photon emission tomography. (pdf file) In Markov Random Fields: Theory and Applications, R. Chellappa and A. Jain, Eds. 93-130, Academic Press, Boston 1993.

Geman, Stuart; McClure, Donald E. Statistical methods for tomographic image reconstruction. (pdf file) Proceedings of the 46th Session of the International Statistical Institute, Vol. 4 (Tokyo, 1987). Bull. Inst. Internat. Statist. 52 (1987), no.4, 5-21. MR1027188

McClure, Donald E. Nonlinear segmented function approximation and analysis of line patterns. (pdf file) Quart. Appl. Math. 33 (1975/76), 1-37. MR0463769

McClure, Donald E.; Vitale, Richard A. Polygonal approximation of plane convex bodies. (pdf file) J. Math. Anal. Appl. 51 (1975), no. 2, 326-358. MR0385714

McClure, Donald E. Perfect spline solutions of $L\sb{\infty}$ extremal problems by control methods. J. Approximation Theory 15 (1975), no. 3, 226-242. MR0397250

### research overview

Donald McClure does research in the areas of image processing and computer vision, ill-posed inverse problems, and analysis of image sequences such as occur in film or progressive video. Current work includes the relationship between optimization problems for discrete probabilistic models of images and continuous variational counterparts of these problems that lead to PDEs. He is also working on methods of nonlinear function approximation that relate to image compression.

### funded research

1986-1991 University Research Initiative Program, Center for Intelligent Control Systems (Brown-Harvard-MIT), funded by the U.S. Army Research Office, Co-principal investigator with Sanjoy Mitter (MIT) and Roger Brockett (Harvard), (joint with W. Fleming, S. Geman, U. Grenander and H.J. Kushner in the Division of Applied Mathematics).

1988-1990 Office of Naval Research Contract, A Mathematical Framework for Image Analysis , Co-principal investigator with S. Geman and U. Grenander.

1989-1992 National Science Foundation Grant, A Mathematical Framework for Image Analysis , Co-principal investigator with S. Geman, B. Gidas and U. Grenander.

1988 Department of Defense University Research Instrumentation Grant, Image Acquisition and Processing Equipment for Machine Vision , Principal Investigator.

1989 National Science Foundation Grant, Instructional Laboratory for Teaching Experimental Mathematics , Co-principal investigator with U. Grenander.

1990-1992 Office of Naval Research Grant, Mathematical Methods for Object Recognition , Co-principal investigator with S. Geman, B. Gidas and U. Grenander.

1992-1997 University Research Initiative Program, Foundations of Intelligent Systems , Center for Intelligent Control Systems (Brown-Harvard-MIT), funded by the US Army Research Office, Co-principal investigator with Sanjoy Mitter (MIT) and Roger Brockett (Harvard), (joint with W. Fleming, S. Geman, B. Gidas, U. Grenander and H.J. Kushner in the Division of Applied Mathematics).

1992 National Science Foundation, Mathematical Sciences Computing Research Environments , Co-principal investigator with M. Maxey, L. Sirovich and C. Jones

1992-95 Office of Naval Research, Co-principal investigator with S. Geman, B. Gidas and U. Grenander, AASERT Grant for Graduate Student Support.

1992-95 US Army Research Office, Co-principal investigator with S. Geman, B. Gidas and U. Grenander, AASERT Grant for Graduate Student Support

1993-96 National Science Foundation, Mathematical and Computational Problems in Object Recognition , Co-principal investigator with S. Geman, B. Gidas and U. Grenander.

1993-96 US Army Research Office, Co-principal investigator with S. Geman, B. Gidas and U. Grenander, AASERT Grant for Graduate Student Support.

1993-1998 Advanced Research Projects Agency (ARPA), Foundations of Object Detection and Recognition , Co-principal investigator with S. Geman, B. Gidas and U. Grenander (PI).

1994-95 Department of Defense University Research Instrumentation Program, Computational Resources for Image Modeling and Object Recognition , Co-principal investigator with S. Geman, B. Gidas and U. Grenander.

1994-95 National Science Foundation Grant, Acquisition of a Parallel Supercomputer (funded in part the IBM SP2 acquisition in summer 1995), Co-principal investigator with G. Karniadakis, D. Gottlieb, M. Maxey, M. Ortiz, J. Savage and F. Preparata.

1995-2000 Department of Defense Focused Research Initiative, Algorithms for Image Compression, Distributed Communication Networks and Distributed Resource Allocation , Co-principal investigator with S. Geman, B. Gidas, U. Grenander and and S. Ghosh (Arizona State University).

1996-1999 National Science Foundation, Mathematical Sciences Computing Research Environments , Co-principal investigator with G. Karniadakis, D. Gottlieb, C. Jones, and M. Maxey.

1996-1997 Office of Naval Research, Recognition Algorithms for Wide-Area Surveillance , Co-principal investigator with S. Geman, B. Gidas, U. Grenander and and D. Geman (UMass).

1996-1998 Department of Defense University Research Instrumentation Program, Network and Graphics Systems for Image Modeling , Principal Investigator.

1996-2002 US Army Research Office, Vision Strategies and ATR Performance: A Mathematical/Statistical Formulation and Critique , Principal Investigator and Project Director, Co-principal investigator with S. Geman, B. Gidas, U. Grenander and D. Mumford, joint with Harvard, MIT, University of Chicago and UMass.

1997-1999 Office of Naval Research, Mathematical Foundations for Object Recognition and Image Analysis , Co-principal investigator with S. Geman, B. Gidas, U. Grenander and and D. Geman (UMass).

1997-2000 National Science Foundation, Acquisition of a CAVE and Shared Memory Supercomputer , Co-principal investigator with 12 other Brown University faculty.

2001-06 National Science Foundation, Mathematical Analysis of the Compositional Structure of Images , Co-principal investigator with S. Geman, B. Gidas, D. Mumford, U. Grenander and M. Johnson

2004-2006, National Science Foundation, Enrichment and Integration of Networked Computing Resources for the Mathematical Sciences , Principal Investigator; Co-principal investigators J. Hesthaven, S. Geman, C-W. Shu and G. Karniadakis.