A tribute to Ulf Grenander
Author:
David Mumford
Journal:
Quart. Appl. Math. 77 (2019), 201-206
MSC (2010):
Primary 62P99
DOI:
https://doi.org/10.1090/qam/1524
Published electronically:
November 26, 2018
MathSciNet review:
3932958
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Additional Information
Abstract: Here I describe the history of my interactions with Ulf, a close friend and inspiring example, and sketch some of the basics of his “Pattern Theory”.
References
- Yali Amit, Ulf Grenander, and M. Piccioni, Structural image restoration through deformable templates, J. Amer. Stat. Soc., 1991, pp. 376–387.
- David Mumford and Agnès Desolneux, Pattern theory, Applying Mathematics, A K Peters, Ltd., Natick, MA, 2010. The stochastic analysis of real-world signals. MR 2723182
- Albrecht Dürer, Four Books on Human Proportion, 1528.
- Donald Geman and Stuart Geman, Stochastic relaxation, Gibbs Distributions and the Bayesian restoration of Images, IEEE Trans. pattern analysis and machine intelligence, 6, pp. 721–741, 1984.
- Ulf Grenander, Lectures in Pattern Theory. Volume I:Pattern Synthesis. Volume II: Pattern Analysis. Volume III: Regular Structures, 1980., Applied Mathematicl Sciences 18, 24, 33 resp., Springer-Verlag.
- Ulf Grenander, General pattern theory, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1993. A mathematical study of regular structures; Oxford Science Publications. MR 1270904
- Ulf Grenander, Elements of pattern theory, Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, MD, 1996. MR 1405164
- Ulf Grenander, A Calculus of Ideas, World Scientific Press, 2012.
- U. Grenander, Y. Chow, and D. M. Keenan, Hands, Research Notes in Neural Computing, vol. 2, Springer-Verlag, New York, 1991. A pattern-theoretic study of biological shapes. MR 1084371
- Ulf Grenander and Michael I. Miller, Computational anatomy: an emerging discipline, Quart. Appl. Math. 56 (1998), no. 4, 617–694. Current and future challenges in the applications of mathematics (Providence, RI, 1997). MR 1668732, DOI https://doi.org/10.1090/qam/1668732
- Michael Miller, Alain Trouve, and Laurent Younes, On the Metrics and Euler-Lagrange Equations of Computational Anatomy, Annual Review of Biomedical Engineering, 2002.
- David Mumford, Pattern theory: a unifying perspective, First European Congress of Mathematics, Vol. I (Paris, 1992) Progr. Math., vol. 119, Birkhäuser, Basel, 1994, pp. 187–224. MR 1341824
- David Mumford, Pattern theory: a unifying perspective, Perception as Bayesian Inference, D. Knill and W. Richards, eds., Cambridge Univ. Press, 1996, pp. 25–62.
- David Mumford, Pattern theory: the mathematics of perception, Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002) Higher Ed. Press, Beijing, 2002, pp. 401–422. MR 1989195
- David Mumford and Jayant Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 42 (1989), no. 5, 577–685. MR 997568, DOI https://doi.org/10.1002/cpa.3160420503
- V. Propp, Morphology of Folktales, transl. from Russian, Univ. of Texas, 1971.
- D’Arcy Wentworth Thompson, On Growth and Form, New edition, Cambridge University Press, Cambridge, England, 1942. MR 0006348
References
- Yali Amit, Ulf Grenander, and M. Piccioni, Structural image restoration through deformable templates, J. Amer. Stat. Soc., 1991, pp. 376–387.
- David Mumford and Agnès Desolneux, Pattern theory, The stochastic analysis of real-world signals, Applying Mathematics, A K Peters, Ltd., Natick, MA, 2010. MR 2723182
- Albrecht Dürer, Four Books on Human Proportion, 1528.
- Donald Geman and Stuart Geman, Stochastic relaxation, Gibbs Distributions and the Bayesian restoration of Images, IEEE Trans. pattern analysis and machine intelligence, 6, pp. 721–741, 1984.
- Ulf Grenander, Lectures in Pattern Theory. Volume I:Pattern Synthesis. Volume II: Pattern Analysis. Volume III: Regular Structures, 1980., Applied Mathematicl Sciences 18, 24, 33 resp., Springer-Verlag.
- Ulf Grenander, General pattern theory, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1993. A mathematical study of regular structures; Oxford Science Publications. MR 1270904
- Ulf Grenander, Elements of pattern theory, Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, MD, 1996. MR 1405164
- Ulf Grenander, A Calculus of Ideas, World Scientific Press, 2012.
- U. Grenander, Y. Chow, and D. M. Keenan, Hands, Research Notes in Neural Computing, vol. 2, Springer-Verlag, New York, 1991. A pattern-theoretic study of biological shapes. MR 1084371
- Ulf Grenander and Michael I. Miller, Computational anatomy: an emerging discipline, Current and future challenges in the applications of mathematics (Providence, RI, 1997), Quart. Appl. Math. 56 (1998), no. 4, 617–694. MR 1668732, DOI https://doi.org/10.1090/qam/1668732
- Michael Miller, Alain Trouve, and Laurent Younes, On the Metrics and Euler-Lagrange Equations of Computational Anatomy, Annual Review of Biomedical Engineering, 2002.
- David Mumford, Pattern theory: a unifying perspective, First European Congress of Mathematics, Vol. I (Paris, 1992) Progr. Math., vol. 119, Birkhäuser, Basel, 1994, pp. 187–224. MR 1341824
- David Mumford, Pattern theory: a unifying perspective, Perception as Bayesian Inference, D. Knill and W. Richards, eds., Cambridge Univ. Press, 1996, pp. 25–62.
- David Mumford, Pattern theory: the mathematics of perception, Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002) Higher Ed. Press, Beijing, 2002, pp. 401–422. MR 1989195
- David Mumford and Jayant Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 42 (1989), no. 5, 577–685. MR 997568, DOI https://doi.org/10.1002/cpa.3160420503
- V. Propp, Morphology of Folktales, transl. from Russian, Univ. of Texas, 1971.
- D’Arcy Wentworth Thompson, On Growth and Form, New edition, Cambridge University Press, Cambridge, England, 1942. MR 0006348
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Additional Information
David Mumford
Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
MR Author ID:
128175
Email:
dbmumford@gmail.com
Received by editor(s):
February 1, 2018
Published electronically:
November 26, 2018
Article copyright:
© Copyright 2018
Brown University
