On the mathematics of growth
Author:
Ulf Grenander
Journal:
Quart. Appl. Math. 65 (2007), 205-257
MSC (2000):
Primary 92B05
DOI:
https://doi.org/10.1090/S0033-569X-07-01028-8
Published electronically:
May 1, 2007
MathSciNet review:
2330557
Full-text PDF Free Access
References |
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Additional Information
References
- A. Antoniadis (2003): Optimal Testing in Functional Analysis Models, University of Florida, Department of Statistics, Fifth Annual Winter Workshop.
- M. F. Beg, M. I. Miller, A. Trouve, L. Younes (2002): Computing Metrics on Anatomical Shapes in Computational Anatomy. Second Joint Meeting of IEEE EMBS-BMES Society.
- J. T. Bonner, ed. (1982): Evolution and Development. Report of the Dahlem Workshop on Evolution and Development, Berlin 1981. Berlin/New York: Springer Verlag.
- F. L. Bookstein (1978): The Measurement of Biological Shape and Shape Change. Lecture Notes in Biomathematics, Vol. 24 (Springer Lecture Notes in Computer Science).
- Fred L. Bookstein, Morphometric tools for landmark data, Cambridge University Press, Cambridge, 1997. Geometry and biology; Reprint of the 1991 original. MR 1469220
- Jin Cao and Keith J. Worsley, The detection of local shape changes via the geometry of Hotelling’s $T^2$ fields, Ann. Statist. 27 (1999), no. 3, 925–942. MR 1724036, DOI https://doi.org/10.1214/aos/1018031263
- G. E. Christiansen (1994): Deformable shape models for anatomy, Ph.D. Thesis, Washington University.
- Ulf Grenander, Abstract inference, John Wiley & Sons, Inc., New York, 1981. Wiley Series in Probability and Mathematical Statistics. MR 599175
- 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
- U. Grenander (2005): Power Point presentation on www.dam.brown.edu/ptg
- U. Grenander, M. I. Miller and J. Zhang (2003): FANOVA of genetically modified mouse brains, Div. Appl. Math., Brown University, Rep. No. 3.
- 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
- A. L. Hodgkin, A. F. Huxley (1952): A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol.
- D. Khavinson (2005): oral communication.
- D. G. Kendall, D. Barden, T. K. Carne, and H. Le, Shape and shape theory, Wiley Series in Probability and Statistics, John Wiley & Sons, Ltd., Chichester, 1999. MR 1891212
- Øyvind Langsrud, 50-50 multivariate analysis of variance for collinear responses, The Statistician 51 (2002), no. 3, 305–317. MR 1920760, DOI https://doi.org/10.1111/1467-9884.00320
- R. C. Lewontin (1974): The Genetic Basis of Evolutionary Change, Columbia University Press, New York.
- L. Matejic (1997): Group cascades for representing biological variability, Ph.D. Thesis, Brown University.
- M. I. Miller (2004): Computational anatomy: Shape, growth, and atrophy comparison via diffeomorphisms, NeuroImage, 23.
- M. I. Miller, S. C. Joshi and G. E. Christensen (1999): Large Deformation Fluid Diffeomorphisms For Landmark and Image Matching, Brain Warping, Academic Press.
- D. Mumford (2002): Pattern Theory: The Mathematics of Perception. APPTS Report No. 02-10, Div. Appl. Math., Brown University.
- N. Rashevsky (1938): Mathematical Biophysics: Physico-Mathematical Foundations of Biology, Univ. of Chicago Press.
- A. Srivastava, U. Grenander, S. Saini (2006): Characterization of Biological Growth Using Iterated Diffeomorphisms, Lecture at IEEE International Symposium on Biomedical Imaging.
- D’Arcy Wentworth Thompson, On Growth and Form, New edition, Cambridge University Press, Cambridge, England, 1942. MR 0006348
- P. M. Thompson, A. W. Toga (2002): A Framework for Computational Anatomy, Comput. Visual. Sci. 5:13–34.
- R. A. Vitale (1974): Convolutions on a group arising in pattern analysis, Ph.D. Thesis, Brown University.
- N. Wiener (1933): The Fourier Integral, Cambridge University Press.
References
- A. Antoniadis (2003): Optimal Testing in Functional Analysis Models, University of Florida, Department of Statistics, Fifth Annual Winter Workshop.
- M. F. Beg, M. I. Miller, A. Trouve, L. Younes (2002): Computing Metrics on Anatomical Shapes in Computational Anatomy. Second Joint Meeting of IEEE EMBS-BMES Society.
- J. T. Bonner, ed. (1982): Evolution and Development. Report of the Dahlem Workshop on Evolution and Development, Berlin 1981. Berlin/New York: Springer Verlag.
- F. L. Bookstein (1978): The Measurement of Biological Shape and Shape Change. Lecture Notes in Biomathematics, Vol. 24 (Springer Lecture Notes in Computer Science).
- F. L. Bookstein (1997): Morphometric Tools for Landmark Data : Geometry and Biology, Cambridge University Press; Reprint edition. MR 1469220 (99d:92003)
- J. Cao, K.J. Worsley (1999): The detection of local shape changes via the geometry of Hotelling’s T$^2$ fields. Annals of Statistics, 27, 925–942. MR 1724036 (2001g:60121)
- G. E. Christiansen (1994): Deformable shape models for anatomy, Ph.D. Thesis, Washington University.
- U. Grenander (1981): Abstract Inference, John Wiley. MR 0599175 (82g:62004)
- U. Grenander (1993): General Pattern theory, Oxford University Press. MR 1270904 (96e:68118)
- U. Grenander (2005): Power Point presentation on www.dam.brown.edu/ptg
- U. Grenander, M. I. Miller and J. Zhang (2003): FANOVA of genetically modified mouse brains, Div. Appl. Math., Brown University, Rep. No. 3.
- U. Grenander, M. I. Miller (1998) Computational anatomy: An emerging discipline, Quarterly of Appl. Math., LVI, 617–694. MR 1668732 (2000e:92011)
- A. L. Hodgkin, A. F. Huxley (1952): A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol.
- D. Khavinson (2005): oral communication.
- D. G. Kendall, D. Barden, T. K. Carne, H. Le (1999): Shape and Shape Theory, Wiley Series in Probability and Statistics. MR 1891212 (2003g:60018)
- O. Langsrud (2002): 50-50 Multivariate Analysis of Variance for Collinear Responses, The Statistician, 51, 305–317. MR 1920760
- R. C. Lewontin (1974): The Genetic Basis of Evolutionary Change, Columbia University Press, New York.
- L. Matejic (1997): Group cascades for representing biological variability, Ph.D. Thesis, Brown University.
- M. I. Miller (2004): Computational anatomy: Shape, growth, and atrophy comparison via diffeomorphisms, NeuroImage, 23.
- M. I. Miller, S. C. Joshi and G. E. Christensen (1999): Large Deformation Fluid Diffeomorphisms For Landmark and Image Matching, Brain Warping, Academic Press.
- D. Mumford (2002): Pattern Theory: The Mathematics of Perception. APPTS Report No. 02-10, Div. Appl. Math., Brown University.
- N. Rashevsky (1938): Mathematical Biophysics: Physico-Mathematical Foundations of Biology, Univ. of Chicago Press.
- A. Srivastava, U. Grenander, S. Saini (2006): Characterization of Biological Growth Using Iterated Diffeomorphisms, Lecture at IEEE International Symposium on Biomedical Imaging.
- d’Arcy Wentworth Thompson (1917, 1942): On Growth and Form. Cambridge University Press. MR 0006348 (3:291k)
- P. M. Thompson, A. W. Toga (2002): A Framework for Computational Anatomy, Comput. Visual. Sci. 5:13–34.
- R. A. Vitale (1974): Convolutions on a group arising in pattern analysis, Ph.D. Thesis, Brown University.
- N. Wiener (1933): The Fourier Integral, Cambridge University Press.
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Additional Information
Ulf Grenander
Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Received by editor(s):
February 21, 2006
Published electronically:
May 1, 2007
Additional Notes:
This work has been supported by NSF DMS-00774276
Dedicated:
Dedicated to d’Arcy Thompson in memory of a great pioneer, 1860-1948
Article copyright:
© Copyright 2007
Brown University
