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General Pattern Theory: A Mathematical Study of Regular Structures
Abstract
The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behaviour as well as through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.
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Cited by
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Srivastava, A., Joshi, S. H., Mio, W., & Liu, X. (2005) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2005.86 · Cited by 2,727
Hierarchical Bayesian inference in the visual cortex
Lee, T. S., & Mumford, D. (2003) · Journal of the Optical Society of America A · doi:10.1364/josaa.20.001434 · Cited by 1,473
A generic geometric transformation that unifies a wide range of natural and abstract shapes
Gielis, J. (2003) · American Journal of Botany · doi:10.3732/ajb.90.3.333 · Cited by 585
On Advances in Statistical Modeling of Natural Images
Srivastava, A., Lee, A. B., Simoncelli, E. P., & Zhu, S.-C. (2003) · Journal of Mathematical Imaging and Vision · doi:10.1023/a:1021889010444 · Cited by 485
On the Metrics and Euler-Lagrange Equations of Computational Anatomy
Miller, M. I., Trouvé, A., & Younes, L. (2002) · Annual Review of Biomedical Engineering · doi:10.1146/annurev.bioeng.4.092101.125733 · Cited by 438
Metadata
- Authors
- Grenander, U.
- Publisher
- Oxford University PressOxford
- Published
- 1994-01-20
- OpenAlex
- W4388322158
- Cited by
- 287
- References
- 0
- FWCI
- 2.86
- Type
- book
- Language
- en
- Open access
- closed
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