Composition systems
Authors:
Stuart Geman, Daniel F. Potter and Zhiyi Chi
Journal:
Quart. Appl. Math. 60 (2002), 707-736
MSC:
Primary 68T45; Secondary 68U10
DOI:
https://doi.org/10.1090/qam/1939008
MathSciNet review:
MR1939008
Full-text PDF Free Access
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Additional Information
I. Biederman, Recognition-by-components: A theory of human image understanding, Psychological Review, 94, 115–147 (1987)
E. Bienenstock, Notes on the growth of a composition machine, In D. Andler, E. Bienenstock, and B. Laks, editors, Proceedings of the Royaumont Interdisciplinary Workshop on Compositionality in Cognition and Neural Networks, 1991
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J. Canning, A minimum description length model for recognizing objects with variable appearances (the VAPOR model), IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 1032–1036 (1994)
S. Casadei and S.K. Mitter, A hierarchical approach to high resolution edge contour reconstruction, In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996
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I. Biederman, Recognition-by-components: A theory of human image understanding, Psychological Review, 94, 115–147 (1987)
E. Bienenstock, Notes on the growth of a composition machine, In D. Andler, E. Bienenstock, and B. Laks, editors, Proceedings of the Royaumont Interdisciplinary Workshop on Compositionality in Cognition and Neural Networks, 1991
T.L. Booth and R.A. Thompson, Applying probability measures to abstract languages, IEEE Trans. on Computers, C-22, 442–450 (1973)
J. Canning, A minimum description length model for recognizing objects with variable appearances (the VAPOR model), IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 1032–1036 (1994)
S. Casadei and S.K. Mitter, A hierarchical approach to high resolution edge contour reconstruction, In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996
Z. Chi, Probability Models for Complex Systems, Ph.D. thesis, Division of Applied Mathematics, Brown University, 1998
N. Chomsky, Syntactic Structures, Mouton, 1976
N. Chomsky, Knowledge of Language: Its Nature, Origin, and Use, Praeger, 1986
D. B. Cooper, Feature selection and super data compression for pictures in remote conference and classroom communications, In Proceedings of the Second International Joint Conference on Pattern Recognition, 1974, pp. 111-115
T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley and Sons, 1991
W. Ellis, editor, A Source Book of Gestalt Psychology, Humanities Press, 1938
J. Feldman, Formal constraints on cognitive interpretations of causal structure, In Proceedings of the IEEE Workshop on Architectures for Semiotic Modeling and Situation Analysis, 1995
J. Feldman, Perceptual models of small dot clusters, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 19, 331–357 (1995)
J. Feldman, Regularity-based perceptual grouping, Computational Intelligence, 13, 582–621 (1997)
J. Fodor and Z. Pylyshyn, Connectionism and cognitive architecture: a critical analysis, Cognition, 28, 3–71 (1988)
K. S. Fu, Syntactic Methods in Pattern Recognition, Academic Press, 1974
K. S. Fu. Syntactic Pattern Recognition and Applications, Prentice-Hall, 1982
U. Grenander, General Pattern Theory: A Study of Regular Structures, Oxford University Press, 1993
H. Gu, Y. Shirai, and M. Asada, MDL-based segmentation and motion modeling in a long image sequence of scene with multiple independently moving objects, IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, 58–64, (1996)
T.E. Harris, The Theory of Branching Processes. Springer-Verlag, Berlin, 1963.
G. E. Hinton, P. Dayan, B. J. Frey, and R. M. Neal, The “wake-sleep” algorithm for unsupervised neural networks, Science, 268, 1158–1161 (1995)
J. Hopcroft and J. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA 1979
S.-H. Huang, Compositional Approach to Recognition Using Multi-Scale Computations, Ph.D. thesis, Division of Applied Mathematics, Brown University, 2001
J. E. Hummel and I. Biederman, Dynamic binding in a neural network for shape recognition, Psychological Review, 99, 480–517 (1992)
K. Knight, Unification: a multidisciplinary survey, ACM Computing Surveys, 21, 93–124 (1989)
P. S. Laplace, Essai philosophique sur les probabilités, 1812. Translation of Truscott and Emory, New York, 1902
Y. G. Leclerc, Constructing simple stable descriptions for image partitioning, International Journal of Computer Vision, 3, 73–102 (1989)
E. Mjolsness, Connectionist grammars for high-level vision, In V. Honavar and L. Uhr, editors, Artificial Intelligence and Neural Networks: Steps Toward Principled Integration, Academic Press, 1994
R. Narasimhan, Labeling schemata and syntactic description of pictures, Information and Control, 7, 151–179 (1964)
T. Pavlidis, Structural Pattern Recognition, Springer-Verlag, 1977
D. F. Potter, Compositional Pattern Recognition, Ph.D. thesis, Division of Applied Mathematics, Brown University, 1998
A. Prince and P. Smolensky, Optimality: From neural networks to universal grammar, Science, 275, 1604–1610 (1997)
J. Rissanen, Stochastic Complexity in Statistical Inquiry, World Scientific Press, 1989
N. Saito, Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion, In E. Foufoula-Georgiou and P. Kumar, editors, Wavelets in Geophysics, Academic Press, 1994, pp. 299–324
H. Schweitzer, Occam algorithms for computing visual motion, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 1033–1042 (1995)
A. C. Shaw, A formal picture description scheme as a basis for picture processing systems, Information and Control, 14, 9–52 (1969)
S. Shieber, Constraint-Based Grammar Formalisms, MIT Press, 1992
P. Smolensky, Tensor product variable binding and the representation of symbolic structures in connectionist systems, Artificial Intelligence, 46, 159–216 (1990)
C. von der Malsburg, Synaptic plasticity as a basis of brain organization, In J.P. Changeux and M. Konishi, editors, The Neural and Molecular Bases of Learning, John Wiley and Sons, 1987, pp. 411–432
C.S. Wetherell, Probabilistic languages: a review and some open questions, Computing Surveys, 12, 361–379 (1980)
S. C. Zhu and A. Yuille, Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, 884–900 (1996)
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© Copyright 2002
American Mathematical Society