Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] I. Biederman, Recognition-by-components: A theory of human image understanding, Psychological Review, 94, 115-147 (1987)
  • [2] 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
  • [3] Taylor L. Booth and Richard A. Thompson, Applying probability measures to abstract languages, IEEE Trans. Computers C-22 (1973), 442–450. MR 0356587
  • [4] 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)
  • [5] 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
  • [6] Zhiyi Chi, Probability models for complex systems, ProQuest LLC, Ann Arbor, MI, 1998. Thesis (Ph.D.)–Brown University. MR 2697382
  • [7] N. Chomsky, Syntactic Structures, Mouton, 1976
  • [8] N. Chomsky, Knowledge of Language: Its Nature, Origin, and Use, Praeger, 1986
  • [9] 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
  • [10] Thomas M. Cover and Joy A. Thomas, Elements of information theory, Wiley Series in Telecommunications, John Wiley & Sons, Inc., New York, 1991. A Wiley-Interscience Publication. MR 1122806
  • [11] W. Ellis, editor, A Source Book of Gestalt Psychology, Humanities Press, 1938
  • [12] 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
  • [13] J. Feldman, Perceptual models of small dot clusters, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 19, 331-357 (1995)
  • [14] Jacob Feldman, Regularity-based perceptual grouping, Comput. Intelligence 13 (1997), no. 4, 582–623. MR 1492295, https://doi.org/10.1111/0824-7935.00052
  • [15] J. Fodor and Z. Pylyshyn, Connectionism and cognitive architecture: a critical analysis, Cognition, 28, 3-71 (1988)
  • [16] K. S. Fu, Syntactic methods in pattern recognition, Academic Press, New York-London, 1974. Mathematics in Science and Engineering, Vol. 112. MR 0351178
  • [17] K. S. Fu. Syntactic Pattern Recognition and Applications, Prentice-Hall, 1982
  • [18] 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
  • [19] 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)
  • [20] Theodore E. Harris, The theory of branching processes, Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin; Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0163361
  • [21] 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)
  • [22] John E. Hopcroft and Jeffrey D. Ullman, Introduction to automata theory, languages, and computation, Addison-Wesley Publishing Co., Reading, Mass., 1979. Addison-Wesley Series in Computer Science. MR 645539
  • [23] Shih-Hsiu Huang, Compositional approach to recognition using multi-scale computations, ProQuest LLC, Ann Arbor, MI, 2001. Thesis (Ph.D.)–Brown University. MR 2701899
  • [24] J. E. Hummel and I. Biederman, Dynamic binding in a neural network for shape recognition, Psychological Review, 99, 480-517 (1992)
  • [25] Kevin Knight, Unification: a multidisciplinary survey, ACM Comput. Surveys 21 (1989), no. 1, 93–124. MR 1072798, https://doi.org/10.1145/62029.62030
  • [26] P. S. Laplace, Essai philosophique sur les probabilités, 1812. Translation of Truscott and Emory, New York, 1902
  • [27] Y. G. Leclerc, Constructing simple stable descriptions for image partitioning, International Journal of Computer Vision, 3, 73-102 (1989)
  • [28] 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
  • [29] R. Narasimhan, Labeling schemata and syntactic description of pictures, Information and Control, 7, 151-179 (1964)
  • [30] Theodosios Pavlidis, Structural pattern recognition, Springer-Verlag, Berlin-New York, 1977. Springer Series in Electrophysics, Vol. 1. MR 0471479
  • [31] Daniel Frederic Potter, Compositional pattern recognition, ProQuest LLC, Ann Arbor, MI, 1999. Thesis (Ph.D.)–Brown University. MR 2699183
  • [32] Alan Prince and Paul Smolensky, Optimality: from neural networks to universal grammar, Science 275 (1997), no. 5306, 1604–1610. MR 1435275, https://doi.org/10.1126/science.275.5306.1604
  • [33] Jorma Rissanen, Stochastic complexity in statistical inquiry, World Scientific Series in Computer Science, vol. 15, World Scientific Publishing Co., Inc., Teaneck, NJ, 1989. MR 1082556
  • [34] Naoki Saito, Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion, Wavelets in geophysics (Baltimore, MD, 1993) Wavelet Anal. Appl., vol. 4, Academic Press, San Diego, CA, 1994, pp. 299–324. MR 1295685, https://doi.org/10.1016/B978-0-08-052087-2.50017-7
  • [35] H. Schweitzer, Occam algorithms for computing visual motion, IEEE Transactions on Pattern Analysis and Machine Intelligence, 17, 1033-1042 (1995)
  • [36] A. C. Shaw, A formal picture description scheme as a basis for picture processing systems, Information and Control, 14, 9-52 (1969)
  • [37] Stuart M. Shieber, Constraint-based grammar formalisms, A Bradford Book, MIT Press, Cambridge, MA, 1992. Parsing and type inference for natural and computer languages. MR 1208730
  • [38] Paul Smolensky, Tensor product variable binding and the representation of symbolic structures in connectionist systems, Artificial Intelligence 46 (1990), no. 1-2, 159–216. MR 1080409, https://doi.org/10.1016/0004-3702(90)90007-M
  • [39] 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
  • [40] C. S. Wetherell, Probabilistic languages: a review and some open questions, Comput. Surveys 12 (1980), no. 4, 361–379. MR 600174
  • [41] 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)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 68T45, 68U10

Retrieve articles in all journals with MSC: 68T45, 68U10


Additional Information

DOI: https://doi.org/10.1090/qam/1939008
Article copyright: © Copyright 2002 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website