The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
The mean field theory in EM procedures for Markov random fields
Abstract
In many signal processing and pattern recognition applications, the hidden data are modeled as Markov processes, and the main difficulty of using the maximisation (EM) algorithm for these applications is the calculation of the conditional expectations of the hidden Markov processes. It is shown how the mean field theory from statistical mechanics can be used to calculate the conditional expectations for these problems efficiently. The efficacy of the mean field theory approach is demonstrated on parameter estimation for one-dimensional mixture data and two-dimensional unsupervised stochastic model-based image segmentation. Experimental results indicate that in the 1-D case, the mean field theory approach provides results comparable to those obtained by Baum's (1987) algorithm, which is known to be optimal. In the 2-D case, where Baum's algorithm can no longer be used, the mean field theory provides good parameter estimates and image segmentation for both synthetic and real-world images.>
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Cites
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
A tutorial on hidden Markov models and selected applications in speech recognition
Rabiner, L. R. (1989) · Proceedings of the IEEE · doi:10.1109/5.18626 · Cited by 22,743
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949
Spatial Interaction and the Statistical Analysis of Lattice Systems
Besag, J. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00999.x · Cited by 6,067
Ballard, D. H., & Brown, C. M. (1982) · Cited by 5,303
Maximum Likelihood from Incomplete Data via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1976) · Cited by 4,517
Baum, L. E., Petrie, T., Soules, G., & Weiss, N. (1970) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177697196 · Cited by 4,297
On the Statistical Analysis of Dirty Pictures
Besag, J. (1986) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1986.tb01412.x · Cited by 4,191
Pattern Recognition Principles
(2009) · Classification Methods for Remotely Sensed Data, Second Edition · doi:10.1201/9781420090741.ch2 · Cited by 3,188
Mixture Densities, Maximum Likelihood and the EM Algorithm
Redner, R. A., & Walker, H. F. (1984) · SIAM Review · doi:10.1137/1026034 · Cited by 2,693
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Automated model-based tissue classification of MR images of the brain
Van Leemput, K., Maes, F., Vandermeulen, D., & Suetens, P. (1999) · IEEE Transactions on Medical Imaging · doi:10.1109/42.811270 · Cited by 1,024
The EM Algorithm—an Old Folk-song Sung to a Fast New Tune
Meng, X.-L., & Van Dyk, D. (1997) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00082 · Cited by 802
Medical image segmentation on GPUs – A comprehensive review
Smistad, E., Falch, T. L., Bozorgi, M., Elster, A. C., & Lindseth, F. (2015) · Medical Image Analysis · doi:10.1016/j.media.2014.10.012 · Cited by 264
Bayesian Methods for Neural Networks and Related Models
Titterington, D. M. (2004) · Statistical Science · doi:10.1214/088342304000000099 · Cited by 162
Metadata
- Authors
- Zhang, J.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 1992
- Volume
- 40
- Issue
- 10
- Pages
- 2570-2583
- ISSN
- 1053-587X (ISSN-L)
- OpenAlex
- W2166916666
- Cited by
- 339
- References
- 19
- FWCI
- 3.13
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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