Nonparametric Bayesian image segmentation

International Journal of Computer Vision

Volumn 77, Issue 1-3, 2008, Pages 25-45

  Orbanz, Peter ^a   Buhmann, Joachim M ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Clustering; Dirichlet process mixtures; Image segmentation; Markov chain Monte Carlo; Markov random fields; Nonparametric Bayesian methods; Spatial statistics

Indexed keywords

BAYESIAN NETWORKS; CLUSTER ANALYSIS; CLUSTERING ALGORITHMS; HIDDEN MARKOV MODELS; PARAMETERIZATION; STATISTICS;

DIRICHLET PROCESS MIXTURES; MARKOV RANDOM FIELDS; NONPARAMETRIC BAYESIAN METHODS; SPATIAL STATISTICS;

IMAGE SEGMENTATION;

EID: 39749140347     PISSN: 09205691     EISSN: 15731405     Source Type: Journal    
DOI: 10.1007/s11263-007-0061-0     Document Type: Article

References (38)

1. Antoniak, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric estimation. Annals of Statistics, 2(6), 1152-1174.
2. Bach, F., & Jordan, M. I. (2004). Learning spectral clustering. In S. Thrun, L. K. Saul, & B. Schölkopf (Eds.), Advances in neural information processing system 16 (pp. 305-312). Cambridge: MIT.
3. Besag, J. (1986). On the statistical analysis of dirty pictures (with discussion). Journal of the Royal Statistical Society Series B, 48(3), 259-302.
4. Besag, J., Green, P., Higdon, D., & Mengersen, K. (1995). Bayesian computation and stochastic systems. Statistical Science, 10(1), 3-66.
5. Blei, D. M. (2004). Probabilistic models for text and images. PhD thesis, U. C. Berkeley.
6. Blei, D. M., & Jordan, M. I. (2006). Variational methods for the Dirichlet process. Bayesian Analysis, 1(1), 121-144.
7. Breckenridge, J. (1989). Replicating cluster analysis: Method, consistency and validity. Multivariate Behavioral Research, 24, 147-161.
8. Devroye, L. (1986). Non-uniform random variate generation. Berlin: Springer.
9. Dudoit, S., & Fridyland, J. (2002). A prediction-based resampling method for estimating the number of clusters in a dataset. Genome Biology, 3(7).
10. Escobar, M. D. (1994). Estimating normal means with a Dirichlet process prior. Journal of the American Statistical Association, 89(425), 268-277.
11. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1(2).
12. Fischer, B., & Buhmann, J. M. (2003). Bagging for path-based clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(11), 1411-1415.
13. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721-741.
14. Geman, D., Geman, S., Graffigne, C., & Dong, P. (1990). Boundary detection by constrained optimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), 609-628.
15. Hermes, L., Zöller, T., & Buhmann, J. M. (2002). Parametric distributional clustering for image segmentation. In Lecture notes in computer science : Vol. 2352. Computer vision-ECCV '02 (pp. 577-591). Berlin: Springer.
16. Hofmann, T., Puzicha, J., & Buhmann, J. M. (1998). Unsupervised texture segmentation in a deterministic annealing framework. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8), 803-818.
17. Kotz, S., Balakrishnan, N., & Johnson, N. L. (2000). Continuous multivariate distributions (Vol. 1, 2nd ed.). New York: Wiley.
18. Lange, T., Roth, V., Braun, M., & Buhmann, J. M. (2004). Stability-based validation of clustering solutions. Neural Computation, 16(6), 1299-1323.
19. Lehmann, E. L., & Romano, J. P. (2005). Testing statistical hypotheses (3rd ed.). Berlin: Springer.
20. Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information Theory, 37, 145-151.
21. MacEachern, S. N. (1994). Estimating normal means with a conjugate style Dirichlet process prior. Communications in Statistics: Simulation and Computation, 23, 727-741.
22. MacEachern, S. N. (1998). Computational methods for mixture of Dirichlet process models. In D. Dey, P. Müller, & D. Sinha (Eds.), Lecture notes in statistics : Vol. 133. Practical nonparametric and semiparametric Bayesian statistics (pp. 23-43). Berlin: Springer.
23. MacEachern, S. N., & Müller, P. (2000). Efficient MCMC schemes for robust model extensions using encompassing Dirichlet process mixture models. In D. Rios Insua & F. Ruggeri (Eds.), Robust Bayesian analysis (pp. 295-315). Berlin: Springer.
24. Martin, D., Fowlkes, C., & Malik, J. (2004). Learning to detect natural image boundaries using local brightness, color, and texture cues. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(5), 530-549.
25. McAuliffe, J. D., Blei, D. M., & Jordan, M. I. (2004). Nonparametric empirical Bayes for the Dirichlet process mixture model. Technical report, UC Berkeley.
26. Morel, J.-M., & Solimini, S. (1995). Variational methods for image segmentation. Basel: Birkhäuser.
27. Müller, P., & Quintana, F. A. (2004). Nonparametric Bayesian data analysis. Statistical Science, 19(1), 95-111.
28. Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9, 249-265.
29. Puzicha, J., Hofmann, T., & Buhmann, J. M. (1999). Histogram clustering for unsupervised segmentation and image retrieval. Pattern Recognition Letters, 20, 899-909.
30. Rissanen, J. (1983). A universal prior for integers and estimation by minimum description length. Annals of Statistics, 11, 416-431.
31. Roberts, C. P. (1996). Mixtures of distributions: inference and estimation. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice (pp. 441-464). London: Chapman & Hall.
32. Roth, V., Laub, J., Motoaki, K., & Buhmann, J. M. (2003). Optimal cluster preserving embedding of non-metric proximity data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(12), 1540-1551.
33. Samson, C., Blanc-Féraud, L., Aubert, G., & Zerubia, J. (2000). A variational model for image classification and restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(5), 460-472.
34. Shi, J., & Malik, J. (2000). Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), 888-905.
35. Tu, Z., & Zhu, S.-C. (2002). Image segmentation by data-driven Markov chain Monte Carlo. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(5), 657-673.
36. Walker, S. G., Damien, P., Laud, P. W., & Smith, A. F. M. (1999). Bayesian nonparametric inference for random distributions and related functions. Journal of the Royal Statistical Society B, 61(3), 485-527.
37. Winkler, G. (2003). Image analysis, random fields and Markov chain Monte Carlo methods. Berlin: Springer.
38. Zaragoza, H., Hiemstra, D., Tipping, D., & Robertson, S. (2003). Bayesian extension to the language model for ad hoc information retrieval. In Proceedings of SIGIR 2003.