Quantization from Bayes factors with application to multilevel thresholding

Murtagh, F. and Starck, J.L.

(2003)

Murtagh, F. and Starck, J.L. (2003) Quantization from Bayes factors with application to multilevel thresholding. Pattern Recognition Letters, 24 (12).

Our Full Text Deposits

Full text access: Open

Full Text - 548.4 KB

Links to Copies of this Item Held Elsewhere


Abstract

We are concerned with the optimal selection of multiple thresholds in image analysis. We propose the use of the Bayes information criterion, a minimal information measure, for this and illustrate its use in practical cases. Applications of multiple threshold selection of interest to us include the closely related problems of (i) quantization for lossy encoding, and (ii) segmentation. Our examples relate to segmentation as a post-processing phase in edge detection.

Information about this Version

This is a Published version
This version's date is: 2003
This item is not peer reviewed

Link to this Version

https://repository.royalholloway.ac.uk/items/6339481f-1296-ca36-8c31-d4b1fbaed254/1/

Item TypeJournal Article
TitleQuantization from Bayes factors with application to multilevel thresholding
AuthorsMurtagh, F.
Starck, J.L.
Uncontrolled KeywordsImage thresholding; Model selection; Bayes factor; Bayes information criterion; Edge detection; Wavelet transform
DepartmentsFaculty of Science\Computer Science

Identifiers

doi10.1016/S0167-8655(03)00038-2

Deposited by () on 23-Dec-2009 in Royal Holloway Research Online.Last modified on 23-Dec-2009

References

Belge, M., Miller, E. and Kilmer, M., 2000. Wavelet domain image restoration with adaptive edge-preserving regularization. IEEE Trans. Image Proc. 9, pp. 598–608.

Buccigrossi, R.W. and Simoncelli, E.P., 1999. Image compression via joint statistical characterization in the wavelet domain. IEEE Trans. Image Proc. 8, pp. 1688–1701. Abstract-INSPEC | Abstract-Compendex | Order Document | Full Text via CrossRef | Abstract + References in Scopus | Cited By in Scopus

Canny, J., 1986. Computational approach to edge detection. IEEE Trans. Pattern Anal. Machine Intell. 8, pp. 679–698. Abstract-INSPEC | Abstract-Compendex | Order Document | Abstract + References in Scopus | Cited By in Scopus

Chipman, H., Kolaczyk, E. and McCulloch, R., 1997. Adaptive Bayesian wavelet shrinkage. J Amer. Statist. Assoc. 92, pp. 1413–1421. Abstract + References in Scopus | Cited By in Scopus

Choi, H. and Baraniuk, R.G., 2001. Multiscale image segmentation using wavelet-domain hidden Markov models. IEEE Trans. Image Proc. 10, pp. 1309–1320.

Coates, M.J. and Kuruolu, 2002. Time-frequency-based detection in impulsive noise environments using α-stable noise models. Signal Proc. 82, pp. 1917–1925. SummaryPlus | Full Text + Links | PDF (241 K) | Abstract + References in Scopus | Cited By in Scopus

Dempster, A.P., Laird, N.M. and Rubin, D.B., 1977. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. 39 Series B, pp. 1–22. Abstract + References in Scopus | Cited By in Scopus

Gray, R.M., 2002. Gauss mixtures quantization: Clustering Gauss mixtures. In: Nonlinear Methods in Estimation and Classification. Springer-Verlag, forthcoming

Gray, R.M. and Neuhoff, D.L., 1998. Quantization. IEEE Trans. Information Theory 44, pp. 2325–2384.

Hansen, M.H. and Yu, B., 2001. Model selection and the principle of minimum description length. J. Amer. Statist. Assoc. 96, pp. 746–774. Full Text via CrossRef | Abstract + References in Scopus | Cited By in Scopus

Kass, R.E. and Raftery, A.E., 1995. Bayes factors. J. Amer. Statist. Assoc. 90, pp. 773–795. Abstract + References in Scopus | Cited By in Scopus

Kominek, J., Waterloo BragZone, 2000. Available from . Images:

Lee, Y. and Kozaitis, S.P., 2000. Multiresolution gradient-based edge detection in noisy images using wavelet domain filters. Opt. Eng. 39, pp. 2405–2412. Abstract-Compendex | Abstract-INSPEC | Order Document | Full Text via CrossRef | Abstract + References in Scopus | Cited By in Scopus

Lloyd, S.P., 1957. Least squares quantization in PCM. Bell Labs technical note, partly presented at Institute of Mathematical Statistics Meeting, Atlantic City, NJ, September 1957. Published in IEEE Trans. Information Theory 28 (1982) 129–137

Lu, J., Healy, D.M. and Weaver, J.B., 1994. Contrast enhancement of medical images using multiscale edge representation. Opt. Eng. 33, pp. 2151–2161. Abstract-Compendex | Order Document | Full Text via CrossRef | Abstract + References in Scopus | Cited By in Scopus

Lukaszewicz, J. and Steinhaus, H., 1955. On measuring by comparison. Zastos. Mat. 2, pp. 225–231 (in Polish) . MathSciNet

McLachlan, G. and Krishnan, T., 1997. The EM Algorithm and Extensions. , Wiley.

Murtagh, F., Starck, J.L., 2003. Bayes factors for edge detection from wavelet product spaces. Opt. Eng., in press

Rissanen, J., 1986. Stochastic complexity and modeling. Ann. Statist. 14, pp. 1080–1100. MathSciNet

Sadler, B.M. and Swami, A., 1999. Analysis of multiscale products for step detection and estimation. IEEE Trans. Information Theory 45, pp. 1043–1051. Abstract-Compendex | Abstract-INSPEC | Order Document | MathSciNet | Full Text via CrossRef | Abstract + References in Scopus | Cited By in Scopus

Schwarz, G., 1978. Estimating the dimension of a model. Ann. Statist. 6, pp. 461–464. MathSciNet | Abstract + References in Scopus | Cited By in Scopus

Starck, J.L., Murtagh, F. and Bijaoui, A., 1998. Image and Data Analysis: The Multiscale Approach. , Cambridge University Press.

Swami, A. and Sadler, B.M., 2002. On some detection and estimation problems in heavy-tailed noise. Signal Proc. 82, pp. 1829–1846. SummaryPlus | Full Text + Links | PDF (553 K) | Abstract + References in Scopus | Cited By in Scopus

Tsakalides, P., Reveliotis, P. and Nikias, C.L., 2000. Scalar quantisation of heavy-tailed signals. IEE Vision, Image Signal Proc. 147, pp. 475–484. Abstract-Compendex | Abstract-INSPEC | Order Document | Full Text via CrossRef | Abstract + References in Scopus | Cited By in Scopus

Xu, Y., Weaver, J.B., Healy, D.M. and Liu, J., 1994. Wavelet transform domain filters: A spatially selective noise filtration technique. IEEE Trans. Image Proc. 3, pp. 747–758. Abstract-Compendex | Order Document | Abstract + References in Scopus | Cited By in Scopus

Yin, P.-Y., 2002. Maximum entropy-based optimal threshold selection using deterministic reinforcement learning with controlled randomization. Signal Proc. 82, pp. 993–1006. SummaryPlus | Full Text + Links | PDF (520 K) | Abstract + References in Scopus | Cited By in Scopus


Details