Electronic Journal of Statistics

Plugin procedure in segmentation and application to hyperspectral image segmentation

Robin Girard
Source: Electron. J. Statist. Volume 4 (2010), 655-676.

Abstract

In this work we give our contribution to the problem of segmentation with plug-in procedures. We propose general sufficient conditions under which plug in procedure are efficient. We also give an algorithm that satisfy these conditions. We apply this algorithm to hyperspectral images segmentation. Hyperspectral images are images that have both spatial and spectral coherence with thousands of spectral bands on each pixel. In the proposed procedure we combine a reduction dimension technique and a spatial regularization technique. This regularization is based on the mixlet modeling of Kolaczyck et al. [10].

First Page: Show Hide
Primary Subjects: 60K35
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ejs/1280758357
Digital Object Identifier: doi:10.1214/10-EJS567
Mathematical Reviews number (MathSciNet): MR2678966

References

[1] A. Antoniadis, J. Bigot, and R. von Sachs. A multiscale approach for statistical characterization of functional images., Journal of Computational and Graphical Statistics, 18(1):216–237, 2009.
[2] A. Barron, L. Birgé, and P. Massart. Risk bound for model selection via penalization., probability theory and related field, 113:301–413, 1999.
Mathematical Reviews (MathSciNet): MR1679028
Zentralblatt MATH: 0946.62036
Digital Object Identifier: doi:10.1007/s004400050210
[3] L. Birgé. Model selection via testing: an alternative to (penalized) maximum likelihood estimators., Annales de l’I.H.P. Probabilités et statistiques, 42(3):273–325, 2006.
Mathematical Reviews (MathSciNet): MR2219712
Zentralblatt MATH: 05024238
Digital Object Identifier: doi:10.1016/j.anihpb.2005.04.004
[4] V. I. Bogachev., Gaussian Measures. AMS, 1998.
Mathematical Reviews (MathSciNet): MR1642391
[5] O. Bousquet, S. Boucheron, and G. Lugosi. Theory of classification: a survey of recent advances., ESAIM: Probability and Statistics, 2004.
[6] L. Devroye, L. Gyorfi, and G. Lugosi., A probabilistic theory of pattern recognition. Springer-Verlag, 1996.
Mathematical Reviews (MathSciNet): MR1383093
Zentralblatt MATH: 0853.68150
[7] D. Donoho. Wedgelets: Nearly-minimax estimation of edges., Annals of Statistics, pages 859–897, 1999.
Mathematical Reviews (MathSciNet): MR1724034
Zentralblatt MATH: 0957.62029
Digital Object Identifier: doi:10.1214/aos/1018031261
Project Euclid: euclid.aos/1018031261
[8] D. Donoho and I. Johnstone. Ideal spatial adaptation by wavelet shrinkage., Biometrica, 81(3):425–455, 1994.
Mathematical Reviews (MathSciNet): MR1311089
Zentralblatt MATH: 0815.62019
Digital Object Identifier: doi:10.1093/biomet/81.3.425
[9] S. Geman and D. Nowak. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell, 6:721–741, 1984.
[10] E. Kolaczyk, J. Junchang, and S. Gopal. Multiscale, multigranular statistical image segmentation., JASA, 100(472) :1358, December 2005.
Mathematical Reviews (MathSciNet): MR2236447
Zentralblatt MATH: 1117.62371
Digital Object Identifier: doi:10.1198/016214505000000385
[11] E. Kolaczyk and R. Nowak. Multiscale likelihood analysis and complexity penalized estimation., Annals of Statistics, 32(2):500–527, 2004.
Mathematical Reviews (MathSciNet): MR2060167
Zentralblatt MATH: 1048.62036
Digital Object Identifier: doi:10.1214/009053604000000076
Project Euclid: euclid.aos/1083178936
[12] Korostelev and A. Tsybacov., Minimax Theory of Image Reconstruction, volume 82 of Lecture Notes In Statistics. Springer-Verlag, 1993.
Mathematical Reviews (MathSciNet): MR1226450
[13] Q. J. Li., Estimation of mixture Models. PhD thesis, Yale university, 1999.
Mathematical Reviews (MathSciNet): MR2699116
Zentralblatt MATH: 1023.93060
[14] F. Schmidt., Classification de la surface de Mars par imagerie hyperspectrale OMEGA. Suivi spatio-temporel et études des dépôts saisonniers de CO2 et H2O. PhD thesis, UJF, 2007.

2012 © Institute of Mathematical Statistics

Electronic Journal of Statistics

Electronic Journal of Statistics