Girard, Robin Plugin procedure in segmentation and application to hyperspectral image segmentation. (English) Zbl 1329.62280 Electron. J. Stat. 4, 655-676 (2010). Summary: 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 E. D. Kolaczyk et al. [J. Am. Stat. Assoc. 100, No. 472, 1358–1369 (2005; Zbl 1117.62371)]. MSC: 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62H35 Image analysis in multivariate analysis 62M40 Random fields; image analysis Keywords:segmentation; mixture model; penalized maximum likelihood estimation; dimensionality reduction Citations:Zbl 1117.62371 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid 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. · doi:10.1198/jcgs.2009.0013 [2] A. Barron, L. Birgé, and P. Massart. Risk bound for model selection via penalization., probability theory and related field , 113:301-413, 1999. · Zbl 0946.62036 · 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. · Zbl 1333.62094 · doi:10.1016/j.anihpb.2005.04.004 [4] V. I. Bogachev., Gaussian Measures . AMS, 1998. [5] O. Bousquet, S. Boucheron, and G. Lugosi. Theory of classification: a survey of recent advances., ESAIM: Probability and Statistics , 2004. · Zbl 1136.62355 [6] L. Devroye, L. Gyorfi, and G. Lugosi., A probabilistic theory of pattern recognition . Springer-Verlag, 1996. · Zbl 0853.68150 [7] D. Donoho. Wedgelets: Nearly-minimax estimation of edges., Annals of Statistics , pages 859-897, 1999. · Zbl 0957.62029 · doi:10.1214/aos/1018031261 [8] D. Donoho and I. Johnstone. Ideal spatial adaptation by wavelet shrinkage., Biometrica , 81(3):425-455, 1994. · Zbl 0815.62019 · 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. · Zbl 0573.62030 · doi:10.1109/TPAMI.1984.4767596 [10] E. Kolaczyk, J. Junchang, and S. Gopal. Multiscale, multigranular statistical image segmentation., JASA , 100(472) :1358, December 2005. · Zbl 1117.62371 · 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. · Zbl 1048.62036 · doi:10.1214/009053604000000076 [12] Korostelev and A. Tsybacov., Minimax Theory of Image Reconstruction , volume 82 of Lecture Notes In Statistics . Springer-Verlag, 1993. · Zbl 0833.62039 [13] Q. J. Li., Estimation of mixture Models . PhD thesis, Yale university, 1999. [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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.