Unsupervised Amplitude and Texture Classification of SAR Images With Multinomial Latent Model

In this paper, we combine amplitude and texture statistics of the synthetic aperture radar images for the purpose of model-based classification. In a finite mixture model, we bring together the Nakagami densities to model the class amplitudes and a 2-D auto-regressive texture model with t-distributed regression error to model the textures of the classes. A non-stationary multinomial logistic latent class label model is used as a mixture density to obtain spatially smooth class segments. The classification expectation-maximization algorithm is performed to estimate the class parameters and to classify the pixels. We resort to integrated classification likelihood criterion to determine the number of classes in the model. We present our results on the classification of the land covers obtained in both supervised and unsupervised cases processing TerraSAR-X, as well as COSMO-SkyMed data.

[1]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[2]  Anil K. Jain,et al.  Markov Random Field Texture Models , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Haluk Derin,et al.  Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Jon Atli Benediktsson,et al.  Classification of remote sensing images from urban areas using a fuzzy model , 2004, IGARSS 2004. 2004 IEEE International Geoscience and Remote Sensing Symposium.

[5]  Gabriele Moser,et al.  Dictionary-based probability density function estimation for high-resolution SAR data , 2009, Electronic Imaging.

[6]  Michael A. Malcolm,et al.  Computer methods for mathematical computations , 1977 .

[7]  D R Adam,et al.  Signal and Image Processing , 2001, Yearbook of Medical Informatics.

[8]  C. Oliver.  The interpretation and simulation of clutter textures in coherent images , 1986 .

[9]  Amar Mitiche,et al.  Unsupervised Variational Image Segmentation/Classification Using a Weibull Observation Model , 2006, IEEE Transactions on Image Processing.

[10]  Josiane Zerubia,et al.  Texture feature analysis using a gauss-Markov model in hyperspectral image classification , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[11]  J. S. Lee,et al.  Unsupervised segmentation of dual-polarization SAR images based on amplitude and texture characteristics , 2002 .

[12]  Jirí Grim,et al.  Multivariate statistical pattern recognition with nonreduced dimensionality , 1986, Kybernetika.

[13]  Theo Gevers,et al.  A Spatially Constrained Generative Model and an EM Algorithm for Image Segmentation , 2007, IEEE Transactions on Neural Networks.

[14]  Josiane Zerubia,et al.  Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation , 2009, IEEE Transactions on Image Processing.

[15]  Bülent Sankur,et al.  Adaptive Langevin Sampler for Separation of $t$-Distribution Modelled Astrophysical Maps , 2010, IEEE Transactions on Image Processing.

[16]  D. V. Dyk.  NESTING EM ALGORITHMS FOR COMPUTATIONAL EFFICIENCY , 2000 .

[17]  Josiane Zerubia,et al.  Segmentation of Textured Satellite and Aerial Images by Bayesian Inference and Markov Random Fields , 2001 .

[18]  Fawwaz T. Ulaby,et al.  Use of SAR image texture in terrain classification , 1997, IGARSS'97. 1997 IEEE International Geoscience and Remote Sensing Symposium Proceedings. Remote Sensing - A Scientific Vision for Sustainable Development.

[19]  Nikolas P. Galatsanos,et al.  A Bayesian Framework for Image Segmentation With Spatially Varying Mixtures , 2010, IEEE Transactions on Image Processing.

[20]  Shin Ishii,et al.  Edge-Preserving Bayesian Image Superresolution Based on Compound Markov Random Fields , 2007, ICANN.

[21]  Gustav Zeuner,et al.  Markov chain Monte Carlo for Bayesian inference , 2007 .

[22]  Florence Tupin,et al.  Unsupervised classification of radar images using hidden Markov chains and hidden Markov random fields , 2003, IEEE Trans. Geosci. Remote. Sens..

[23]  Amar Mitiche,et al.  Variational and Level Set Methods in Image Segmentation , 2010 .

[24]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[25]  G. Pólya,et al.  Über die Statistik verketteter Vorgänge , 1923 .

[26]  Gabriele Moser,et al.  Dictionary-based stochastic expectation-maximization for SAR amplitude probability density function estimation , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[27]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[28]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[29]  Carlos Vázquez,et al.  Image segmentation as regularized clustering: a fully global curve evolution method , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[30]  Jianhua Lin,et al.  Divergence measures based on the Shannon entropy , 1991, IEEE Trans. Inf. Theory.

[31]  Amar Mitiche,et al.  Multiregion level-set partitioning of synthetic aperture radar images , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  K. S. Shanmugan,et al.  Crop Classification Using Airborne Radar and Landsat Data , 1982, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Tony F. Chan,et al.  A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model , 2002, International Journal of Computer Vision.

[34]  Gérard Govaert,et al.  Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  Josef Kittler,et al.  Divergence Based Feature Selection for Multimodal Class Densities , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[36]  C. S. Wallace,et al.  Estimation and Inference by Compact Coding , 1987 .

[37]  Josiane Zerubia,et al.  A Gauss-Markov model for hyperspectral texture analysis of urban areas , 2002, Object recognition supported by user interaction for service robots.

[38]  Francesca Bovolo,et al.  A Novel Context-Sensitive SVM for Classification of Remote Sensing Images , 2006, 2006 IEEE International Symposium on Geoscience and Remote Sensing.

[39]  Josiane Zerubia,et al.  A Level Set Model for Image Classification , 1999, International Journal of Computer Vision.

[40]  C. S. Wallace,et al.  An Information Measure for Classification , 1968, Comput. J..

[41]  Josiane Zerubia,et al.  SAR image classification with non-stationary Multinomial Logistic mixture of amplitude and texture densities , 2011, 2011 18th IEEE International Conference on Image Processing.

[42]  Fady Alajaji,et al.  Image segmentation and labeling using the Polya urn model , 1999, IEEE Trans. Image Process..

[43]  G. Celeux,et al.  A Classification EM algorithm for clustering and two stochastic versions , 1992 .

[44]  Jean-Marie Nicolas,et al.  Gamma mixture modeled with "second kind statistics": application to SAR image processing , 2002, IEEE International Geoscience and Remote Sensing Symposium.

[45]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[46]  Nikolas P. Galatsanos,et al.  Spatially Varying Mixtures Incorporating Line Processes for Image Segmentation , 2009, Journal of Mathematical Imaging and Vision.

[47]  Dina E. Melas,et al.  Double Markov random fields and Bayesian image segmentation , 2002, IEEE Trans. Signal Process..

[48]  D. Rubin,et al.  ML ESTIMATION OF THE t DISTRIBUTION USING EM AND ITS EXTENSIONS, ECM AND ECME , 1999 .

[49]  Anil K. Jain,et al.  Unsupervised Learning of Finite Mixture Models , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[50]  Donald Geman,et al.  Bayes smoothing algorithms for segmentation of images modeled by Markov random fields , 1984, ICASSP.

[51]  Gilles Celeux,et al.  A Component-Wise EM Algorithm for Mixtures , 2001, 1201.5913.

[52]  Rama Chellappa,et al.  Classification of textures using Gaussian Markov random fields , 1985, IEEE Trans. Acoust. Speech Signal Process..

[53]  Gabriele Moser,et al.  Modeling the Statistics of High Resolution Sar Images Modeling the Statistics of High Resolution Sar Images Modélisation Des Statistiques Des Images Radar (rso) Haute Résolution , 2022 .

[54]  Stephen M. Smith,et al.  Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm , 2001, IEEE Transactions on Medical Imaging.

[55]  Lawrence Carin,et al.  Sparse multinomial logistic regression: fast algorithms and generalization bounds , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[56]  Josiane Zerubia,et al.  Texture analysis through Markov random fields: urban areas extraction , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

[57]  José M. Bioucas-Dias,et al.  Bayesian Hyperspectral Image Segmentation With Discriminative Class Learning , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[58]  Jorge Herbert de Lira,et al.  Two-Dimensional Signal and Image Processing , 1989 .

[59]  Gabriele Moser,et al.  Classification of very high resolution SAR images of urban areas by dictionary-based mixture models, copulas, and Markov random fields using textural features , 2010, Remote Sensing.

[60]  Peter Hoogeboom,et al.  Classification of Agricultural Crops in Radar Images , 1983, IEEE Transactions on Geoscience and Remote Sensing.

[61]  Anil K. Jain,et al.  Simultaneous feature selection and clustering using mixture models , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[62]  Nikolas P. Galatsanos,et al.  Robust Image Segmentation with Mixtures of Student's t-Distributions , 2007, 2007 IEEE International Conference on Image Processing.

[63]  S. Quegan,et al.  Understanding Synthetic Aperture Radar Images , 1998 .

[64]  Nikolas P. Galatsanos,et al.  Variational Bayesian Image Restoration Based on a Product of $t$-Distributions Image Prior , 2008, IEEE Transactions on Image Processing.

[65]  Wojciech Pieczynski,et al.  SEM algorithm and unsupervised statistical segmentation of satellite images , 1993, IEEE Trans. Geosci. Remote. Sens..

[66]  Adrian E. Raftery,et al.  Model-Based Clustering, Discriminant Analysis, and Density Estimation , 2002 .

[67]  Robert M. Haralick,et al.  Textural Features for Image Classification , 1973, IEEE Trans. Syst. Man Cybern..

[68]  Thomas J. Hebert,et al.  Bayesian pixel classification using spatially variant finite mixtures and the generalized EM algorithm , 1998, IEEE Trans. Image Process..

[69]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[70]  Jiri Matas,et al.  On Combining Classifiers , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[71]  Qi Chen,et al.  Automatic variogram parameter extraction for textural classification of the panchromatic IKONOS imagery , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[72]  R. M. Haralick,et al.  Textural features for image classification. IEEE Transaction on Systems, Man, and Cybernetics , 1973 .

[73]  J. H. Ward.  Hierarchical Grouping to Optimize an Objective Function , 1963 .

[74]  M. Hassner,et al.  The Use of Markov Random Fields as Models of Texture , 1981 .

[75]  Donald Geman,et al.  Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[76]  Gilles Celeux,et al.  On Stochastic Versions of the EM Algorithm , 1995 .