Multilook Polarimetric SAR Change Detection Using Stochastic Distances Between Matrix-Variate Gd0 Distributions

In this article, we propose an efficient heterogeneous change detection algorithm based on stochastic distance measure between two <inline-formula> <tex-math notation="LaTeX">$\mathcal {G}_{d}^{0}$ </tex-math></inline-formula> distributions. Due to its flexibility and simplicity, the matrix-variate <inline-formula> <tex-math notation="LaTeX">$\mathcal {G}_{d}^{0}$ </tex-math></inline-formula> distribution has been successfully used to model the multilook polarimetric synthetic aperture radar (PolSAR) data and has been tested for classification, segmentation, and image analysis. Concretely, closed-form expressions for the Kullback–Leibler, Renyi of order <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula>, Bhattacharyya, and Hellinger distances are provided to compute the stochastic distance between <inline-formula> <tex-math notation="LaTeX">$\mathcal {G}_{d}^{0}$ </tex-math></inline-formula> distributions. In this context, we resort to the expectation–maximization (EM) to estimate accurately with low complexity for the parameters of the probability distribution of the two multilook polarimetric covariance matrices to be compared. Finally, the performance of the method is compared firstly to the performance of other known distributions, such as the scaled complex Wishart distribution, and secondly to other known statistical tests using simulated and real multilook PolSAR data.

[1]  Shiyong Cui,et al.  A Comparative Study of Statistical Models for Multilook SAR Images , 2014, IEEE Geoscience and Remote Sensing Letters.

[2]  Jakob J. van Zyl,et al.  Change detection techniques for ERS-1 SAR data , 1993, IEEE Trans. Geosci. Remote. Sens..

[3]  Shiyong Cui,et al.  A Benchmark Evaluation of Similarity Measures for Multitemporal SAR Image Change Detection , 2016, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[4]  Corina da Costa Freitas,et al.  A model for extremely heterogeneous clutter , 1997, IEEE Trans. Geosci. Remote. Sens..

[5]  G. Lauricella,et al.  Sulle funzioni ipergeometriche a piu variabili , 1893 .

[6]  Lorenzo Bruzzone,et al.  An unsupervised approach based on the generalized Gaussian model to automatic change detection in multitemporal SAR images , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Michel Lubrano,et al.  A minimum Hellinger distance estimator for stochastic differential equations: An application to statistical inference for continuous time interest rate models , 2008, Comput. Stat. Data Anal..

[8]  Lorenzo Bruzzone,et al.  Automatic analysis of the difference image for unsupervised change detection , 2000, IEEE Trans. Geosci. Remote. Sens..

[9]  Renato J. Cintra,et al.  Hypothesis Testing in Speckled Data With Stochastic Distances , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[10]  Josef Kittler,et al.  Minimum error thresholding , 1986, Pattern Recognit..

[11]  Carlos H. Muravchik,et al.  Unsupervised Polarimetric SAR Image Classification Using $\mathcal {G}_{p}^{0}$ Mixture Model , 2017, IEEE Geoscience and Remote Sensing Letters.

[12]  Pierre Soille,et al.  Change Detection Based on Information Measure , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[13]  H. Jeffreys.  An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  Knut Conradsen,et al.  Change detection in polarimetric SAR data over several time points , 2014, 2014 IEEE Geoscience and Remote Sensing Symposium.

[15]  A. M. Mathai.  Jacobians of matrix transformations and functions of matrix argument , 1997 .

[16]  Dong Liu,et al.  A novel fuzzy classification entropy approach to image thresholding , 2006, Pattern Recognit. Lett..

[17]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[18]  Thomas L. Ainsworth,et al.  Unsupervised classification of polarimetric synthetic aperture Radar images using fuzzy clustering and EM clustering , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[19]  Alejandro C. Frery,et al.  Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory , 2018, IEEE Transactions on Geoscience and Remote Sensing.

[20]  Jordi Inglada,et al.  A New Statistical Similarity Measure for Change Detection in Multitemporal SAR Images and Its Extension to Multiscale Change Analysis , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[21]  Renato J. Cintra,et al.  Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions , 2013, IEEE Transactions on Geoscience and Remote Sensing.

[22]  Shuang Wang,et al.  Unsupervised Change Detection in SAR Image Based on Gauss-Log Ratio Image Fusion and Compressed Projection , 2014, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[23]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[24]  Shiyong Cui,et al.  Statistical Wavelet Subband Modeling for Multi-Temporal SAR Change Detection , 2012, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[25]  Knut Conradsen,et al.  Change Detection in Full and Dual Polarization, Single- and Multifrequency SAR Data , 2015, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[26]  Torbjørn Eltoft,et al.  Application of the Matrix-Variate Mellin Transform to Analysis of Polarimetric Radar Images , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[27]  Knut Conradsen,et al.  A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data , 2003, IEEE Trans. Geosci. Remote. Sens..

[28]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[29]  Lionel Bombrun,et al.  Fisher Distribution for Texture Modeling of Polarimetric SAR Data , 2008, IEEE Geoscience and Remote Sensing Letters.

[30]  Gabriela Palacio,et al.  Unsupervised Classification of SAR Images Using Markov Random Fields and ${\cal G}_{I}^{0}$ Model , 2011, IEEE Geoscience and Remote Sensing Letters.

[31]  T. Kailath.  The Divergence and Bhattacharyya Distance Measures in Signal Selection , 1967 .

[32]  Nizar Bouhlel,et al.  Maximum-Likelihood Parameter Estimation of the Product Model for Multilook Polarimetric SAR Data , 2019, IEEE Transactions on Geoscience and Remote Sensing.

[33]  Francesca Bovolo,et al.  A Split-Based Approach to Unsupervised Change Detection in Large-Size Multitemporal Images: Application to Tsunami-Damage Assessment , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[34]  James R. Bunch,et al.  A constant-false-alarm-rate algorithm , 1992 .

[35]  Gabriele Moser,et al.  Polarimetric SAR Change Detection With the Complex Hotelling–Lawley Trace Statistic , 2016, IEEE Transactions on Geoscience and Remote Sensing.

[36]  G. Crooks.  On Measures of Entropy and Information , 2015 .

[37]  Shiyong Cui,et al.  Comparison of Kullback-Leibler divergence approximation methods between Gaussian mixture models for satellite image retrieval , 2015, 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS).

[38]  Alejandro C. Frery,et al.  The polarimetric 𝒢 distribution for SAR data analysis , 2005 .

[39]  Knut Conradsen,et al.  Determining the Points of Change in Time Series of Polarimetric SAR Data , 2016, IEEE Transactions on Geoscience and Remote Sensing.

[40]  E. Hellinger,et al.  Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen. , 1909 .

[41]  Abdourrahmane M. Atto,et al.  Multivariate statistical modeling for multi-temporal SAR change detection using wavelet transforms , 2015, 2015 8th International Workshop on the Analysis of Multitemporal Remote Sensing Images (Multi-Temp).

[42]  J. Kong,et al.  K-Distribution and Polarimetric Terrain Radar Clutter , 1990, Progress In Electromagnetics Research.

[43]  J.S. Lee,et al.  A comparison of change detection statistics in POLSAR images , 2005, Proceedings. 2005 IEEE International Geoscience and Remote Sensing Symposium, 2005. IGARSS '05..

[44]  Laurent Ferro-Famil,et al.  A New Coherent Similarity Measure for Temporal Multichannel Scene Characterization , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[45]  Raffaella Guida,et al.  On Fractional Moments of Multilook Polarimetric Whitening Filter for Polarimetric SAR Data , 2014, IEEE Transactions on Geoscience and Remote Sensing.