Abstract：Classification is one of the core components in the interpretation of Polarimetric Synthetic Aperture Radar (PolSAR) images. A new PolSAR image classification approach employs the structural properties of the Riemannian manifold formed by PolSAR covariance matrices. In this paper, we first review the Riemannian manifold metrics generally used in PolSAR image analysis. Then, we describe a sparse coding method for the covariance matrices in the Riemannian manifold. For supervised classification, we propose a PolSAR image classification method that considers spatial information based on kernel space sparse coding. As for unsupervised PolSAR image classification, a method that takes advantage of Riemannian sparse induced similarity is proposed. Experimental results on EMISAR and AIRSAR data demonstrate the effectiveness of the proposed methods.
杨 文, 钟 能, 严天恒, 杨祥立. 基于黎曼流形的极化SAR图像分类[J]. 雷达学报, 2017, 6(5): 433-441.
Yang Wen, Zhong Neng, Yan Tianheng, Yang Xiangli. Classification of Polarimetric SAR Images Based on the Riemannian Manifold. JOURNAL OF RADARS, 2017, 6(5): 433-441.
Yang Wen, Song Hui, Xia Gui-song, et al.. Dissimilarity measurements for processing and analyzing PolSAR data:A survey[C]. Proceedings of 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Milan, Italy, 2015:1562-1565.
[2]
Lee J S, Grunes M R, Ainsworth T L, et al.. Unsupervised classification using polarimetric decomposition and the complex Wishart classifier[J]. IEEE Transactions on Geoscience and Remote Sensing, 1999, 37(5):2249-2258.[DOI:10.1109/36.789621]
[3]
Frery A C, Correia A H, and Freitas C D C. Classifying multifrequency fully polarimetric imagery with multiple sources of statistical evidence and contextual information[J]. IEEE Transactions on Geoscience and Remote Sensing, 2007, 45(10):3098-3109.[DOI:10.1109/TGRS.2007.903828]
[4]
Anfinsen S N, Jenssen R, and Eltoft T. Spectral clustering of polarimetric SAR data with the Wishart-derived distance measures[C/OL]. Proceedings of the 3rd International Workshop on Science and Applications of SAR Polarimetry and Polarimetric Interferometry, Noordwijk, Netherlands, 2007. http://adsabs.harvard.edu/abs/2007ESASP.644E..10A.
[5]
Banerjee A, Merugu S, Dhillon I S, et al.. Clustering with Bregman divergences[J]. The Journal of Machine Learning Research, 2005, 6:1705-1749.
[6]
Kersten P R, Lee J S, and Ainsworth T L. Unsupervised classification of polarimetric synthetic aperture radar images using fuzzy clustering and EM clustering[J]. IEEE Transactions on Geoscience and Remote Sensing, 2005, 43(3):519-527.[DOI:10.1109/TGRS.2004.842108]
[7]
Song H, Yang W, Bai Y, et al.. Unsupervised classification of polarimetric SAR imagery using large-scale spectral clustering with spatial constraints[J]. International Journal of Remote Sensing, 2015, 36(11):2816-2830.[DOI:10.1080/01431161.2015.1043759]
[8]
Song Hui, Yang Wen, Xu Xin, et al.. Unsupervised PolSAR imagery classification based on Jensen-Bregman LogDet divergence[C]. Proceedings of the 10th European Conference on Synthetic Aperture Radar, Berlin, Germany, 2014:1-4.
[9]
Cherian A, Sra S, Banerjee A, et al.. Jensen-Bregman LogDet divergence with application to efficient similarity search for covariance matrices[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(9):2161-2174.[DOI:10.1109/TPAMI.2012.259]
[10]
Zhang La-mei, Sun Liang-jie, Zou Bin, et al.. Fully polarimetric SAR image classification via sparse representation and polarimetric features[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2015, 8(8):3923-3932.[DOI:10.1109/JSTARS.2014.2359459]
[11]
Harandi M T, Hartley R, Lovell B, et al.. Sparse coding on symmetric positive definite manifolds using Bregman divergences[J]. IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(6):1294-1306.[DOI:10.1109/TNNLS.2014.2387383]
[12]
Yang Fan, Gao Wei, Xu Bin, et al.. Multi-frequency polarimetric SAR classification based on Riemannian manifold and simultaneous sparse representation[J]. Remote Sensing, 2015, 7(7):8469-8488.[DOI:10.3390/rs70708469]
[13]
Song Hui, Yang Wen, Zhong Neng, et al.. Unsupervised classification of PolSAR imagery via kernel sparse subspace clustering[J]. IEEE Geoscience and Remote Sensing Letters, 2016, 13(10):1487-1491.[DOI:10.1109/LGRS.2016.2593098]
[14]
Cherian A and Sra S. Riemannian sparse coding for positive definite matrices[C]. Proceedings of European Conference on Computer Vision (ECCV), Zurich, Switzerland, 2014:299-314.
[15]
Yang Wen, Zhong Neng, Yang Xiang-li, et al.. Riemannian sparse coding for classification of PolSAR images[C]. Proceedings of 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China, 2016:5698-5701.
[16]
Pennec X, Fillard P, and Ayache N. A Riemannian framework for tensor computing[J]. International Journal of Computer Vision, 2006, 66(1):41-66.[DOI:10.1007/s11263-005-3222-z]
[17]
Arsigny V, Fillard P, Pennec X, et al.. Log-Euclidean metrics for fast and simple calculus on diffusion tensors[J]. Magnetic Resonance in Medicine, 2006, 56(2):411-421.[DOI:10.1002/(ISSN)1522-2594]
[18]
Jayasumana S, Hartley R, Salzmann M, et al.. Kernel methods on Riemannian manifolds with Gaussian RBF kernels[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 37(12):2464-2477.[DOI:10.1109/TPAMI.2015.2414422]
[19]
Tibshirani R. Regression shrinkage and selection via the lasso:A retrospective[J]. Journal of the Royal Statistical Society, 2011, 73(3):273-282.[DOI:10.1111/rssb.2011.73.issue-3]
[20]
Elhamifar E and Vidal R. Sparse subspace clustering:Algorithm, theory, and applications[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(11):2765-2781.[DOI:10.1109/TPAMI.2013.57]
[21]
Cherian A and Sra S. Riemannian dictionary learning and sparse coding for positive definite matrices[J]. IEEE Transactions on Neural Networks and Learning Systems, 2016. DOI:10.1109/TNNLS.2016.2601307.
[22]
Birgin E G, Martínez J M, and Raydan M. Algorithm 813:SPG-software for convex-constrained optimization[J]. ACM Transactions on Mathematical Software, 2001, 27(3):340-349.[DOI:10.1145/502800.502803]
[23]
Wright J, Yang A Y, Ganesh A, et al.. Robust face recognition via sparse representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2):210-227.[DOI:10.1109/TPAMI.2008.79]
[24]
Zhang Hong-yan, Li Jia-yi, Huang Yuan-cheng, et al.. A nonlocal weighted joint sparse representation classification method for hyperspectral imagery[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2014, 7(6):2056-2065.[DOI:10.1109/JSTARS.2013.2264720]
[25]
Deledalle C A, Denis L, Poggi G, et al.. Exploiting patch similarity for SAR image processing:The nonlocal paradigm[J]. IEEE Signal Processing Magazine, 2014, 31(4):69-78.[DOI:10.1109/MSP.2014.2311305]
[26]
Cheng Hong, Liu Zi-cheng, and Yang Jie. Sparsity induced similarity measure for label propagation[C]. Proceedings of the 2009 IEEE 12th International Conference on Computer Vision, Kyoto, Japan, 2009:317-324.
[27]
Zelnik-Manor L and Perona P. Self-tuning spectral clustering[C]. Advances in Neural Information Processing Systems, Vancouver, 2004:1601-1608.
[28]
Achanta R, Shaji A, Smith K, et al.. SLIC superpixels compared to state-of-the-art superpixel methods[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(11):2274-2282.[DOI:10.1109/TPAMI.2012.120]
[29]
Lee J S, Grunes M R, and Kwok R. Classification of multi-look polarimetric SAR imagery based on complex Wishart distribution[J]. International Journal of Remote Sensing, 1994, 15(11):2299-2311.[DOI:10.1080/01431169408954244]
[30]
Foody G M. Status of land cover classification accuracy assessment[J]. Remote Sensing of Environment, 2002, 80(1):185-201.[DOI:10.1016/S0034-4257(01)00295-4]
[31]
Cherian A, Morellas V, and Papanikolopoulos N. Bayesian nonparametric clustering for positive definite matrices[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016, 38(5):862-874.[DOI:10.1109/TPAMI.2015.2456903]
[32]
Xu Kan, Yang Wen, Liu Gang, et al.. Unsupervised satellite image classification using Markov field topic model[J]. IEEE Geoscience and Remote Sensing Letters, 2013, 10(1):130-134.[DOI:10.1109/LGRS.2012.2194770]
2017, Vol. 6 
