Abstract
Hyperspectral Image (HSI) classification refers to classifying hyperspectral data into features, where labels are given to pixels sharing the same features, distinguishing the present materials of the scene from one another. Naturally a HSI acquires spectral features of pixels, but spatial features based on neighborhood information are also important, which results in the problem of spectral-spatial classification. There are various ways to account to spatial information, one of which is through Mathematical Morphology, which is explored in this work. A HSI is a third-order data block, and building new spatial diversities may increase this order. In many cases, since pixel-wise classification requires a matrix of pixels and features, HSI data are reshaped as matrices which causes high dimensionality and ignores the multi-modal structure of the features. This work deals with HSI classification by modeling the data as tensors of high order. More precisely, multi-modal hyperspectral data is built and dealt with using tensor Canonical Polyadic (CP) decomposition. Experiments on real HSI show the effectiveness of the CP decomposition as a candidate for classification thanks to its properties of representing the pixel data in a matrix compact form with a low dimensional feature space while maintaining the multi-modality of the data.
References
[1] T. Adão et al. Hyperspectral imaging: A review on uav-based sensors, data processing and applications for agriculture and forestry. Remote Sensing, 9(11):1110, 2017.10.3390/rs9111110Search in Google Scholar
[2] H. Akbari, K. Uto, Y. Kosugi, K. Kojima, and N. Tanaka. Cancer detection using infrared hyperspectral imaging. Cancer science, 102(4):852–857, 2011.10.1111/j.1349-7006.2011.01849.xSearch in Google Scholar PubMed
[3] E. Aptoula, M. Dalla Mura, and S. Lefèvre. Vector attribute profiles for hyperspectral image classification. IEEE Transactions on Geoscience and Remote Sensing, 54(6):3208–3220, 2016.10.1109/TGRS.2015.2513424Search in Google Scholar
[4] J. A. Benediktsson and P. Ghamisi. Spectral-Spatial Classification of Hyperspectral Remote Sensing Images. Artech House, 2015.Search in Google Scholar
[5] J. A. Benediktsson, J. A. Palmason, and J. R. Sveinsson. Classification of hyperspectral data from urban areas based on extended morphological profiles. IEEE Transactions on Geoscience and Remote Sensing, 43(3):480–491, 2005.10.1109/TGRS.2004.842478Search in Google Scholar
[6] J. A. Benediktsson, M. Pesaresi, and K. Amason. Classification and feature extraction for remote sensing images from urban areas based on morphological transformations. IEEE Transactions on Geoscience and Remote Sensing, 41(9):1940–1949, 2003.10.1109/TGRS.2003.814625Search in Google Scholar
[7] G. Camps-Valls and L. Bruzzone. Kernel-based methods for hyperspectral image classification. IEEE Transactions on Geo-science and Remote Sensing, 43(6):1351–1362, 2005.10.1109/TGRS.2005.846154Search in Google Scholar
[8] Y. Chen, H. Jiang, C. Li, X. Jia, and P. Ghamisi. Deep feature extraction and classification of hyperspectral images based on convolutional neural networks. IEEE Transactions on Geoscience and Remote Sensing, 54(10):6232–6251, 2016.10.1109/TGRS.2016.2584107Search in Google Scholar
[9] Y. Chen, Z. Lin, X. Zhao, G. Wang, and Y. Gu. Deep learning-based classification of hyperspectral data. IEEE Journal of Selected topics in applied earth observations and remote sensing, 7(6):2094–2107, 2014.10.1109/JSTARS.2014.2329330Search in Google Scholar
[10] J. Cohen, R. C. Farias, and P. Comon. Fast decomposition of large nonnegative tensors. IEEE Signal Processing Letters, 22(7):862–866, 2014.10.1109/LSP.2014.2374838Search in Google Scholar
[11] P. Comon. Tensors: a brief introduction. IEEE Signal Processing Magazine, 31(3):44–53, 2014. hal-00923279.10.1109/MSP.2014.2298533Search in Google Scholar
[12] M. Dalla Mura, J. A. Benediktsson, B. Waske, and L. Bruzzone. Morphological attribute filters for the analysis of very high resolution remote sensing images. In 2009 IEEE International Geoscience and Remote Sensing Symposium, volume 3, pages III–97. IEEE, 2009.10.1109/IGARSS.2009.5418096Search in Google Scholar
[13] M. Dalla Mura, J. A. Benediktsson, B. Waske, and L. Bruzzone. Extended profiles with morphological attribute filters for the analysis of hyperspectral data. International Journal of Remote Sensing, 31(22):5975–5991, 2010.10.1080/01431161.2010.512425Search in Google Scholar
[14] M. Dalla Mura, J. A. Benediktsson, B. Waske, and L. Bruzzone. Morphological attribute profiles for the analysis of very high resolution images. IEEE Transactions on Geoscience and Remote Sensing, 48(10):3747–3762, 2010.10.1109/TGRS.2010.2048116Search in Google Scholar
[15] L. De Lathauwer, B. De Moor, and J. Vandewalle. A multilinear singular value decomposition. SIAM journal on Matrix Analysis and Applications, 21(4):1253–1278, 2000.10.1137/S0895479896305696Search in Google Scholar
[16] M. Fauvel, Y. Tarabalka, J. A. Benediktsson, J. Chanussot, and J. C. Tilton. Advances in spectral-spatial classification of hyperspectral images. Proceedings of the IEEE, 101(3):652–675, 2012.10.1109/JPROC.2012.2197589Search in Google Scholar
[17] L. Gao and R. T. Smith. Optical hyperspectral imaging in microscopy and spectroscopy – a review of data acquisition. Journal of biophotonics, 8(6):441–456, 2015.10.1002/jbio.201400051Search in Google Scholar PubMed PubMed Central
[18] Y. Gu, T. Liu, and J. Li. Superpixel tensor model for spatial–spectral classification of remote sensing images. IEEE Transactions on Geoscience and Remote Sensing, 57(7):4705–4719, 2019.10.1109/TGRS.2019.2892516Search in Google Scholar
[19] C.-W. Hsu, C.-C. Chang, C.-J. Lin, et al. A practical guide to support vector classification, 2003.Search in Google Scholar
[20] K. Huang, N. D. Sidiropoulos, and A. P. Liavas. A flexible and eflcient algorithmic framework for constrained matrix and tensor factorization. IEEE Transactions on Signal Processing, 64(19):5052–5065, 2016.10.1109/TSP.2016.2576427Search in Google Scholar
[21] J. R. Jensen. Remote Sensing of the Environment: An Earth Resource Perspective 2/e. Pearson Education India, 2009.Search in Google Scholar
[22] I. Jolliffe. Principal Component Analysis. Springer, 2011.10.1007/978-3-642-04898-2_455Search in Google Scholar
[23] M. Jouni, M. Dalla Mura, and P. Comon. Classification of hyperspectral images as tensors using nonnegative cp decomposition. In International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, pages 189–201. Springer, 2019.10.1007/978-3-030-20867-7_15Search in Google Scholar
[24] M. Jouni, M. Dalla Mura, and P. Comon. Hyperspectral image classification using tensor cp decomposition. In IGARSS 2019-2019 IEEE International Geoscience and Remote Sensing Symposium, pages 1164–1167. IEEE, 2019.10.1109/IGARSS.2019.8898346Search in Google Scholar
[25] J. B. Kruskal. Three-way arrays: Rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear algebra and its applications, 18(2):95–138, 1977.10.1016/0024-3795(77)90069-6Search in Google Scholar
[26] P. R. Marpu et al. Classification of hyperspectral data using extended attribute profiles based on supervised and unsupervised feature extraction techniques. International Journal of Image and Data Fusion, 3(3):269–298, 2012.10.1080/19479832.2012.702687Search in Google Scholar
[27] S. Murchie et al. Compact reconnaissance imaging spectrometer for mars (crism) on mars reconnaissance orbiter (mro). Journal of Geophysical Research: Planets, 112(E5), 2007.10.1029/2006JE002682Search in Google Scholar
[28] L. Najman and H. Talbot. Mathematical Morphology: From Theory to Applications. John Wiley & Sons, 2013.10.1002/9781118600788Search in Google Scholar
[29] C. Pilorget and J.-P. Bibring. Nir reflectance hyperspectral microscopy for planetary science: Application to the micromega instrument. Planetary and Space Science, 76:42–52, 2013.10.1016/j.pss.2012.11.004Search in Google Scholar
[30] Y. Qi, P. Comon, and L.-H. Lim. Uniqueness of nonnegative tensor approximations. IEEE Transactions on Information Theory, 62(4):2170–2183, 2016. arXiv:1410.8129.10.1109/TIT.2016.2532906Search in Google Scholar
[31] C. Rodarmel and J. Shan. Principal component analysis for hyperspectral image classification. Surveying and Land Information Science, 62(2):115–122, 2002.Search in Google Scholar
[32] J. Serra. Image Analysis and Mathematical Morphology. Number v. 1 in Image Analysis and Mathematical Morphology. Academic Press, 1984.Search in Google Scholar
[33] J. Serra. Image Analysis and Mathematical Morphology: Theoretical Advances. Image Analysis and Mathematical Morphology. Academic Press, 1988.Search in Google Scholar
[34] G. A. Shaw and H. K. Burke. Spectral imaging for remote sensing. Lincoln laboratory journal, 14(1):3–28, 2003.Search in Google Scholar
[35] P. Soille. Morphological Image Analysis: Principles and Applications. Springer Science & Business Media, 2013.Search in Google Scholar
[36] Y. Tarabalka, M. Fauvel, J. Chanussot, and J. A. Benediktsson. Svm- and mrf-based method for accurate classification of hyperspectral images. IEEE Geoscience and Remote Sensing Letters, 7(4):736–740, 2010.10.1109/LGRS.2010.2047711Search in Google Scholar
[37] D. Tuia, F. Pacifici, M. Kanevski, and W. J. Emery. Classification of very high spatial resolution imagery using mathematical morphology and support vector machines. IEEE Transactions on Geoscience and Remote Sensing, 47(11):3866–3879, 2009.10.1109/TGRS.2009.2027895Search in Google Scholar
[38] M. A. Veganzones, J. E. Cohen, R. C. Farias, J. Chanussot, and P. Comon. Nonnegative tensor cp decomposition of hyper-spectral data. IEEE Transactions on Geoscience and Remote Sensing, 54(5):2577–2588, 2015.10.1109/TGRS.2015.2503737Search in Google Scholar
[39] S. Velasco-Forero and J. Angulo. Classification of hyperspectral images by tensor modeling and additive morphological decomposition. Pattern Recognition, 46(2):566–577, 2013.10.1016/j.patcog.2012.08.011Search in Google Scholar
[40] L. Vincent. Morphological grayscale reconstruction in image analysis: Applications and eflcient algorithms. IEEE transactions on image processing, 2(2):176–201, 1993.10.1109/83.217222Search in Google Scholar
[41] Y. Xu, Z. Wu, J. Chanussot, P. Comon, and Z. Wei. Nonlocal coupled tensor cp decomposition for hyperspectral and multi-spectral image fusion. IEEE Transactions on Geoscience and Remote Sensing, 58(1):348–362, 2019.10.1109/TGRS.2019.2936486Search in Google Scholar
© 2020 Mohamad Jouni et al., published by De Gruyter
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