Skip to main content

On the Use of Matrix Information Geometry for Polarimetric SAR Image Classification

  • Chapter
  • First Online:
Matrix Information Geometry

Abstract

Polarimetric SAR images have a large number of applications. To extract a physical interpretation of such images, a classification on their polarimetric properties can be a real advantage. However, most classification techniques are developed under a Gaussian assumption of the signal and compute cluster centers using the standard arithmetical mean. This paper will present classification results on simulated and real images using a non-Gaussian signal model, more adapted to the high resolution images and a geometrical definition of the mean for the computation of the class centers. We will show notable improvements on the classification results with the geometrical mean over the arithmetical mean and present a physical interpretation for these improvements, using the Cloude-Pottier decomposition.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Salembier, C., Alonso-Gonzalez, P., Lopez-Martinez, A.: Filtering and segmentation of polarimetric sar images with binary partition trees. In: Geoscience and Remote Sensing Symposium (IGARSS), 2010 IEEE International, 2010

    Google Scholar 

  2. Arthur, D., Vassilvitskii, S.: k-means++: the advantages of careful seeding.Technical Report 2006–13, Stanford InfoLab, June 2006

    Google Scholar 

  3. Barbaresco, F.: Innovative tools for radar signal processing based on cartan’s geometry of spd matrices and information geometry. In: IEEE International Radar Conference, 2008

    Google Scholar 

  4. Barbaresco, F.: Robust median-based stap in inhomogeneous secondary data : frechet information geometry of covariance matrices. In: 2nd French-Singaporian SONDRA Workshop on EM Modeling, New Concepts and Signal Processing For Radar Detection and Remote Sensing, 2010

    Google Scholar 

  5. Barbaresco, F.: Information geometry of covariance matrix: cartan-siegel homogeneous bounded domains, mostow/berger fibration and frechet median. In: Proceedings of MIG, Springer, 2012

    Google Scholar 

  6. Cameron, W.L., Youssef, N., Leung, L.K.: Simulated polarimetric signatures of primitive geometrical shapes. IEEE Trans. Geosci. Remote Sens. 34(3), 793–803 (1996)

    Google Scholar 

  7. Cloude, S.R., Pottier, E.: An entropy based classification scheme for land applications of polarimetric SAR. IEEE Trans. Geosci. Remote Sens. 35(1), 68–78 (1997)

    Google Scholar 

  8. Conte, E., De Maio, A., Ricci, G.: Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection. IEEE Trans. Signal Process. 50(8), 1908–1915 (2002)

    Google Scholar 

  9. Devlaminck, V., Terrier, P.: Geodesic distance on non-singular coherency matrix space in polarization optics. J. Opt. Soc. Am. A, 27(3), 1756-1763 (2010)

    Google Scholar 

  10. Freeman, A., Durden, S.: A three component scattering model to describe polarimetric SAR data. Radar Polarimetry 1748 213–225 (1992)

    Google Scholar 

  11. Gini, F., Greco, M.V.: Covariance matrix estimation for CFAR detection in correlated heavy-tailed clutter. Signal Proc. 82(12), 1847–1859 (2002)

    Article  Google Scholar 

  12. Kersten, P.R., Lee, J-S., Ainsworth, T.L.: Unsupervised classification of polarimetric synthetic aperture radar images using fuzzy clustering and em clustering. IEEE Trans. Geosci. Remote Sens. 43(3), 519–527 (2005)

    Google Scholar 

  13. Kong, J.A., Swartz, A.A., Yueh, H.A.: Identification of terrain cover using the optimal terrain classifier. J. Electronmagn. Waves Applicat. 2, 171–194 (1988)

    Google Scholar 

  14. Krogager, E.: New decomposition of the radar target scattering matrix. Electron. Lett. 26(18), 1525–1527 (August 1990)

    Article  Google Scholar 

  15. Lee, Jong-Sen, Grunes, Mitchell R., Ainsworth, Thomas L., Schuler, Dale L., Cloude, Shane R.: Unsupervised classification using polarimetric decomposition and the complex Wishart classifier. IEEE Trans. Geosci. Remote Sens. 37(5), 2249–2258 (September 1999)

    Article  Google Scholar 

  16. Lee, J-S., Grunes, M.R., Kwok, R.: Classification of multi-look polarimetric SAR imagery based on complex Wishart distribution. Int. J. Remote Sens. 15(11), 2299–2311 (1994)

    Google Scholar 

  17. Moakher, M.: Differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 26(3), 735–747 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Pascal, F., Ovarlez, J-P., Forster, P., Larzabal, P.: Performance analysis of covariance matrix estimates in impulsive noise. Signal Proc. 56(6), 2206–2216 (2008)

    Google Scholar 

  19. Piro, P., Nielsen, F., Barlaud, M.: Tailored bregman ball trees for effective nearest neighbors. In: IEEE European Workshop on Computational Geometry (EuroCG), LORIA, Nancy, France, March 2009

    Google Scholar 

  20. van Zyl, J.J., Burnette, C.F.: Bayesian classification of polarimetric SAR images using adaptive a priori probability. Int. J. Remote Sens. 13(5), 835–840 (1992)

    Google Scholar 

  21. Wang, Y-H., Han, C-Z.: Polsar image segmentation by mean shift clustering in the tensor space. Acta Automatica Sinica 36(6), 798–806 (2010)

    Google Scholar 

  22. Yao, Kung: A representation theorem and its applications to spherically-invariant random processes. IEEE Trans. Inf. Theory 19(5), 600–608 (1973)

    Article  MATH  Google Scholar 

  23. Yueh, H.A., Swartz, A.A., Kong, J.A., Shin., R.T., Novak, L.M.: Optimal classification of terrain cover using normalized polarimetric data. J. Geophys. Res. 15261–15267 (1993)

    Google Scholar 

Download references

Acknowledgments

The authors would like to thank the DGA for funding this research.

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Formont, P., Ovarlez, JP., Pascal, F. (2013). On the Use of Matrix Information Geometry for Polarimetric SAR Image Classification. In: Nielsen, F., Bhatia, R. (eds) Matrix Information Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30232-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30232-9_10

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30231-2

  • Online ISBN: 978-3-642-30232-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics