Variogram Fractal Dimension Based Features for Hyperspectral Data Dimensionality Reduction

  • Kriti Mukherjee
  • Jayanta K Ghosh
  • Ramesh C. Mittal
Research Article
First Online:
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Accepted:

Abstract

In this paper a new approach for fractal based dimensionality reduction of hyperspectral data has been proposed. The features have been generated by multiplying variogram fractal dimension value with spectral energy. Fractal dimension bears the information related to the shape or characteristic of the spectral response curves and the spectral energy bears the information related to class separation. It has been observed that, the features provide accuracy better than 90 % in distinguishing different land cover classes in an urban area, different vegetation types belonging to an agricultural area as well as various types of minerals belonging to the same parent class. Statistical comparison with some conventional dimensionality reduction methods validates the fact that the proposed method, having less computational burden than the conventional methods, is able to produce classification statistically equivalent to those of the conventional methods.

Keywords

Hyperspectral Fractal Variogram Dimensionality reduction Computational complexity 
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References

  1. Ahlberg, J.H., Nilson, E.N., & Walsh, J.L. (1967). The theory of splines and their applications. Academic Press: Newyork and London, ch 2.Google Scholar
  2. Anderson, J.R. (1976). A land use and land cover classification system for use with remote sensor data. URL:http://landcover.usgs.gov/pdf/anderson.pdf
  3. Comon, P. (1994). Independent component analysis, a new concept? Signal Processing, 36, 287–314.CrossRefGoogle Scholar
  4. Cormen, T.H., Leiserson, C.L., Rivest, R.L., Stein, C. (2001) Introduction to algorithms, 2nd Edition, MIT Press, McGraw Hill Book Co.Google Scholar
  5. Davis, J.C. (1973) Statistics and data analysis in geology, 2nd edition. John Wiley & Sons, pp 239–246Google Scholar
  6. Foody, G. M. (2004). Thematic map comparison: evaluating the statistical significance of difference in classification accuracy, Photogrammetric Engineering and Remote Sensing 70(5), 627–633.Google Scholar
  7. Foody, G. M. (2009). Classification accuracy comparison: hypothesis tests and the use of confidence intervals in evaluations of difference, equivalence and non-inferiority. Remote Sensing of Environment, 113, 1658–1663.CrossRefGoogle Scholar
  8. Fukunaga, K. (1989). Effect of sample size in classifier design. IEEE Pattern Analysis and Machine Intelligence, 11(8), 873–885.CrossRefGoogle Scholar
  9. Ghosh, J.K. & Mukherjee, K. (2009) Fractal based dimensionality reduction of hyper-spectral images using power spectrum method, advances in computational vision and medical image processing : methods and applications. In J. M. R. S. Tavares, R. M. Natal Jorge (Eds), Springer Publication, pp 89–94. (ISBN: 978-0-415-57041-1)Google Scholar
  10. Ghosh, J. K., & Somvanshi, A. (2008). Fractal based dimensionality reduction of hyperspectral images. Journal of Indian Society of Remote Sensing, 36, 235–241.CrossRefGoogle Scholar
  11. Ghosh, J. K., Somvanshi, A., & Mittal, R. C. (2008). Fractal feature for classification of hyperspectral images of Moffit field, U.S.A. Current Science, 94, 356–358.Google Scholar
  12. Ghosh, J. K., Singh, A., & Mukherjee, K. (2009). Detection of anomaly in water body using hyperspectral images. Journal of Geomatics, 3(2), 53–56.Google Scholar
  13. Green, A. A., Berman, M., Switzer, P., & Craig, M. D. (1988). A transformation for ordering multispectral data in terms of image quality with implications for noise removal. IEEE Transactions on Geoscience and Remote Sensing, 26(1), 65–74.CrossRefGoogle Scholar
  14. Horvath, G. (2003). Neural networks in measurement systems, advances in learning theory: methods, models and applications (p. 392). In J. A. K. Suykens, G. Horvath, S. Basu, C. Micchelli, J. Vandewalle (Eds.), Amsterdam, The Netherlands: IOC Press.Google Scholar
  15. Hughes, G.F. (1968). On the mean accuracy of statistical pattern recognizers. IEEE Transactions on Information Theory, 14(1)Google Scholar
  16. Kendall, M.G. (1961). A course in the geometry of n-dimensions. Hafner PublishingGoogle Scholar
  17. Klinkenberg, B. (1994). A review of methods used to determine the fractal dimension of linear features. Mathematical Geology, 26(1), 23–46.CrossRefGoogle Scholar
  18. Landgrebe, D.A. (2003) Signal theory methods in multispectral remote sensing. John Wiley & SonsGoogle Scholar
  19. Mandelbrot, B. B. (1977). The fractal geometry of nature. New York: W.H. Freeman and Company.Google Scholar
  20. Mandelbrot, B. B. (1982). The fractal geometry of nature. San Fransisco: W.H. Freeman and Company. Google Scholar
  21. Moigne, J. L., Cole-Rhodes, A., Eastman, R., El-Ghazawi, T., Johnson, K., Kaewpijit, S., Laporte, N., Morisette, J., Nethanyahu, N. S., Stone, H. S., & Zavorin, I. (2002). Multiple sensor image registration, image fusion and dimension reduction of earth science imagery. IEEE Proceedings of the fifth international conference on information fusion, 2, 999–1006.Google Scholar
  22. Oppenheim, A.V., Schafer, R.W., & Buck, J.R. (2005). Discrete time signal processing, 2nd Edn, Pearson Education.Google Scholar
  23. Pu, R., & Gong, P. (2004). Wavelet transform applied to EO-1 hyperspectral data for forest LAI and crown closure mapping. Remote Sensing of Environment, 91, 212–224.CrossRefGoogle Scholar
  24. Robila, S.A., ed (2004). Advanced image processing techniques for remotely sensed images. Springer-Verlag.Google Scholar

Copyright information

© Indian Society of Remote Sensing 2012

Authors and Affiliations

  • Kriti Mukherjee
    • 1
  • Jayanta K Ghosh
    • 1
  • Ramesh C. Mittal
    • 2
  1. 1.Civil Engineering DepartmentIndian Institute of TechnologyRoorkeeIndia
  2. 2.Mathematics DepartmentIndian Institute of TechnologyRoorkeeIndia

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