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Estimation of Uncertainty Using Entropy on Noise Based Soft Classifiers

  • Rakesh Dwivedi
  • Anil Kumar
  • S. K.  Ghosh
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 236)

Abstract

In remote sensing noise is some kind of ambiguous data that occurs due to some inadequacy in the sensing, digitization or data recording process. This paper examines the effect of noise clustering algorithm of image classification. In remotely sensed data the easiest and usual assumption is that each pixel represents a homogeneous area on the ground. However in real world, it is found to be heterogeneous in nature. For this reason, it has been proposed that fuzziness should be accommodated in the classification procedure and preserves the extracted information. Classification of satellite images are complex process and accuracy of the output is dependent on classifier parameters. This paper examines the effect of various parameters like weighted exponent ‘m’ as well as resolution parameter ‘\(\partial \)’ for noise clustering (NC) classifier. The prime focus in this work is to select suitable parameters for classification of remotely sensed data which improves the accuracy of classification output to study the behaviour of associated learning parameters for optimization estimation using noise clustering classifier. A concept of “Noise Cluster” is introduced such that noisy data points may be assigned to the noise class. In this research work it has been tried to generate, a fraction outputs of noise clustering based classifier. The remote sensing data used has been from AWiFS, LISS-III and LISS-IV sensors of IRS-P6 satellite. This study proposes the entropy, as a special criterion for visualising and evaluating the uncertainty and it has been used as an absolute uncertainty indicator from output data. From the resultant aspect, while monitoring entropy of fraction images for different values, optimum weighting exponent ‘m’ and resolution parameter ‘\(\partial \)’ has been obtained for AWIFS, LIIS-III and LISS-IV images and that is ‘m\(\,=\,\)2.9 and ‘\(\partial \)\(\,=\,\) \(10^{6}\), providing highest degree of membership value with minimum entropy value as shown in Table 1.

Keywords

Entropy Noise clustering (NC) Fuzzy c-mean (FCM) Possibilistic c-mean (PCM) All wide field sensor (AWiFS) Linear imaging self scanning (LISS). 

References

  1. 1.
    Binaghi, E., Rampini, A.: Fuzzy decision making in the classification of multisource remote sensing data. Opt. Eng. 6, 1193–1203 (1993)CrossRefGoogle Scholar
  2. 2.
    Binaghi, E., Rampini, A., Brivio, P.A., Schowengerdt, R.A. (eds.): Special issue on non-conventional pattern analysis in remote sensing. Pattern Recogn. Lett. 17(13) (1996)Google Scholar
  3. 3.
    Binaghi, E., Brivio, P.A., Chessi, P., Rampini, A.: A fuzzy set based accuracy assessment of soft classification. Pattern Recogn. Lett. 20, 935–948 (1999)CrossRefGoogle Scholar
  4. 4.
    Bezdek, J.C.: A convergence theorem for the fuzzy ISODATA clustering algorithms. IEEE Trans. Pattern Anal. Mach. Intell. PAMI 2(1), 1–8 (1980)Google Scholar
  5. 5.
    Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy c-means clustering algorithm. Comput. Geosci. 10(2–3), 191–203 (1984)CrossRefGoogle Scholar
  6. 6.
    Bezdek, J.C., Hathaway, R.J., Sabin, M.J., Tucker, W.T.: Convergence theory for fuzzy c-means: counterexamples and repairs. IEEE Trans. Syst. Man, Cybern. SMC-17(5), 873–877 (1987)Google Scholar
  7. 7.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)CrossRefMATHGoogle Scholar
  8. 8.
    Dav’e, R.N.: Fuzzy-shell clustering and applications to circle detection in digital images. Int. J. Gen. Syst. 16, 343–355 (1990)Google Scholar
  9. 9.
    Dave, R.N.: Characterization and detection of noise in clustering. Pattern Recogn. Lett. 12, 657–664 (1991)CrossRefGoogle Scholar
  10. 10.
    Dav’e, R.N., Krishnapuram, R.: Robust clustering methods: a unified view. IEEE Trans. Fuzzy Syst. 5(2), 270–293 (1997)Google Scholar
  11. 11.
    Fisher, P.: The pixel: a snare and a delusion. Int. J. Remote Sens. 18(3), 679–685 (1997)CrossRefGoogle Scholar
  12. 12.
    Foody, G.M.: Cross-entropy for the evaluation of the accuracy of a fuzzy land cover classification with fuzzy ground data. ISPRS J. Photogramm. Remote Sens. 50, 2–12 (1995)CrossRefGoogle Scholar
  13. 13.
    Foody, G.M.: Approaches for the production and evaluation of fuzzy land cover classifications from remotely sensed data. Int. J. Remote Sens. 17(7), 1317–1340 (1996)CrossRefGoogle Scholar
  14. 14.
    Foody, G.M., Arora, M.K.: Incorporating mixed pixels in the training, allocation and testing stages of supervised classification. Pattern Recogn. Lett. 17, 1389–1398 (1996)CrossRefGoogle Scholar
  15. 15.
    Foody, G.M., Lucas, R.M., Curran, P.J., Honzak, M.: Non-linear mixture modelling without end-members using an ANN. Int. J. Remote Sens. 18(4), 937–953 (1997)CrossRefGoogle Scholar
  16. 16.
    Foody, G.M.: Estimation of sub-pixel land cover composition in the presence of untrained classes. Comput. Geosci. 26, 469–478 (2000)CrossRefGoogle Scholar
  17. 17.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1(2), 98–110 (1993)Google Scholar
  18. 18.
    Kumar, A., Ghosh, S.K., Dadhwal, V.K.: Study of sub-pixel classification algorithms for high dimensionality data set. In: IEEE International Geoscience and Remote Sensing Symposium and 27th Canadian Symposium on Remote Sensing, Denver, Colorado, USA, 31 July–04 August (accepted) (2006)Google Scholar
  19. 19.
    Okeke, F., Karnieli, A.: Methods for fuzzy classification and accuracy assessment of historical aerial photographs for vegetation change analyses. Part I: algorithm development. Int. J. Remote Sens. 27(1–2), 153–176 (2006)Google Scholar
  20. 20.
    Pontius, Jr, R.G., Cheuk, M.L.: A generalized cross tabulation matrix to compare soft classified maps at multiple resolutions. Int. J. Geogr. Inf. Sci. 20(1), 1–30 (2006)Google Scholar
  21. 21.
    Verhoeye, J., Robert, D.W.: Sub-pixel mapping of sahelian wetlandsusing multi-temporal SPOT vegetation images. Laboratory of Forest Management and Spatial Information Techniques, Faculty of Agricultural and Applied Biological Sciences, University of Gent, Belgium (2000)Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Indian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Indian Institute of Remote SensingDehradunIndia

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