In this paper, we present a statistical approach to spectral unmixing with unknown endmember spectra and unknown illuminant power spectrum. The method presented here is quite general in nature, being applicable to settings in which sub-pixel information is required. The method is formulated as a simultaneous process of illuminant power spectrum prediction and basis material reflectance decomposition via a statistical approach based upon deterministic annealing and the maximum entropy principle. As a result, the method presented here is related to soft clustering tasks with a strategy for avoiding local minima. Furthermore, the final endmembers depend on the similarity between pixel reflectance spectra. Hence, the method does not require a preset number of material clusters or spectral signatures as input. We show the utility of our method on trichromatic and hyperspectral imagery and compare our results to those yielded by alternatives elsewhere in the literature.


Multispectral Image Maximum Entropy Principle Spectral Angle Mapper Hyperspectral Imagery Spectral Unmixing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Lennon, M., Mercier, G., Mouchot, M.C., Hubert-moy, L.: Spectral unmixing of hyperspectral images with the independent component analysis and wavelet packets. In: Proc. of the International Geoscience and Remote Sensing Symposium (2001)Google Scholar
  2. 2.
    Stainvas, I., Lowe, D.: A generative model for separating illumination and reflectance from images. Journal of Machine Learning Research 4(7-8), 1499–1519 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Klinker, G.J., Shafer, S.A., Kanade, T.: A physical approach to color image understanding. Int. J. Comput. Vision 4(1), 7–38 (1990)CrossRefGoogle Scholar
  4. 4.
    Tajima, J.: Illumination chromaticity estimation based on dichromatic reflection model and imperfect segmentation. In: Trémeau, A., Schettini, R., Tominaga, S. (eds.) CCIW 2009. LNCS, vol. 5646, pp. 51–61. Springer, Heidelberg (2009)Google Scholar
  5. 5.
    Li, C., Li, F., Kao, C., Xu, C.: Image Segmentation with Simultaneous Illumination and Reflectance Estimation: An Energy Minimization Approach. In: ICCV 2009: Proceedings of the Twelfth IEEE International Conference on Computer Vision (2009)Google Scholar
  6. 6.
    Bergman, M.: Some unmixing problems and algorithms in spectroscopy and hyperspectral imaging. In: Proc. of the 35th Applied Imagery and Pattern Recognition Workshop (2006)Google Scholar
  7. 7.
    Fu, Z., Tan, R., Caelli, T.: Specular free spectral imaging using orthogonal subspace projection. In: Proc. Intl. Conf. Pattern Recognition, vol. 1, pp. 812–815 (2006)Google Scholar
  8. 8.
    Shafer, S.A.: Using color to separate reflection components. Color Research and Applications 10(4), 210–218 (1985)CrossRefGoogle Scholar
  9. 9.
    Jaynes, E.: On the rationale of maximum-entropy methods. In: Proceedings of the IEEE, 70(9), 939–952 (1982)Google Scholar
  10. 10.
    Jaynes, E.T.: Information Theory and Statistical Mechanics. Phys. Rev. 106(4), 620–630 (1957)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Finlayson, G.D., Schaefer, G.: Convex and Non-convex Illuminant Constraints for Dichromatic Colour Constancy. In: CVPR, vol. 1, pp. 598–604 (2001)Google Scholar
  12. 12.
    Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Barnard, K., Martin, L., Coath, A., Funt, B.V.: A comparison of computational color constancy Algorithms – Part II: Experiments with image data. IEEE Transactions on Image Processing 11(9), 985–996 (2002)CrossRefGoogle Scholar
  14. 14.
    Buchsbaum, G.: A Spatial Processor Model for Object Color Perception. Journal of The Franklin Institute 310, 1–26 (1980)CrossRefGoogle Scholar
  15. 15.
    McCann, J.J., Hall, J.A., Land, E.H.: Color mondrian experiments: the study of average spectral distributions. Journal of Optical Society America 67, 1380 (1977)Google Scholar
  16. 16.
    Finlayson, G.D., Trezzi, E.: Shades of gray and colour constancy. In: Color Imaging Conference, pp. 37–41 (2004)Google Scholar
  17. 17.
    van de Weijer, J., Gevers, T., Gijsenij, A.: Edge-Based Color Constancy. IEEE Transactions on Image Processing 16(9), 2207–2214 (2007)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Kruse, F.A., Lefkoff, A.B., Boardman, J.B., Heidebrecht, K.B., Shapiro, A.T., Barloon, P.J., Goetz, A.F.H.: The Spectral Image Processing System (SIPS) - Interactive Visualization and Analysis of Imaging Spectrometer Data. Remote Sensing of Environment, Special issue on AVIRIS 44(2), 145–163 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Cong Phuoc Huynh
    • 1
  • Antonio Robles-Kelly
    • 1
    • 2
  1. 1.School of EngineeringAustralian National UniversityCanberraAustralia
  2. 2.National ICT Australia (NICTA)CanberraAustralia

Personalised recommendations