Skip to main content

Fast and Adaptive Low-Pass Whitening Filters for Natural Images

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4233))

Abstract

A fast and simple solution was suggested to reduce the inter-pixels correlations in natural images, of which the power spectra roughly fell off with the increasing spatial frequency f according to a power law; but the 1/f exponent, α, was different from image to image. The essential of the proposed method was to flatten the decreasing power spectrum of each image by using an adaptive low-pass and whitening filter. The act of low-pass filtering was just to reduce the effects of noise usually took place in the high frequencies. The act of whitening filtering was a special processing, which was to attenuate the low frequencies and boost the high frequencies so as to yield a roughly flat power spectrum across all spatial frequencies. The suggested method was computationally more economical than the geometric covariance matrix based PCA method. Meanwhile, the performance degradations accompanied with the computational economy improvement were fairly insignificant.

Supported by the National Natural Science Foundation of China under Grant Nos. 60373029 and the National Research Foundation for the Doctoral Program of Higher Education of China under Grant Nos. 20050004001.

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

Buying options

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 PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Olshausen, B.A., Field, D.J.: Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1? Visual Research 37, 11–25 (1997)

    Google Scholar 

  2. Amari, S.: Natural Gradient Works Efficiently in Learning. Neural Computation 10, 251–276 (1998)

    Article  Google Scholar 

  3. Bell, A., Sejnowski, T.: The Independent Components of Natural Scenes Are Edge Filters. Vision Research 37, 3327–3338 (1997)

    Article  Google Scholar 

  4. van Hateren, J.H., van der Schaaf, A.: Independent Component Filters of Natural Images Compared with Simple Cells in Primary Visual Cortex. Proc. Royal Society ser. B 265, 359–366 (1998)

    Article  Google Scholar 

  5. Hyvärinen, A., Oja, E.: Independent Component Analysis: Algorithms and Applications. Neural Networks 13, 411–430 (2000)

    Article  Google Scholar 

  6. Olshausen, B.A., Field, D.J.: Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images. Nature 381, 607–609 (1996)

    Article  Google Scholar 

  7. Olshausen, B.A.: Principles of Image Representation in Visual Cortex. In: Chalupa, L.M., Werner, J.S. (eds.) The Visual Neurosciences, MIT Press, Cambridge (2003)

    Google Scholar 

  8. Lewicki, M.S., Sejnowski, T.J.: Learning Overcomplete Representations. Neural Computation 12, 337–365 (2000)

    Article  Google Scholar 

  9. Camelio, J.A., Hu, S.J., Marin, S.P.: Compliant Assembly Variation Analysis Using Component Geometric Covariance. Journal of Manufacturing Science and Engineering 126, 355–360 (2004)

    Article  Google Scholar 

  10. Jolliffe, I.: Principal Component Analysis. Springer, New York (1986)

    Google Scholar 

  11. Basilevsky, A.: Statistical Factor Analysis and Related Methods: Theory and Applications. Wiley, New York (1994)

    Book  MATH  Google Scholar 

  12. Schaaf, A., Hateren, J.H.: Modelling the Power Spectrum of Natural Images: Statistics and Information. Vision Research 36, 2759–2770 (1996)

    Article  Google Scholar 

  13. Simoncelli, E.P., Olshausen, B.A.: Natrual Image Statistics and Neural Representation. NeuroSecience, Annual Review 24, 1193–1216 (2001)

    Article  Google Scholar 

  14. Dan, Y., Atick, J.J., Reid, R.C.: Efficient Coding of Natural Scenes in the Lateral Geniculate Nucleus: Experimental Test of a Computational Theory. Neuroscience 16, 3351–3362 (1996)

    Google Scholar 

  15. Field, D.J.: Relations between the Statistics of Natural Images and the Response Properties of Cortical Cells. Optical Society of America 4, 2379–2394 (1987)

    Article  Google Scholar 

  16. Olshausen, B.A.: How Close We Are to Understand V1? Neural Computation 17, 1665–1699 (2005)

    Article  MATH  Google Scholar 

  17. Atick, J.J., Li, Z., Redlich, A.N.: Understanding Retinal Color Coding from First Principles. Neural computation 1, 559–572 (1992)

    Article  Google Scholar 

  18. Field, D.J.: What Is the Goal of Sensory Coding? Neural Computation 6, 559–601 (1994)

    Article  Google Scholar 

  19. Massih, H., Pearl, J.: Comparison of the Cosine and Fourier Transform of Markov-1 Signals. IEEE Trans. on Acoustics, Speech, and Signal Processing, 428–429 (1976)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liao, LZ., Luo, SW., Tian, M., Zhao, LW. (2006). Fast and Adaptive Low-Pass Whitening Filters for Natural Images. In: King, I., Wang, J., Chan, LW., Wang, D. (eds) Neural Information Processing. ICONIP 2006. Lecture Notes in Computer Science, vol 4233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893257_38

Download citation

  • DOI: https://doi.org/10.1007/11893257_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46481-5

  • Online ISBN: 978-3-540-46482-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics