Skip to main content
SpringerLink
Log in

Image Reconstruction from Gabor Magnitudes

  • Conference paper
  • First Online:
Biologically Motivated Computer Vision (BMCV 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2525))

Included in the following conference series:

Abstract

We present an analysis of the representation of images as the magnitudes of their transform with complex-valued Gabor wavelets. Such a representation is very useful for image understanding purposes and serves as a model for an early stage of human visual processing. We show that if the sampling of the wavelet transform is appropriate then the reconstruction from the magnitudes is unique up to the sign for almost all images. We also present an iterative reconstruction algorithm derived from the ideas of the proof, which yields very good reconstruction up to the sign and minor numerical errors in the very low frequencies.

This work has been supported by grants from BMBF, ONR and ARO.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. John G. Daugman. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. Journal of the Optical Society of America A, 2(7):1362–1373, 1985.

    Article  Google Scholar 

  2. Benoît Duc, Stefan Fischer, and Josef Bigün. Face authentication with gabor information on deformable graphs. IEEE Transactions on Image Processing, 8(4):504–516, 1999.

    Article  Google Scholar 

  3. I. Fogel and Dov Sagi. Gabor filters as texture discriminator. Biological Cybernetics, 61:103–113, 1989.

    Article  Google Scholar 

  4. A. Grossmann and J. Morlet. Decomposition of Hardy functions into square integrable wavelets of constant shape. SIAM Journal of Mathematical Analysis, 15(4):723–736, July 1984.

    Article  MathSciNet  MATH  Google Scholar 

  5. Monson H. Hayes. The Reconstruction of a Multidimensional Sequence from the Phase or Magnitude of Its Fourier Transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, 30(2):140–154, April 1982.

    Article  MathSciNet  MATH  Google Scholar 

  6. Monson H. Hayes and James H. McClellan. Reducible Polynomials in More Than One Variable. Proceedings of the IEEE, 70(2):197–198, February 1982.

    Google Scholar 

  7. J.P. Jones and L.A. Palmer. An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex. Journal of Neurophysiology, 58(6):1233–1258, 1987.

    Google Scholar 

  8. Gerald Kaiser. A Friendly Guide to Wavelets. Birkhäuser, 1994.

    Google Scholar 

  9. Martin Lades, Jan C. Vorbrüggen, Joachim Buhmann, Jörg Lange, Christoph von der Malsburg, Rolf P. Würtz, and Wolfgang Konen. Distortion invariant object recognition in the dynamic link architecture. IEEE Transactions on Computers, 42(3):300–311, 1993.

    Article  Google Scholar 

  10. R. Murenzi. Wavelet Transforms Associated to the n-Dimensional Euclidean Group with Dilations: Signal in More Than One Dimension. In J. M. Combes, A. Grossmann, and P. Tchamitchian, editors, Wavelets—Time-Frequency Methods and Phase Space, pages 239–246. Springer, 1989.

    Google Scholar 

  11. Alan V. Oppenheim and Jae S. Lim. The Importance of Phase in Signals. Proceedings of the IEEE, 96(5):529–541, May 1981.

    Google Scholar 

  12. Daniel A. Pollen and Steven F. Ronner. Visual cortical neurons as localized spatial frequency filters. IEEE Transactions on Systems, Man, and Cybernetics, 13(5):907–916, 1983.

    Article  Google Scholar 

  13. Eero P. Simoncelli, William T. Freeman, Edward H. Adelson, and David J. Heeger. Shiftable Multiscale Transforms. IEEE Transactions on Information Theory, 38(2):587–607, March 1992.

    Article  MathSciNet  Google Scholar 

  14. Jochen Triesch and Christoph von der Malsburg. Robust classification of hand postures against complex backgrounds. In Proceedings of the Second International Conference on Automatic Face and Gesture Recognition, pages 170–175. IEEE Computer Society Press, 1996.

    Google Scholar 

  15. Sharon Urieli, Moshe Porat, and Nir Cohen. Optimal reconstruction of images from localized phase. IEEE Trans. Image Processing, 7(6):838–853, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  16. Christoph von der Malsburg and Ladan Shams. Role of complex cells in object recognition. Nature Neuroscience, 2001. Submitted.

    Google Scholar 

  17. Laurenz Wiskott, Jean-Marc Fellous, Norbert Krüger, and Christoph von der Malsburg. Face recognition by elastic bunch graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(7):775–779, 1997.

    Article  Google Scholar 

  18. Xing Wu and Bir Bhanu. Gabor Wavelet Representation for 3-D Object Recognition. IEEE Transactions on Image Processing, 6(1):47–64, January 1997.

    Article  Google Scholar 

  19. Ingo J. Wundrich, Christoph von der Malsburg, and Rolf P. Würtz. Image representation by the magnitude of the discrete Gabor wavelet transform. IEEE Transactions on Image Processing, 1999. In revision.

    Google Scholar 

  20. Rolf P. Würtz. Object recognition robust under translations, deformations and changes in background. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(7):769–775, 1997.

    Article  Google Scholar 

  21. Rolf P. Würtz and Tino Lourens. Corner detection in color images through a multiscale combination of end-stopped cortical cells. Image and Vision Computing, 18(6–7):531–541, 2000.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Neuroinformatik, Ruhr-Universität Bochum, D-44780, Bochum, Germany

    Ingo J. Wundrich, Christoph von der Malsburg & Rolf P. Würtz

  2. Laboratory for Computational and Biological Vision, University of Southern California, Los Angeles, USA

    Christoph von der Malsburg

Authors
  1. Ingo J. Wundrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christoph von der Malsburg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rolf P. Würtz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Max Planck Institute for Biological Cybernetics, Spemannstraße 38, 72076, Tübingen, Germany

    Heinrich H. Bülthoff  & Christian Wallraven  & 

  2. Department of Computer Science and Engineering, Korea University, Anam-dong, Seongbuk-ku, 136-701, Seoul, Korea

    Seong-Whan Lee

  3. Department of Brain and Cognitive Sciences, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 45 Carleton Street, 02142, Cambridge, MA, USA

    Tomaso A. Poggio

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wundrich, I.J., von der Malsburg, C., Würtz, R.P. (2002). Image Reconstruction from Gabor Magnitudes. In: Bülthoff, H.H., Wallraven, C., Lee, SW., Poggio, T.A. (eds) Biologically Motivated Computer Vision. BMCV 2002. Lecture Notes in Computer Science, vol 2525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36181-2_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-36181-2_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00174-4

  • Online ISBN: 978-3-540-36181-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation