Skip to main content
SpringerLink
Log in

Solving the Inverse Problem of Image Zooming Using “Self-Examples”

  • Conference paper
Image Analysis and Recognition (ICIAR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4633))

Included in the following conference series:

Abstract

In this paper we present a novel single-frame image zooming technique based on so-called “self-examples”. Our method combines the ideas of fractal-based image zooming, example-based zooming, and nonlocal-means image denoising in a consistent and improved framework. In Bayesian terms, this example-based zooming technique targets the MMSE estimate by learning the posterior directly from examples taken from the image itself at a different scale, similar to fractal-based techniques. The examples are weighted according to a scheme introduced by Buades et al. to perform nonlocal-means image denoising. Finally, various computational issues are addressed and some results of this image zooming method applied to natural images are presented.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. Alexander, S.K.: Multiscale methods in image modelling and image processing, Ph.D. Thesis, Dept. of Applied Mathematics, University of Waterloo (2005)

    Google Scholar 

  2. Alexander, S.K., Vrscay, E.R., Tsurumi, S.: An examination of the statistical properties of domain-range block matching in fractal image coding (preprint 2007)

    Google Scholar 

  3. Baker, S., Kanade, T.: Limits on super-resolution and how to break them. IEEE Trans. Patt. Analysis and Mach. Intel. 24(9), 1167–1183 (2002)

    Article  Google Scholar 

  4. Barnsley, M.F.: Fractals Everywhere. Academic Press, New York (1988)

    MATH  Google Scholar 

  5. Bone, D.J.: Orthonormal fractal image encoding using overlapping blocks. Fractals 5(Suppl. Issue), 187–199 (1997)

    Article  MATH  Google Scholar 

  6. Buades, A., Coll, B., Morel, J.M.: A nonlocal algorithm for image denoising. In: CVPR. IEEE International conference on Computer Vision and Pattern Recognition, San-Diego, California, June 20-25, 2005, vol. 2, pp. 60–65. IEEE Computer Society Press, Los Alamitos (2005)

    Google Scholar 

  7. Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. SIAM Journal on Multiscale Modeling and Simulation (MMS) 4(2), 490–530 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chaudhuri, S.: Super-resolution imaging. Kluwer, Boston, MA (2001)

    Google Scholar 

  9. Criminisi, A., Perez, P., Toyama, K.: Region filling and object removal by exemplar-based image inpainting. IEEE Trans. on Image Proc. 13(9), 1200–1212 (2004)

    Article  Google Scholar 

  10. Datsenko, D., Elad, M.: Example-based single document image superresolution: A global MAP approach with outlier rejection. The Journal of Mathematical Signal Processing (2006) (to appear)

    Google Scholar 

  11. Donoho, D.L, Johnstone, I.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3), 425–455 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ebrahimi, M., Vrscay, E.R.: Fractal image coding as projections onto convex sets. In: Campilho, A., Kamel, M. (eds.) ICIAR 2006. LNCS, vol. 4141, pp. 493–506. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Ebrahimi, M., Vrscay, E.R.: Regularized fractal image decoding. In: Proceedings of CCECE 2006, Ottawa, Canada, May 7-10, 2006, pp. 1933–1938 (2006)

    Google Scholar 

  14. Efros, A.A., Leung, T.K.: Texture synthesis by non-parametric sampling. In: ICCV. IEEE International Conference on Computer Vision, Corfu, Greece, September 20-25, 1999, pp. 1033–1038 (1999)

    Google Scholar 

  15. Elad, M., Datsenko, D.: Example-Based Regularization Deployed to Super-Resolution Reconstruction of a Single Image. The Computer Journal (to appear)

    Google Scholar 

  16. Elad, M., Feuer, A.: Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images. IEEE Trans. on Image Proc. 6(12), 1646–1658 (1997)

    Article  Google Scholar 

  17. Fisher, Y. (ed.): Fractal image compression, theory and application. Springer, New York (1995)

    Google Scholar 

  18. Forte, B., Vrscay, E.R.: Theory of generalized fractal transforms. In: Fisher, Y. (ed.) Fractal image encoding and analysis, Springer, Heidelberg (1998)

    Google Scholar 

  19. Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning low-level vision. Int. Journal Of Computer Vision 40(1), 25–47 (2000)

    Article  MATH  Google Scholar 

  20. Freeman, W.T., Jones, T.R., Pasztor, E.C.: Example-based super-resolution. IEEE Comp. Graphics And Appl. 22(2), 56–65 (2002)

    Article  Google Scholar 

  21. Gharavi-Al., M., DeNardo, R., Tenda, Y., Huang, T.S.: Resolution enhancement of images using fractal coding. In: Visual Communications and Image Processing, SPIE Proceedings, San Jose, CA, vol. 3024, pp. 1089–1100 (1997)

    Google Scholar 

  22. Ghazel, M., Freeman, G., Vrscay, E.R.: Fractal image denoising. IEEE Trans. on Image Proc. 12(12), 1560–1578 (2003)

    Article  Google Scholar 

  23. Haber, E., Tenorio, L.: Learning regularization functionals. Inverse Problems 19, 611–626 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  24. Ho, H., Cham, W.: Attractor Image Coding using Lapped Partitioned Iterated Function Systems. In: ICASSP’97. IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 4, p. 2917 (1997)

    Google Scholar 

  25. Lu, N.: Fractal Imaging. Academic Press, London (1997)

    MATH  Google Scholar 

  26. Nakagaki, R., Katsaggelos, A.K.: VQ-based blind image restoration algorithm. IEEE Trans. On Image Proc. 12(9), 1044–1053 (2003)

    Article  Google Scholar 

  27. Polidori, E., Dugelay, J.-L.: Zooming using iterated function systems. Fractals 5(Suppl. Issue), 111–123 (1997)

    Article  Google Scholar 

  28. Roth, S., Black, M.J.: Fields of experts: A framework for learning image priors. In: CVPR. IEEE Conference on Computer Vision and Pattern Recog, San-Diego, California, June 20-25, 2005, vol. 2, pp. 860–867 (2005)

    Google Scholar 

  29. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  30. Tikhonov, A.N., Arsenin, V.A.: Solution of Ill-posed Problems. Winston & Sons, Washington (1977)

    Google Scholar 

  31. Vrscay, E.R.: A generalized class of fractal-wavelet transforms for image representation and compression. Can. J. Elect. Comp. Eng. 23(1-2), 69–84 (1998)

    Google Scholar 

  32. Wei, L.Y., Levoy, M.: Fast texture synthesis using tree-structured vector quantization. In: Proc. of SIGGRAPH, New Oleans, Louisiana, pp. 479–488 (2000)

    Google Scholar 

  33. Weickert, J.: Anisotropic Diffusion in Image Processing, Teubner, Stuttgart. ECMI Series (1998)

    Google Scholar 

  34. Xu, W., Fussell, D.: IFS coding with multiple DC terms and domain blocks. Citeseer article 185324, available at: http://citeseer.ist.psu.edu/185324.html

  35. Zhu, S.C., Mumford, D.: Prior learning and Gibbs reaction-diffusion. IEEE Trans. on Patt. Analysis and Machine, Intel. 19(11), 1236–1250 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Mehran Ebrahimi & Edward R. Vrscay

Authors
  1. Mehran Ebrahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edward R. Vrscay
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Mohamed Kamel Aurélio Campilho

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ebrahimi, M., Vrscay, E.R. (2007). Solving the Inverse Problem of Image Zooming Using “Self-Examples”. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2007. Lecture Notes in Computer Science, vol 4633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74260-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74260-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74258-6

  • Online ISBN: 978-3-540-74260-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation