Edge Detection by Sliding Wedgelets

  • Agnieszka Lisowska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6753)

Abstract

In this paper the sliding wedgelet algorithm is presented together with its application to edge detection. The proposed method combines two theories: image filtering and geometrical edge detection. The algorithm works in the way that an image is filtered by a sliding window of different scales. Within the window the wedgelet is computed by the use of the fast moments-based method. Depending on the difference between two wedgelet parameters the edge is drawn. In effect, edges are detected geometrically and multiscale. The computational complexity of the sliding wedgelet algorithm is O(N2) for an image of size N ×N pixels. The experiments confirmed the effectiveness of the proposed method, also in the application to noisy images.

Keywords

sliding wedgelets edge detection moments multiresolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Deans, S.R.: The Radon Transform and Some of Its Applications. John Wiley and Sons, New York (1983)MATHGoogle Scholar
  2. 2.
    Canny, J.: Computational Approach To Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 679–714 (1986)CrossRefGoogle Scholar
  3. 3.
    Gonzalez, R., Woods, R.: Digital Image Processing. Addison-Wesley, Reading (1992)Google Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Meyer, F.G., Coifman, R.R.: Brushlets: A Tool for Directional Image Analysis and Image Compression. Applied and Computational Harmonic Analysis 4, 147–187 (1997)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Donoho, D.L.: Wedgelets: Nearly-minimax estimation of edges. Annals of Statistics 27, 859–897 (1999)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Humphreys, G.W. (ed.): Case Studies in the Neuropsychology of Vision. Psychology Press, UK (1999)Google Scholar
  8. 8.
    Donoho, D.L., Huo, X.: Beamlet Pyramids: A New Form of Multiresolution Analysis, Suited for Extracting Lines, Curves and Objects from Very Noisy Image Data. In: Proceedings of SPIE, vol. 4119 (2000)Google Scholar
  9. 9.
    Demaret, L., Friedrich, F., Führ, H., Szygowski, T.: Multiscale Wedgelet Denoising Algorithms. In: Proceedings of SPIE, vol. 5914, pp. 1–12 (2005)Google Scholar
  10. 10.
    Labate, D., Lim, W., Kutyniok, G., Weiss, G.: Sparse Multidimensional Representation Using Shearlets. In: Proceedings of the SPIE, vol. 5914, pp. 254–262 (2005)Google Scholar
  11. 11.
    Mallat, S., Pennec, E.: Sparse Geometric Image Representation with Bandelets. IEEE Transactions on Image Processing 14(4), 423–438 (2005)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Popovici, I., Withers, W.D.: Custom-Built Moments for Edge Location. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(4), 637–642 (2006)CrossRefGoogle Scholar
  13. 13.
    Lisowska, A.: Geometrical Multiscale Noise Resistant Method of Edge Detection. In: Campilho, A., Kamel, M.S. (eds.) ICIAR 2008. LNCS, vol. 5112, pp. 182–191. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Lisowska, A.: Multiscale Moments-Based Edge Detection. In: Proceedings of EUROCON 2009 Conference, St.Petersburg, Russia, pp. 1414–1419 (2009)Google Scholar
  15. 15.
    Mallat, S.: Geometrical Grouplets. Applied and Computational Harmonic Analysis 26(2), 161–180 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Lisowska, A.: Moments-Based Fast Wedgelet Transform. Journal on Mathematical Imaging and Vision 39(2), 180–192 (2011)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Agnieszka Lisowska
    • 1
  1. 1.Institute of Computer ScienceUniversity of SilesiaSosnowiecPoland

Personalised recommendations