Discrete Pulse Transform of Images

  • Roumen Anguelov
  • Inger Fabris-Rotelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5099)


The Discrete Pulse Transform (DPT) of images is defined by using a new class of LULU operators on multidimensional arrays. This transform generalizes the DPT of sequences and replicates its essential properties, e.g. total variation preservation. Furthermore, the discrete pulses in the transform capture the contrast in the original image on the boundary of their supports. Since images are perceived via the contrast between neighbour pixels, the DPT may be a convenient new tool for image analysis.


LULU discrete pulse transform total variation preservation 


  1. 1.
    Anguelov, R., Plaskitt, I.: A Class of LULU Operators on Multi-Dimensional Arrays, Technical Report UPWT2007/22, University of Pretoria (2008),
  2. 2.
    Acton, S.T., Mukherjee, D.P.: Scale Space Classification Using Area Morphology. IEEE TRansactions on Image Processing 9(4) (2000)Google Scholar
  3. 3.
    Chambolle, A., Lions, P.-L.: Image recovery via total variation minimization and related problems. Numerische Mathematik 76, 167–188 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    du Toit, J.P.: The Discrete Pulse Transform and Applications, Masters Thesis, Univeristy of Stellenbosch (2007)Google Scholar
  5. 5.
    Epp, S.S.: Discrete Mathematics with Applications. International Thomson Publishing (1995)Google Scholar
  6. 6.
    Laurie, D.P., Rohwer, C.H.: The discrete pulse transform. SIAM J. Math. Anal. 38(3) (2007)Google Scholar
  7. 7.
    Matheron, G.: Filters and lattices, in Image Analysis and Mathematical Morphology. In: Serra, J. (ed.) Theoretical Advances, ch. 6, vol. II, pp. 115–140. Academic Press, London (1988)Google Scholar
  8. 8.
    Rohwer, C.H.: Nonlinear Smoothing and Multiresolution Analysis, Birkhäuser (2000)Google Scholar
  9. 9.
    Rohwer, C.H.: Variation reduction and LULU-smoothing. Quaestiones Mathematicae 25, 163–176 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Rohwer, C.H.: Fully trend preserving operators. Quaestiones Mathematicae 27, 217–230 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Rohwer, C.H., Wild, M.: Natural Alternatives for One Dimensional Median Filtering. Quaestiones Mathematicae 25, 135–162 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Rohwer, C.H., Wild, M.: LULU Theory, Idempotent Stack Filters, and the Mathematics of Vision of Marr. Advances in imaging and electron physics 146, 57–162 (2007)CrossRefGoogle Scholar
  13. 13.
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  14. 14.
    Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)Google Scholar
  15. 15.
    Serra, J.: Image Analysis and Mathematical Morphology. In: Serra, J. (ed.) Theoretical Advances, vol. II. Academic Press, London (1988)Google Scholar
  16. 16.
    Serra, J.: A lattice approach to image segmentation. Journal of Mathematical Imaging and Vision 24, 83–130 (2006)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Soille, P.: Morphological Image Analysis. Springer, Heidelberg (1999)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roumen Anguelov
    • 1
  • Inger Fabris-Rotelli
    • 1
  1. 1.Department of Mathematics and Applied MathematicsUniversity of PretoriaPretoriaSouth Africa

Personalised recommendations