Discrete Morphology with Line Structuring Elements

  • C. L. Luengo Hendriks
  • L. J. van Vliet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2756)

Abstract

Discrete morphological operations with line segments are notoriously hard to implement. In this paper we study different possible implementations of the line structuring element, compare them, and examine their rotation and translation invariance in the continuous domain. That is, we are interested in obtaining a morphological operator that is invariant to rotations and translations of the image before sampling.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bresenham, J.E.: Algorithm for computer control of a digital plotter. IBS Systems Journal 4(1), 25–30 (1965)CrossRefGoogle Scholar
  2. 2.
    Chanussot, J., Lambert, P.: An application of mathematical morphology to road network extractions on SAR images. In: Mathematical Morphology and its Applications to Image and Signal Processing, Dordrecht, pp. 399–406. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  3. 3.
    Jones, R., Soille, P.: Periodic lines: Definition, cascades, and application to granulometries. Pattern Recognition Letters 17(10), 1057–1063 (1996)CrossRefGoogle Scholar
  4. 4.
    Keys, R.G.: Cubic convolution interpolation for digital image processing. IEEE Transactions on Acoustics, Speech, and Signal Processing 29(6), 1153–1160 (1981)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Luengo Hendriks, C.L., van Vliet, L.J.: A rotation-invariant morphology for shape analysis of anisotropic objects and structures. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 378–387. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)MATHGoogle Scholar
  7. 7.
    Soille, P., Breen, E.J., Jones, R.: Recursive implementation of erosions and dilations along discrete lines at arbitrary angles. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(5), 562–567 (1996)CrossRefGoogle Scholar
  8. 8.
    Soille, P., Talbot, H.: Directional morphological filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(11), 1313–1329 (2001)CrossRefGoogle Scholar
  9. 9.
    Tuzikov, A., Soille, P., Jeulin, D., Bruneel, H., Vermeulen, M.: Extraction of grid patterns on stamped metal sheets using mathematical morphology. In: Proceedings of the 11th International Conference on Pattern Recognition, The Hague, vol. 1, pp. 425–428 (1992)Google Scholar
  10. 10.
    van Herk, M.: A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernels. Pattern Recognition Letters 13, 517–521 (1992)CrossRefGoogle Scholar
  11. 11.
    van Vliet, L.J.: Grey-Scale Measurements in Multi-Dimensional Digitized Images. PhD thesis, Pattern Recognition Group, Delft University of Technology, Delft (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • C. L. Luengo Hendriks
    • 1
  • L. J. van Vliet
    • 1
  1. 1.Pattern Recognition GroupDelft University of TechnologyDelftThe Netherlands

Personalised recommendations