Digital Operations

  • Ronald Bracewell


Many of the topics already taken up have underlying implications of numerical evaluation, even where the treatment is presented in the form of continuous analysis. In some cases the computational evaluation is straightforward, as with many integrals, but in other cases ideas enter in that are associated with discrete mathematics. Many of these ideas come to the fore the present chapter, which begins with a variety of frequently needed elementary operations, such as smoothing and sharpening digital images, and continues on to introduce morphological operations, such as dilation and erosion, that are prerequisite to handling binary objects and to following the literature of feature recognition in images. Where it helps to clarify numerical procedures, short segments of computer pseudocode have been supplied, and the opportunity has been taken to point out how algebraic notation such as A ∪ B and A ⊕ B translate directly into the simple logical expressions acceptable to computers.


Transfer Function Spatial Frequency Structure Function Digital Representation Laser Printer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. R. N. Bracewell (1963), “Correction for grating response in radio astronomy,” Astrophysical Journal, vol. 137, 175–183.CrossRefGoogle Scholar
  2. J. C. Bresenham (1965), “Algorithm for computer control of digital plotter,” IBM Systems J., 4, pp. 25–30.CrossRefGoogle Scholar
  3. J. C. Bresenham (1977), “A linear algorithm for incremental digital display of circular arcs,” Comm. ACM, vol. 20, pp. 100–106.MATHCrossRefGoogle Scholar
  4. F. Cajori (1929), A History of Mathematical Notations, Open Court Publishing Company, Chicago.MATHGoogle Scholar
  5. E. R. Dougherty AND A. P. N. Plummer (1981), “Thinning algorithms: a critique and a new methodology,” Pattern Recognition, vol. 14, pp. 53–63.MathSciNetCrossRefGoogle Scholar
  6. E. R. Dougherty AND D. Zhao (1992), “Model-based characterization of statistically optimal design for morphological shape recognition algorithms via the hit-and-miss transform,” J. Visual Communication and Image Representation, vol. 3, pp. 147–160.CrossRefGoogle Scholar
  7. J. D Foley, A. van Dam, S. K. Feiner, AND J. F. Hughes (1990), Computer Graphics Principles and Practice, Addison-Wesley, Reading, MA.Google Scholar
  8. B. K. P. Horn AND M.J. Brooks (1989), Shape from Shading, MIT Press, Cambridge, MA.Google Scholar
  9. A. K. Jain (1989), Fundamentals of Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ.MATHGoogle Scholar
  10. A. Lohman (1991), “Object recognition using image algebra,” Angewandte Optik, Annual Report, p. 41, Physikalisches Institutder Universität Erlangen, Nürnberg.Google Scholar
  11. G. Matheron (1975), Random Sets and Integral Geometry, John Wiley, New York.MATHGoogle Scholar
  12. R. Pool (1988), “When crystals collide: grain boundary images,” Science, vol. 30, pp. 1601–1602.CrossRefGoogle Scholar
  13. W. K. Pratt (1978), Digital Image Processing, John Wiley, New York.Google Scholar
  14. A. Rosenfeld AND A. C. Kak (1976), Digital Picture Processing, Academic Press, New York.Google Scholar
  15. F. Y. Spih AND Hong Wu (1991), “Optimization on Euclidean distance transformation using grayscale morphology,” J. Visual Communication and Image Representation, vol. 3, pp. 104–114.Google Scholar
  16. F. Stockton (1963), “Algorithm 162: xymove plotting,” Communications of the ACM, vol. 6, p. 161.CrossRefGoogle Scholar
  17. A. R. Thompson AND R. N. Bracewell (1974), “Interpolation and Fourier transformation of fringe visibilities,” Astronomical Journal, vol. 79, pp. 11–24.CrossRefGoogle Scholar
  18. R. L. Weber (1974), A Random Walk in Science, The Institute of Physics, London.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Ronald Bracewell
    • 1
  1. 1.Stanford UniversityStanfordUSA

Personalised recommendations