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Annular filters for binary images.

H M Heijmans1, C Ronse

  • 1Centre for Math. and Comput. Sci., Amsterdam.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 13, 2008
PubMed
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Binary annular filters remove isolated image points using switch pairs. A specific triangular condition ensures idempotence, enabling strong filter creation through composition of annular opening and closing operations.

Area of Science:

  • Digital Image Processing
  • Mathematical Morphology

Background:

  • Isolated points in image foreground and background are challenging for standard filters.
  • Adjacency relations define pixel connectivity, varying for foreground and background.

Purpose of the Study:

  • To introduce and analyze binary annular filters based on switch pairs.
  • To establish conditions for idempotence and strong filter properties.

Main Methods:

  • Representing annular filters using switch pairs derived from foreground and background adjacencies.
  • Analyzing translation-invariant annular filters using structuring elements A and B.
  • Investigating conditions for idempotence and strong filter behavior.

Main Results:

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  • A triangular condition on adjacencies is necessary for annular filter idempotence.
  • Specific conditions on structuring elements A and B define idempotent and strong filters.
  • Strong annular filters can be constructed by composing annular opening and closing.

    • Conclusions:

    • Binary annular filters offer a flexible framework for noise removal in digital images.
    • The switch pair representation provides a unified approach to annular filter design.
    • Idempotence and strong filter properties are achieved through specific adjacency and structuring element constraints.