Decomposition of geometric-shaped structuring elements using morphological transformations on binary images

Frank Y. Shih, Hong Wu

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Mathematical morphology which is based on geometric shape, provides an approach to the processing and analysis of digital images. Several widely-used geometric-shaped structuring elements can be used to explore the shape characteristics of an object. A unified technique is presented to simplify the decomposition of various types of big geometric-shaped structuring elements into dilations of smaller structuring components by the use of a mathematical transformation. Hence, the desired morphological erosion and dilation are equivalent to a simple inverse transformation over the result of operations on the transformed decomposable structuring elements. A strategy is also presented to decompose a large cyclic cosine structuring element. The technique of decomposing a two-dimensional (2D) convex structuring element into one-dimensional (1D) ones is also developed.

Original languageEnglish (US)
Pages (from-to)1097-1106
Number of pages10
JournalPattern Recognition
Issue number10
StatePublished - Oct 1992

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


  • Decomposition
  • Distance transformation
  • Geometry
  • Mathematical morphology
  • Structuring element


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