Mathematics in Computer Science

, Volume 10, Issue 1, pp 179–205

Detecting Curves of Symmetry in Images Via Hough Transform

  • Giorgio Ricca
  • Mauro C. Beltrametti
  • Anna Maria Massone
Article

Abstract

The Hough transform is a standard pattern recognition technique introduced between the 1960s and the 1970s for the detection of straight lines, circles, and ellipses with several applications including the detection of symmetries in images. Recently, based on algebraic geometry arguments, the procedure has been extended to the automated recognition of special classes of algebraic plane curves. This allows us to detect curves of symmetry present in images, that is, curves that recognize midpoints maps of various shapes extracted by an ad hoc symmetry algorithm, here proposed. Further, in the case of straight lines, the detection of lines of symmetry allows us, by a pre-processing step of the image, to improve the efficiency of the recognition algorithm on which the Hough transform technique is founded, without loss of generality and additional computational costs.

Keywords

Symmetry detection Algebraic plane curves Pattern recognition Hough transform 

Mathematics Subject Classification

Primary 68D18 68U10 Secondary 14H50 92C50 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Giorgio Ricca
    • 1
  • Mauro C. Beltrametti
    • 1
  • Anna Maria Massone
    • 2
  1. 1.Dipartimento di MatematicaUniversità di GenovaGenoaItaly
  2. 2.CNR-SPINGenoaItaly

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