Finding rotational symmetries by cyclic string matching

Josep Lladós1, Horst Bunke2, Enric Martí1
1Computer Vision Center - Dep. Informàtica. Universitat Autònoma de Barcelona.
08193 Bellaterra (Barcelona)
2Institut für Informatik und Angewandte Mathematik. University of Bern, Neubrückstr. 10, 
CH-3012 Bern, Switzerland
e-mail: josep@cvc.uab.es, bunke@iam.unibe.ch, enric@cvc.uab.es

Abstract:

Symmetry is an important shape feature. In this paper, a simple and fast method to detect perfect and distorted rotational symmetries of 2D objects is described. The boundary of a shape is polygonally approximated and represented as a string. Rotational symmetries are found by cycling string matching between two identical copies of the shape string. The set of minimum cost edit sequences that transform the shape string to a cyclically shifted version of itself define the rotational symmetry and its order. Finally, a modification of the algorithm is proposed to detect reflectional symmetries.  Some experimental results are presented to show the reliability of the proposed algorithm.

Keywords: Rotational Symmetry, Reflectional Symmetry, String Matching.