<title>Symmetry measure computation for binary images</title>

Abstract

This report is devoted to developing algorithms of symmetry measure computation for binary images. We consider central, rotation and reflection symmetry measures. The algorithms are based either on contour representation of objects or on corresponding symmetrization transformations. Boundary representations based on a centroidal profile as well as on an equi- angular signature are applied. Using centroidal profile and signature representations we propose several simple and fast algorithms for measure computation of convex images. These algorithms are also valid for the evaluation of symmetry measures of nonconvex images. The second group of algorithms is based on a set symmetrization. We apply the corresponding symmetrization transformations via Minkowski addition (difference body, Blaschke symmetrization, etc.). Then the ratio of areas of original and symmetrical images defines an evaluation of symmetry measures. Kovner-Besicovitch symmetry measure is also investigated.