The S-kernel and a symmetry measure based on correlation

Abstract

Symmetry is an important feature in vision. Several detectors or transforms have been proposed. In this paper we concentrate on a measure of symmetry. Given a transform S, the kernel SK of a pattern is defined as the maximal included symmetric sub-set of this pattern. The maximum being taken over all directions, the problem arises to know which center to use. Then the optimal direction triggers the shift problem too. We prove that, in any direction, the optimal axis corresponds to the maximal correlation of a pattern with its nipped version. That leads to an efficient algorithm. As for the measure we compute a modified difference between respective surfaces of a pattern and its kernel. A series of experiments supports actual algorithm validation. © Springer-Verlag Berlin Heidelberg 2005.