A normalized parameter for similarity/dissimilarity characterization of sequences

Abstract

We propose a normalized parameter for characterization of similarity/dissimilarity of two sequences providing a smoothly varying measure for varying symmetry score. Such a parameter can be used for analysis of experimental data and fitting to a theoretical model, mirror symmetry estimation with respect to a selected or presumed symmetry axis, in particular, in symmetry detection applications where the selected symmetry parameters must be evaluated multiple times. We compare the proposed parameter, as well as several of the well-known distance and similarity measures, on an ensemble of template functions morphing continuously from symmetric to antisymmetric shape. This comparison allows to evaluate different similarity and symmetry measures in a more controlled and systematic setting than a simple visual estimation in sample images.