Symmetry of fuzzy data

Abstract

Symmetry is usually viewed as a discrete feature: an object is either symmetric or non-symmetric. Following the view that symmetry is a continuous feature, a continuous symmetry measure (CSM) has been developed to evaluate symmetries of shapes and objects. In this paper the authors extend the symmetry measure to evaluate the imperfect symmetry of fuzzy shapes, i.e. shapes with uncertain point localization. The authors find the probability distribution of symmetry values for a given fuzzy shape. Additionally, for every such fuzzy shape, the authors find the most probable symmetric shape.