Approximate reflectional symmetries of fuzzy objects with an application in model-based object recognition

This paper is devoted to the study of reflectional symmetries of fuzzy objects. We introduce a symmetry measure which defines the degree of symmetry of an object with respect to a given plane. It is computed by measuring the similarity between the original object and its reflection. The choice of an appropriate measure of comparison is based on the desired properties of the symmetry measure. Then, an algorithm for computing the symmetry plane of fuzzy objects is proposed. This is done using an optimization technique in the space of plane parameters. Finally, we illustrate our approach with an application where the symmetry measure is used as an attribute in graph matching for model-based object recognition.