FUZZY SIMILARITIES TO COMPARE DEFORMED IMAGES

Abstract

We use the concept of fuzzy similarity to compare the objects of a free image algebra (a set of objects which a group is acting on). In particular, we study those fuzzy similarities that are preserved by the action of the group. Later we consider a deformation mechanism of the image algebra and trackle the problem of comparing deformed images. For that purpose, we characterize those deformation mechanisms that are equivalent to the induced action from a subgroup of the group of deformations. In that case, by using techniques from group representation theory, we extend any fuzzy similarity defined on the image algebra to a fuzzy similarity defined on the whole space of deformed images. Moreover, we prove that the invariance of the similarity with respect to the group action is preserved by this extension.