On shape similarity

An algorithm for the detection of 'perceptual similarity' among planar shapes is suggested. Current state-of-the-art matching algorithms deal mainly with shapes which are similar modulo a well defined geometric transformation. The goal of this paper is to suggest a similarity measure among shapes which 'look similar', such as different fonts of a letter or pictures of different 'perceptually similar' chairs. The essence of the authors' approach consists in the representation of the shapes as special weighted graphs, the vertices of which represent the 'lumps' of the shapes in a given orientation. Then, these graphs are gradually reduced by a 'small leaf' trimming procedure until the resulting graphs are isomorphic. A similarity measure is calculated based on this representation. Since the graphs are orientation dependent, the similarity measure is minimized over all orientations of one of the shapes. Experimental results of pairwise comparisons of a 24 shape database are presented.