A new method of estimating shape similarity

The goal of this paper is to describe a measure of similarity among shapes which "look" similar, such as the same letter in different fonts, or pictures of different, yet "perceptually" similar, chairs. We represent shapes as special weighted graphs, the vertices of which represent the "lumps" of the shapes in a given orientation. We then reduce these graphs using a "small leaf" trimming procedure until the resulting graphs are isomorphic. A similarity measure is calculated based on this representation via a polynomial-time complexity algorithm. A significant improvement in the complexity of the method presented is provided by eliminating the need to minimize the similarity measure over all orientations. A test database on which the method has been examined consists of 25 pairs of perceptually similar shapes, which includes the letters of the Hebrew alphabet.