A Skeletal Measure of 2D Shape Similarity

This paper presents a geometric measure that can be used to gauge the similarity of 2D shapes by comparing their skeletons. The measure is defined to be the rate of change of boundary length with distance along the skeleton. We demonstrate that this measure varies continuously when the shape undergoes deformations. Moreover, we show that ligatures are associated with low values of the shape-measure. The measure provides a natural way of overcoming a number of problems associated with the structural representation of skeletons. The first of these is that it allows us to distinguish between perceptually distinct shapes whose skeletons are ambiguous. Second, it allows us to distinguish between the main skeletal structure and its ligatures, which may be the result of local shape irregularities or noise. We illustrate how the new shapemeasure can be used for the purposes of clustering shock-trees of the same shape class. 2004 Elsevier Inc. All rights reserved.