Matching of shapes bound by freeform curves

Matching and retrieval of shapes, both in two and three dimensions, have been a topic of interest to researchers in the field of computer graphics, vision and geometric modeling for at least a decade. In this paper, a shape is assumed to be represented as set of freeform curved boundaries. A prominent approach to matching curved outline is the graph-based approach, where a skeleton is used as a basis for obtaining the graph. In general, graph-matching is a hard problem and the comparison costs increase proportionally with graph size and hence slows down the process. In this paper, the skeleton, and in particular, medial axis of curved boundaries has been used. As opposed to using graph-based matching, statistical-based methods of signatures obtained from the properties of the skeleton have been employed. This enables a faster construction of shape signatures thereby increasing the speed of matching. Moreover, this facilitates the comparison of shapes that may have the presence of holes (inner loops) in it. In addition to the qualitative visualizations of retrieval results, retrieval performance by calculating quantitative statistics parameters typically used in shape matching is also discussed.© 2012 CAD Solutions, LLC.