A Generalized Shape-Axis Model for Planar Shapes

We describe a generalized shape-axis (SA) model for representing both open and closed planar curves. The SA model is an effective way to represent shapes by comparing their self-similarities. Given a 2D shape, whether it is closed or open, we use two different parameterizations (one parameterization is oriented clockwise and the other counterclockwise) for the curve. To study the self-similarity, the two parameterizations are matched to each other via a variational framework, where the self-similarity criterion is to be defined depending on the class of shapes and human perception factors. Useful self-similarity criteria include symmetry, parallelism and convexity, and so forth. A match is allowed to have discontinuities, and the optimal match can be computed by a dynamic programming algorithm in O(N) time, where N is the size of the shape. We use a grouping process for the shape axis to construct a unique SA-tree, however, when a planar shape is open, it is possible to derive an SA-forest. The generalized SA model provides a compact and informative way for 2D shape representation.