The hierarchical approximation and recognition of two-dimensional shapes based on symmetry

This paper presents a quantitative description of two-dimensional (2-D) shapes using a regional-based analysis based on symmetry, and matching of two such descriptions. The description is extracted along the boundary curves of the shapes uniquely and directly and has important attributes required for their recognition like: hierarchical approximation of shapes, and rotational, scaling and translational invariant properties. Using this description, matching two shapes is efficiently implemented by the dynamic programming (DP) technique. The similarity between two shapes is defined on the basis of the DP calculation, and it facilitates the searching process in recognition. The power of the proposed method is shown through its applications in matching several pairs of map images. As a general case, the matching is implemented to open curves too, which are considerable as the occluded cases of 2-D shapes.