Matching 2D Shapes using their Symmetry Sets

We introduce a shape descriptor that is based on the symmetry set. This set represents pairwise symmetric points and consists of several branches. The begin and end points of the branches relate to extrema of the curvature along the shape. Consequently, extrema of the curvature are pairwise connected via a symmetry set branch with a certain finite length. The novel shape descriptor is given by a string representing these extrema, together with the pair wise connections and a length measure. Next, an algorithm is given to match strings. This algorithm is based on a modified shortest path algorithm, taking into account the allowed changes of the symmetry set. Examples show the usability of the presented theory, applied to different types of shapes, including noise and occlusions