Symmetry of Shapes Via Self-similarity

We describe a simple and novel approach to identify main similarity axes by maximizing self-similarity of object contour parts divided by the axes. For a symmetric or approximately symmetric shape, the main self-similarity axis coincides with the main axis of symmetry. However, the concept of the main self-similarity axis is more general, and significantly easier to compute. By identifying critical points on the contour self-similarity computation can be expressed as a discrete problem of finding two subsets of the critical points such that the two contour parts determined by the subsets are maximally similar. In other words, for each shape, we compute its division into two parts so that the parts are maximally similar. Our experimental results yield correctly placed maximal symmetry axes for articulated and highly distorted shapes.