Bi-directional Shape Correspondences (BSC): A Novel Technique for 2-d Shape Warping in Quadratic Time?

We propose Bidirectional Shape Correspondence (BSC) as a possible improvement on the famous shape contexts (SC) framework. Our proposals derive from the observation that the original SC framework enforces a one-to-one correspondence between sample points, and that this leads to two possible drawbacks. First, this denies the framework of the opportunity to effect a many-to-many matching between points on the two shapes being compared. Second, this calls for the Hungarian algorithm which unfortunately usurps ( ) time. While the dynamic-space-warping dynamic programming algorithm has provided a standard solution to the first problem above, dynamic programming demands ( ) for general multi-contour shapes and ( ) for the special case of single-contour shapes, even after an heuristic search window of width has been chosen. Therefore, in this work, we propose a simple method for computing “manyto –many” correspondences, for the class of all 2-d shapes, in quadratic time. Our approach is to explicitly let each point on the first shape choose a best match on the second shape, and vice versa. Along the way, we also propose the use of data-clustering techniques for dealing with the outliers problem. From another viewpoint, it turns out this clustering can be viewed as an autonomous, rather than pre-computed, sampling of shape boundary.