A heuristic search-based motion correspondence algorithm using fuzzy clustering

Motion correspondence problem between many feature points of consecutive frames is computationally explosive. We present a heuristic algorithm for finding out the most probable motion correspondence of points in consecutive frames, based on fuzzy confidence degrees. The proposed algorithm consists of three stages: (i) reduction of the search space for candidate points of association, (ii) pairwise association cost estimation and (iii) complete association of every feature point between the consecutive frames. In the first stage, all the points in a frame, frame t-1 are grouped into several groups by using fuzzy clustering. This is done with a Euclidean distance as a similarity measure between the points. The points in the following frame, frame t are also clustered into the same number of groups with respect to the cluster centers of the previous frame. The association between the points of the consecutive frames is allowed only for the points that belong to the same group in each frame. In the second stage, the cost of each association of a point in frame t-1 with a point in frame t is estimated by using motion constraints that are based on the velocity vector and the orientation angle of each point. The cost is measured as a fuzzy confidence degree of each head point, i.e., a point in frame t-1, belonging to each measurement, i.e., a point in frame t. In the final stage, we search for the most likely associations among all the possible mappings between the feature points in the consecutive frames. A search tree is constructed in such a way that an ith level node represents an association of ith node in frame t-1 with a node in frame t. We devise a heuristic function of an admissible A* algorithm by using the pairwise association cost developed in the second stage. Experimental results show an accuracy of more than 98%.