Once we obtain two pairs of feature trajectories, and , we compute the symmetric warps and using regularized DTW. We construct the warp as follows:
2where and are the length of trajectories and , respectively. The L'th element of the warp is , where i and j are the time indices of and , respectively. The optimal warp is the minimum distance warp, where the distance of a warp is defined as follows:
3where is the distance between the two values of the given time indices (i, j) in the k'th element of the warp. We propose a regularized distance metric function as follows:
5where and are the first and second derivatives of . The regularization term can be considered a smoothness penalty, where w is the weight (normally, w = 25).