Direct Image Matching by Dynamic Warping

In this paper, a new and efficient 2DDW (2-dimensional Dynamic Warping ) algorithm for direct image matching is proposed. Similar to the 1-dimensional DTW (Dynamic Time Warping) for sequence matching and optimal alignment, the 2DDW is aimed to elastically matching images which may be not aligned well. However, finding the optimal alignment between two images has been proved to be NP-complete [Elastic image matching is np-complete]. Therefore, reasonable constrains are imposed on the warping to bring down the complexity, such as continuity and monotonicity. The best complexity for continuous and monotonic 2DDW so far was reported as O(N^2 9^N) in [An efficient two-dimensional warping algorithm]. Our algorithm also guarantees continuity and monotonicity and the complexity is only O(N^6).