We consider the problem of elastic matching of sequences of real numbers. Since both a query and a target sequence may be noisy, i.e., contain some outlier elements, it is desirable to exclude the outlier elements from matching in order to obtain a robust matching performance. Moreover, in many applications like shape alignment or stereo correspondence it is also desirable to have a one-to-one and onto correspondence (bijection) between the remaining elements. We propose an algorithm that determines the optimal subsequence bijection (OSB) of a query and target sequence. The OSB is efficiently computed since we map the problem's solution to a cheapest path in a DAG (directed acyclic graph). We obtained excellent results on standard benchmark time series datasets. We compared OSB to Dynamic Time Warping (DTW) with and without warping window. We do not claim that OSB is always superior to DTW. However, our results demonstrate that skipping outlier elements as done by OSB can significantly improve matching results for many real datasets. Moreover, OSB is particularly suitable for partial matching. We applied it to the object recognition problem when only parts of contours are given. We obtained sequences representing shapes by representing object contours as sequences of curvatures.