Abstract. Dense and robust optical flow estimation is still a major challenge in low-level computer vision. In recent years, mainly variational methods contributed to the progress in this field. One reason for their success is their suitability to be embedded into hierarchical schemes, which makes them capable of handling large pixel displacements. Matching-based regularization techniques, like dynamic programming or belief propagation concepts, can also lead to accurate optical flow fields. However, results are limited to short-or mid-scale optical flow vectors, because these techniques are usually not coupled with coarse-to-fine strategies. This paper introduces fSGM, a novel algorithm that is based on scan-line dynamic programming. It uses the cost integration strategy of semi-global matching, a concept well known in the area of stereo matching. The major novelty of fSGM is that it embeds the scan-line dynamic programming approach into a hierarchical scheme, which allows it to handle large pixel displacements with an accuracy comparable to variational methods. We prove the exceptional performance of fSGM by comparing it to current state-of-the-art methods on the KITTI Vision Benchmark Suite.