We propose a new algorithm for dense optical flow computation. Dense optical flow schemes are challenged by the presence of motion discontinuities. In state of the art optical flow methods, over-smoothing of flow discontinuities accounts for most of the error. A breakthrough in the performance of optical flow computation has recently been achieved by Brox et al. Our algorithm embeds their functional within a contour-based segmentation framework. Piecewise-smooth flow fields are accommodated and flow boundaries are crisp. Experimental results show the superiority of our algorithm with respect to alternative techniques.