We present a novel variational method for estimating dense disparity maps from stereo images. It integrates the epipolar constraint into the currently most accurate optic flow method (Brox et al. 2004). In this way, a new approach is obtained that offers several advantages compared to existing variational methods: (i) It preservers discontinuities very well due to the use of the total variation as solution-driven regulariser. (ii) It performs favourably under noise since it uses a robust function to penalise deviations from the data constraints. (iii) Its minimisation via a coarse-to-fine strategy can be theoretically justified. Experiments with both synthetic and real-world data show the excellent performance and the noise robustness of our approach.