Optical flow computation consists in recovering the apparent motion field between two images with overlapping fields of view. This paper focuses on a subset of optical flow problems, called epipolar flow, where the camera moves inside a scene containing no moving objects. Accurate solutions exist but their high computational complexities make them non suitable for a large panel of real-time applications. We propose a new epipolar flow approach with low computational complexity achieving the best error rate on the non dense KITTI optical flow 2012 benchmark and running 1000× faster than the second ranked approach. On a 4core 3GHz processor, our multi-core implementation computes a semi dense optical flow field of a 450k pixels image in 260ms. It is a significant advance in reducing the running time of accurate optical flow computation. To achieve such results we rely on the epipolar constraints and the local coherence of the optical flow not only to increase accuracy but also to reduce computational complexity. Our contribution is twofold. It is first, the acceleration and the accuracy increase of current RANSAC based visual odometry algorithms via the estimation of a robust sparse flow field, well distributed over the image domain. And then, the estimation of a semi dense flow field leveraging epipo-lar constraints and a propagation scheme to speedup the estimation and reduce error rates.