A method to compute motion models in real time from point-to-line correspondences using linear programming is presented. Point-to-line correspondences are the most reliable measurements for image motion given the aperture effect, and it is shown how they can approximate other motion measurements as well. An error measure for image alignment using the L1 metric and based on point-to-line correspondences achieves results which are more robust than those for the commonly used L2 metric. The L1 error measure is minimized using linear programming. While estimators based on L1 are not robust in the breakdown point sense, experiments show that the proposed method is robust enough to allow accurate motion recovery over hundreds of consecutive frames. The L1 solution is compared to standard M-estimators and Least Median of Squares (LMedS) and it is shown that the L1 metric provides a reasonable and efficient compromise for various scenarios. The entire computation is performed in real-time on a PC without special hardware.