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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 motion measurements given the aperture effect, and it is shown how they can approximate other motion measurements as well.Using an L1 error measure for image alignment based on point-to-line correspondences and minimizing this measure using linear programming, achieves results which are more robust than the commonly used L2 metric. While estimators based on L1 are not theoretically robust, experiments show that the proposed method is robust enough to allow accurate motion recovery in hundreds of consecutive frames. The entire computation is performed in real-time on a PC with no special hardware.