The modified pbM-estimator method and a runtime analysis technique for the RANSAC family

Robust regression techniques are used today in many computer vision algorithms. Chen and Meer recently presented a new robust regression technique named the projection based M-estimator. Unlike other methods in the RANSAC family of techniques, where performance depends on a user supplied scale parameter, in the pbM-estimator technique this scale parameter is estimated automatically from the data using kernel smoothing density estimation. In this work we improve the performance of the pbM-estimator by changing its cost function. Replacing the cost function of the pbM-estimator with the changed one yields the modified pbM-estimator. The cost function of the modified pbM-estimator is more stable relative to the scale parameter and is also a better classifier. Thus we get a more robust and effective technique. A new general method to estimate the runtime of robust regression algorithms is proposed. Using it we show, that the modified pbM-estimator runs 2-3 times faster than the pbM-estimator. Experimental results of fundamental matrix estimation are presented demonstrating the correctness of the proposed analysis method and the advantages of the modified pbM-estimator.