Uncertainty estimation for random sample consensus

The RANdom SAmple Consensus (RANSAC) algorithm, as a robust parameter estimator, has been widely used to remove gross errors. However, there is less work on analyzing the uncertainty produced by the RANSAC. This paper fills this gap by presenting an uncertainty estimation algorithm for the RANSAC. Based on a thorough analysis on the uncertainty of the model parameters generated during the random hypothesis sampling process of the RANSAC, we derive the probability that each hypothesis is selected as the best hypothesis by the RANSAC. Using the probability of the best hypothesis, we characterize the error expectation and error covariance of the model parameter estimates and compute the probability of each data point being an inlier. Three models including line fitting, homography, and essential matrix are used to evaluate the performance of the uncertainty estimation algorithm. Results demonstrate that the uncertainty produced by the RANSAC is characterized successfully by the proposed algorithm.