Abstract: In order to efficiently and accurately estimate model parameters from data contaminated by heavy outliers, fast resampling optimal sample consensus（FROSAC） algorithm is proposed. Firstly, a pre-validation step is added before model validation, and the quality of models is evaluated by the spline-based loss function. Secondly, inlier set is optimized by iteratively resampling and model validating. Then inlier set is refined gradually according to the bi-threshold. Finally the model is estimated with the optimal inlier set. Experiments on feature matching and fundamental matrix estimation show that the proposed algorithm is high in accuracy and efficiency, and is faster than the traditional algorithms by more than two degrees of magnitude in the case that the percentage of outliers is over 50%.