RANSAC

RANSAC, which stands for Random Sample Consensus, is an iterative method used to estimate the parameters of a mathematical model from data that contains outliers. It operates by repeatedly selecting a random subset of the data, fitting a model to that subset, and evaluating how many data points are well described by the fitted model. The subset that yields the largest agreement with the data—called the inlier consensus—is kept as the best estimate.

In a typical RANSAC procedure, one specifies a minimum sample size needed to fit the model, a distance or residual threshold to classify inliers, and a maximum number of iterations. Each iteration randomly selects the minimum subset, computes a model, and counts inliers as points whose residual to the model is below the threshold. If the current model has more inliers than the best so far, it becomes the new best. After all iterations, the final model is refined by re-fitting to all inliers from the best consensus set, and sometimes re-estimating with a larger dataset to improve accuracy.

RANSAC provides a probabilistic guarantee that a good model will be found with high probability, given a sufficient number of iterations and a reasonably high inlier ratio. The method is robust to a significant proportion of outliers but depends on the choice of threshold and minimum sample size. It is not guaranteed to find the globally optimal model and can struggle when inliers are heavily skewed or when the data contain degeneracies.

Applications of RANSAC are widespread in computer vision and robotics, including line, plane, homography, and fundamental matrix estimation, as well as 3D pose and camera calibration tasks. Variants such as MLESAC, PROSAC, and LO-RANSAC aim to improve efficiency or estimation quality.