LMedS

The outlier rejection algorithm known as the Least Median of Squares (LMedS) is conceptually very similar to RANSAC: Similar to RANSAC, a model is generated from random samples of the input data; however, instead of selecting the model that gathers the highest number of inliers (or that minimizes a loss function), LMdeS selects the model that has the lowest median error among all candidates. Consequently, all input data are compared with the model, sorted by error, and the median value is examined.

The relationship between the probability of identifying inliers and the number of iterations is the same as in RANSAC. However, RANSAC requires two parameters (the number of iterations and the threshold to determine whether an element belongs to the dataset), while LMedS only requires the first. By design, LMedS, however, tolerates a maximum presence of 50% outliers.

A good overview of the RANSAC, M-SAC, and LMedS techniques can be found in (CKY09).