LMedS

The Least Median of Squares (LMedS) outlier-rejection algorithm is conceptually very similar to RANSAC: as in RANSAC, a model is generated from random samples of the input data, but instead of selecting the model that obtains the largest number of consensus elements (or minimizes a loss function), LMedS selects the model with the smallest median error. All input data are therefore 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 for RANSAC. RANSAC, however, requires two parameters (the number of iterations and the threshold used to determine whether an element belongs to the data set), whereas LMedS requires only the former. By construction, however, LMedS tolerates at most 50% outliers.

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