MLESAC

MLESAC stands for Maximum Likelihood Estimation Sample Consensus, a robust estimation technique used to fit parametric models to data that contain outliers. It extends the RANSAC framework by embedding the inlier/outlier decision in a probabilistic model and choosing the model parameters that maximize the likelihood of the observed data under that model.

The method operates similarly to RANSAC in its iterative, sample-based approach. For each randomly drawn minimal sample, a model is fit; for every data point, a residual to the model is computed. The data are modeled as a two-component mixture: an inlier distribution (often Gaussian around zero residual) and an outlier distribution (often uniform over the error range). The likelihood of the data under the hypothesized model is computed as the product across points of p_inlier f_in(res) + p_outlier f_out(res). The model with the largest likelihood is selected, and the inlier set is formed according to the posterior probabilities, typically using a threshold derived from the mixture, followed by re-estimation using all inliers. The process repeats until a budget is exhausted or convergence is reached.

MLESAC generally yields higher accuracy than plain RANSAC, particularly when data contain significant noise and mixed outliers, because it uses a probabilistic framework rather than a simple inlier count. However, it is more computationally demanding and requires choosing a noise model and mixture parameters, which can influence performance. Common applications include estimating fundamental matrices, homographies, and other geometric models in computer vision, where robust fitting is crucial.