Elimination of Outliers from 2-D Point Sets Using the Helmholtz Principle

A method for modeling and removing outliers from 2-D sets of scattered points is presented. The method relies on a principle due to Helmholtz stating that every large deviation from uniform noise should be perceptible, provided that the deviation is generated by an a contrario model of geometric structures. By assuming local linearity, we first employ a robust algorithm to model the local manifold of the corrupted data by local line segments. Our rationale is that long line segments should not be expected in a noisy set of points. This assumption leads to the modeling of the lengths of the line segments by a Pareto distribution, which is the adopted a contrario model for the observations. The model is successfully evaluated on two problems in computer vision: shape recovery and linear regression.