Analytic line fitting in the presence of uniform random noise

One of the most fundamental tasks in pattern recognition involves fitting a curve such as a line segment to a given set of data points. Using the conventional ordinary least-squares (OLS) method of fitting a line to a set of data points is notoriously unreliable when the data contain points coming from two different populations: (i) randomly distributed points ('random noise'), (ii) points correlated with the line itself (e.g., obtained by perturbing the line with zero-mean Gaussian noise). Points which lie far away from the line (i.e., 'outliers') usually belong to the random noise population; since they contribute the most to the squared distances, they skew the line estimate from its correct position. In this paper we present an analytic method of separating the components of the mixture. Unlike previous methods, we derive a closed-form solution. Applying a variant of the method of moments (MoM) to the assumed mixture model yields an analytic estimate of the desired line. Finally, we provide experimental results obtained by our method.