Monte Carlo maximum likelihood circle fitting using circular density functions

Finding the “best-fitting” circle to describe a set of points in two dimensions is discussed in terms of maximum likelihood estimation. Several combinations of distributions are proposed to describe the stochastic nature of points in the plane, as the points are considered to have a common, typically unknown center, a random radius, and random angular orientation. A Monte Carlo search algorithm over part of the parameter space is suggested for finding the maximum likelihood parameter estimates. Examples are presented, and comparisons are drawn between circles fit by this proposed method, least squares, and other maximum likelihood methods found in the literature. Copyright Springer-Verlag 2013