Reducing bias in Bayesian shape estimation

This work considers the problem of estimating the parameters of an extended object based on noisy point observations from its boundary. The intention is to explore relationships between common approaches by breaking them down into their basic assumptions within the Bayesian framework. In doing so, we find that distance-minimizing curve fitting algorithms can be modeled by using a special Spatial Distribution Model, where the source distribution is approximated by a greedy one-to-one association of points to sources on the shape boundary. Based on this insight, we explore the origin of the estimation bias, which is a well-known issue of curve fitting algorithms. Furthermore, we derive a general scheme to alleviate its effect for arbitrary shapes, as well as for non-isotropic noise. This procedure is shown to be a generalization of related special solutions.