Bayesian approach for circle fitting including prior knowledge

Abstract

The fitting of geometric shapes into measurement data is a frequently occurring task in metrology, computer vision or pattern recognition. Least-Squares methods correspond to the state of the art, but do not make use of existing prior knowledge about the measurement system or the measurement object. By using prior knowledge, the uncertainty of a measurement can be reduced. A simple example for prior knowledge is the diameter of a bore hole, which is always greater than zero. The Bayesian approach offers the possibility to include this prior knowledge for the fitting of geometric shapes. In the following, a Bayesian approach for fitting a circle is presented and compared with the established Total-Least-Squares method.