Bayesian analysis of uncertainties in circle, straight-line and ellipse fitting considering a-priori knowledge − comparative analysis with total-least-squares approaches

Fitting standard geometric elements into measurement data using Least-Squares techniques is a common task in signal processing across various technical applications. However, the application of these well-established but purely data-based methods does not consider potentially available prior knowledge about the measurand of interest or the measuring device. Thus, up to this day, additional information is usually left unused beyond a few academic applications. By applying a Bayesian approach, this prior knowledge can be incorporated into the fitting task, potentially leading to a reduction in overall uncertainty and fragility of the evaluation result. In this study, Bayesian models are proposed for incorporating prior knowledge into circular, linear, and ellipse fitting tasks. The general approaches as well as specific results are compared to the established Total-Least-Squares method within the example of the application of the F-operator in surface texture measurement illustrating the practical benefits of the approach.