Method for determining the probing points for efficient measurement and reconstruction of freeform surfaces

In this paper we present a novel method for determining the probing points for achieving efficient measurement and reconstruction of freeform surfaces. A B-spline is adopted for modelling the freeform surface. In the framework of Bayesian statistics, we develop a model selection strategy to obtain an optimal model structure for the freeform surface. Based on the selected model structure, a set of probing points is then determined where measurements are to be made. In order to obtain reliable parameter estimation for the B-spline model, we analyse the uncertainty of the model and use the statistical analysis of the Fisher information matrix to optimize the locations of the probing points needed in the measurements. Using a 'data cloud' of a surface acquired by a 3D vision system, we implemented the proposed method for reconstructing freeform surfaces. The experimental results show that the method is effective and promises useful applications in multi-sensor measurements including a vision guided coordinate measuring machine for reverse engineering.