Model-based sphere localization (MBSL) in x-ray projections

The detection of spherical markers in x-ray projections is an important task in a variety of applications, e.g. geometric calibration and detector distortion correction. Therein, the projection of the sphere center on the detector is of particular interest as the used spherical beads are no ideal point-like objects. Only few methods have been proposed to estimate this respective position on the detector with sufficient accuracy and surrogate positions, e.g. the center of gravity, are used, impairing the results of subsequent algorithms. We propose to estimate the projection of the sphere center on the detector using a simulation-based method matching an artificial projection to the actual measurement. The proposed algorithm intrinsically corrects for all polychromatic effects included in the measurement and absent in the simulation by a polynomial which is estimated simultaneously. Furthermore, neither the acquisition geometry nor any object properties besides the fact that the object is of spherical shape need to be known to find the center of the bead. It is shown by simulations that the algorithm estimates the center projection with an error of less than 1% of the detector pixel size in case of realistic noise levels and that the method is robust to the sphere material, sphere size, and acquisition parameters. A comparison to three reference methods using simulations and measurements indicates that the proposed method is an order of magnitude more accurate compared to these algorithms. The proposed method is an accurate algorithm to estimate the center of spherical markers in CT projections in the presence of polychromatic effects and noise.