A method to determine the detector locations of the cone-beam projection of the balls' centers.

In geometric calibration of cone-beam computed tomography (CBCT), sphere-like objects such as balls are widely imaged, the positioning information of which is obtained to determine the unknown geometric parameters. In this process, the accuracy of the detector location of CB projection of the center of the ball, which we call the center projection, is very important, since geometric calibration is sensitive to errors in the positioning information. Currently in almost all the geometric calibration using balls, the center projection is invariably estimated by the center of the support of the projection or the centroid of the intensity values inside the support approximately. Clackdoyle's work indicates that the center projection is not always at the center of the support or the centroid of the intensity values inside, and has given a quantitative analysis of the maximum errors in evaluating the center projection by the centroid. In this paper, an exact method is proposed to calculate the center projection, utilizing both the detector location of the ellipse center and the two axis lengths of the ellipse. Numerical simulation results have demonstrated the precision and the robustness of the proposed method. Finally there are some comments on this work with non-uniform density balls, as well as the effect by the error occurred in the evaluation for the location of the orthogonal projection of the cone vertex onto the detector.