Cone-Beam Imaging of Delta Functions

In this work we study the estimation error of ball center cone beam projections. This problem arises in the context of cone beam system calibration. The cone beam projection of a ball is generally an ellipse. It is well known that the ellipse center is usually different from the ball center projection. We show that the centroid of the ellipse (gray level gravity center) is also different from the ball center projection, even if closer to the ball center projection than the ellipse center is. However, we numerically show that in usual applications (focal length around 1 m and detector size less than 0.4 m), the centroid or the ellipse center estimation are good approximations of the ball center projection. We study numerically the ball center estimation error as a function of the ball size, the noise quantity and the X-ray source (or optical center) finite size.