Exact computation of projected sphere centres in cone beam x-ray projections

Abstract

A method is presented for fitting the projected centres of spheres in cone beam X-ray imaging. By using a suitable coordinate system, the method allows direct and exact calculation of the sphere centre without fitting the projection shape with an ellipse and correcting from the ellipse centre to the sphere centre. Advantages in numerical implementation result from the number of unknown variables being reduced compared to ellipse fits. Additionally, the orientation of the detector relative to the X-ray source can be obtained from fitting the shapes of projections of multiple spheres without knowledge of the positions or dimensions of the spheres. The accuracy of the method is compared to other techniques using simulated X-ray projections.