The geometric calibration of cone-beam systems with arbitrary geometry

A method is proposed to determine the cone-beam x-ray acquisition geometry of an imaging system using a phantom consisting of discrete x-ray opaque markers defining two parallel rings sharing a common axis. The phantom generates an image of two ellipses which are fitted to an ellipse model. A phantom-centric coordinate system is used to simplify the equations describing the ellipse coefficients such that a solution describing the acquisition geometry can be obtained via numerical optimization of only three of the nine unknown variables. We perform simulations to show how errors in the fit of the ellipse coefficients affect estimates of the acquisition geometries. These simulations show that for ellipse projections sampled with 1200 markers, 25 microm errors in marker positions and a source-detector distance (SDD) of 1.6 m, we can measure angles describing detector rotation with a mean error of <0.002 degrees and a standard deviation (SD) of <0.03 degrees. The SDD has a mean error of 0.004 mm and SD = 0.24 mm. The largest error is associated with the determination of the point on the detector closest to the x-ray source (mean error = 0.05 mm, SD = 0.85 mm). A prototype phantom was built and results from x-ray experiments are presented.