Estimation of geometrical parameters and collimator evaluation for cone beam tomography

A method is presented for estimating the geometrical parameters for a cone beam detector geometry from the coordinates of the centroid of a projected point source sampled over 360 degrees. Nonlinear expressions are derived for the coordinates of the centroids in terms of the geometrical parameters which include: the two-dimensional coordinates of the projection of the center of rotation onto the detector image plane; the focal length; the distance from the focal point to the center of rotation; and the spatial coordinates of the point source itself. Experimental data were obtained using a rotating gamma camera with a symmetrically converging collimator. The Marquardt algorithm was used to estimate the parameters for this particular cone beam geometry. The method was able to estimate the geometrical parameters and evaluate the accuracy of the collimator construction.