Registering coordinate systems on an image is carried out by positioning a calibration jig having at least two collinear marker quadruples that are opaque to an imaging modality. Collinear quadruples are detected on an image of the jig and respective image cross ratios of the collinear quadruples are computed. Candidate lines are established by associating at least one collinear marker quadruple and at least one collinear image quadruple that have matching cross ratios. Respective registrations of the calibration jig with the image are performed using pairs of the candidate lines. One of the registrations is selected, wherein the selected registration has a residual that is smaller than a predetermined value.