1. A method for determining, for a fourth-generation computed tomography (CT) scanner that includes a third-generation X-ray source and detector system and a plurality fixed, sparse photon-counting detectors (PCDs), a position of each PCD of the plurality of PCDs, the method comprising: obtaining, for a given PCD of the plurality of PCDs, sinogram data from a reference scan of a plurality of line attenuators arranged at fixed, known positions within the CT scanner; determining, by analyzing the sinogram data, a set of view angles of the X-ray source for which the sinogram data exhibits a decrease in count value, indicating a shadow cast by one of the line attenuators; generating, for each view angle in the set of view angles, a line connecting a position of the X-ray source at the view angle, and a position of a line attenuator, of the plurality of line attenuators, that is closest to the position of the X-ray source at the view angle, to generate a set of lines; extending each line in the set of lines a predetermined distance to generate an extended set of lines; determining locations of all intersection points of the extended set of lines; and determining a PCD centerline of the given PCD based on the determined locations of the intersection points.