Properties of the projective mapping of cameras and projectors

The geometric pinhole camera model (PCM) for cameras and projectors which is used in computer vision research is examined. The author also analyzes the closely-related central projection equations (CPEs) for the camera mapping of object points to projected rays. The equations of five planes which characterize the PCM are shown to arise neatly from the CPEs. A simple degree-of-freedom (DOF) analysis performed on the CPEs and the PCM reveals that both models contain one redundant DOF. Finally, it is shown that the location of the lens center, in world coordinates, can be found for a calibrated optical device (i.e., an optical device whose central projection parameters have been estimated), by simply solving three simultaneous linear equations in the three unknown point coordinates