Re-projective vs. projective camera calibration: effects on 3D-reconstruction

The camera mapping can be seen in two ways. The classic approach is to emphasize the projective nature of the camera. But also every point in the image plane determines a viewing ray by its re-projection. Both mappings can be described by the same set of parameters. In fact the re-projective camera mapping can be seen as the inversion of the projective camera mapping. In this article we compare two error functions for a camera calibration. The projective error function measures the distance of the projected prototype to the observed points in the image plane. The re-projective error function measures the distance of the prototype to the reprojected rays which are determined by the observed points. We present calibration algorithms for both error functions and compare them with regard to the 3D-reconstruction problem.