Euclidean vs. projective camera calibration: Algorithms and 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 the re-projective nature can be taken into account: Every point in the image plane determines a viewing ray. 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. A calibration algorithm determines the parameters which describe the camera mapping in a non-linear optimization algorithm. In this article we compare two error functions: 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 re-projected rays, which are determined by the observed points. We present calibration algorithms considering distortions for both error functions and compare them with regard to the 3D-reconstruction problem. ∗{hanning,grafs}@forwiss.uni-passau.de