From projective to Euclidean space under any practical situation, a criticism of self-calibration

For many practical applications it is important to relax the self-calibration conditions to allow for changing internal camera parameters (e.g. zooming/focusing...). Classical techniques failed for such conditions. We present the available constraints that allow us to right a projective calibration to a Euclidean one. Meanwhile, we found that the estimations of the internal parameters were rather inaccurate. We discuss theoretically this difficulty and above all the resulting effect on the 3D reconstruction. In fact, we show that the uncertainty on the focal length estimation leads to an Euclidean calibration up to a quasi anisotropic homothety whereas the error on the principal point can often be interpreted as a translation. Hopefully, the calibration we come up with, is quite acceptable for reconstruction of models.