Minimal Conditions on Intrinsic Parameters for Euclidean Reconstruction

In this paper will be investigated what constraints on the intrinsic parameters that are needed in order to reconstruct an unknown scene from a number of its projective images. Two such minimal cases are studied in detail. Firstly, it is shown that it is sufficient to know the skew parameter, even if all other parameters are unknown and varying, to obtain a Euclidean reconstruction. Secondly, the same thing can be done for known aspect ratio, again when all other intrinsic parameters are unknown and varying. In fact, we show that it is sufficient to know any of the intrinsic parameters to make Euclidean reconstruction. An algorithm, based upon bundle adjustment techniques, to obtain Euclidean reconstruction in the above mentioned cases are presented. Experiments are shown on the slightly simpler case of both known aspect ratio and skew.