Flexible calibration: minimal cases for auto-calibration

This paper deals with the concept of auto-calibration, i.e. methods to calibrate a camera on-line. In particular we deal with minimal conditions on the intrinsic parameters needed to make a Euclidean reconstruction, called flexible calibration. The main theoretical results are that it is only needed to know that one intrinsic parameter is constant. The method is based on an initial projective reconstruction, which is upgraded to a Euclidean one. The number of images needed increases with the complexity of the constraints, but the number of points needed is only the number needed in order to obtain a projective reconstruction. The theoretical results are exemplified in a number of experiments. An algorithm, based on bundle adjustments and a linear initialization method are presented and experiments are performed on both synthetic and real data.