Methods and geometry for plane-based self-calibration

We consider the problem of camera self-calibration, from images of a planar object with unknown Euclidean structure. The general case of possibly varying focal length is addressed. This problem is non-linear in general. One of our contributions is a non-linear approach, that makes abstraction of the (possibly varying) focal length, resulting in a computationally efficient algorithm. In addition, it does not require a good initial estimate of the focal length, unlike previous approaches. As for the initialization of other parameters, we propose a practical approach, that simply requires to take one image in roughly fronto-parallel position. Closed-form solutions for various configurations of unknown intrinsic parameters are provided. Our methods are evaluated and compared to previous approaches, using simulated and real images. Besides our practical contributions, we also provide a detailed geometrical interpretation of the principles underlying our approach.