This article raises the problem of autocalibration of a camera undergoing rigid motions under the assumption of constant intrinsic camera parameters.
Many methods of autocalibrating monocular and stereo sensors have been developed in the recent years. Faugeras, Luong and Maybank [FLM92] propose to solve the Kruppa equations from points matches in 3 images. However, this requires non-linear resolution methods. An alternative solution consists to first recover affine structure and then solve for the camera calibration using this. This ``stratified'' approach [Fau95] can be applied to a single camera motion [LV93] or to a stereo rig in motion [DF96] and requires no knowledge about the observed scene.
Affine calibration has already been studied by many authors and amounts to recovering the equation of the plane at infinity, or equivalently the infinite homographies between the views. Many classes of motions have been treated and theoretically solved : pure translation [RCH98], rotations around the camera's center of projection [Har94], planar motions [BZ95] [CDRH98] and general displacements [ZBR95] [HC98].
The infinite homographies then allow the Euclidean calibration to be computed and it is well known that this computation is possible when at least 2 motions with non zero rotations and non parallel rotation axes are available. However, it is not always possible to have such motions. One solution is to add a constraint on the internal parameters (e.g. that the image axes are perfectly orthogonal or that the aspect ratio is known). But, even in this case there exist some critical motions [Stu97] which prevent an unambiguous calibration.
The main contribution of this article is a detailed analysis of affine-to-Euclidean autocalibration, based on the real Jordan decomposition of the infinite homographies. This provides a new way to calculate the Euclidean calibration. Critical motions (where the intrinsic parameters can not all be recovered) are also studied. However, in some cases, if the correct constraint is applied, the problem can be solved and all of the intrinsic parameters can be calculated.