One noticed very soon that not all motion sequences are suited for self-calibration. Some obvious cases are the restricted motions described in the previous section (i.e. pure translation, pure rotation and planar motion). However there are more motion sequences which do not lead to unique solutions for the self-calibration problem. This means that at least two reconstructions are possible which satisfy all constraints on the camera parameters for all the images of the sequence and which are not related by a similarity transformation.
Several researchers realized this problem and mentioned some specific cases or did a partial analysis of the problem [157,176,121]. Sturm [144,145] provided a complete catalogue of critical motion sequences (CMS) for constant intrinsic parameters. Additionally, he identified specific degeneracies for some algorithms .
However it is very important to notice that the classes of CMS that exist depend on the constraints that are enforced during self-calibration. The extremes being all parameters known, in which case almost no degeneracies exist, and, no constraints at all, in which case all motion sequences are critical.
In table 6.1 and 6.2 the most important critical motion sequences for self-calibration using the constraint of constant -but unknown- intrinsics respectively intrinsics known up to a freely moving focal length are listed. More details can be found in .
For self-calibration to be successful it is important that the global motion over the sequence is general enough so that it is not contained in any of the critical motion sequence classes.