Camera self-calibration: A case against Kruppa's equations

In this paper, we consider the self-calibration problem fbr perspective cameras, and especially the best known practical method, the so-called Kruppa equation approach. It is known that for several common types of camera motion, self-calibration is degenerate, which manifests itself through the existence of ambiguous solutions. In a previous paper, we have studied these critical motion sequences in derail and have revealed their importance for practical application. In this paper, we reveal a type of camera motion that is not critical for the generic self-calibration problem, but for which the Kruppa equation approach fails. This is the case if all optical centers lie oil a sphere and if the optical axes pass through the sphere's center. This situation is very natural for 3D object modeling from photographs or image sequences. Our result is thus a contribution to the understanding of how to successfully apply self-calibration in practice.