Camera self-calibration: a case against Kruppa´s equations

We consider the self-calibration problem for 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 detail and have revealed their importance for practical applications. 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 on 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