Do Ambiguous Reconstructions Always Give Ambiguous Images?

In many cases self-calibration is not able to yield a unique solution for the 3D reconstruction of a scene. This is due to the occurrence of critical motion sequences. If this is the case, an ambiguity is left on the reconstruction. In this paper it is derived under which conditions correct novel views can be generated from ambiguous reconstructions. The problem is first approached from a theoretical point of view. It is proven that novel views are correct as long as the inclusion of the new view in the sequence yields the same ambiguity on the reconstruction. The problem is therefore much related to the problem of critical motion sequences since the virtual camera can be arbitrarily moved within the smallest critical motion set that contains the recovered camera motion without distortions becoming visible. Based on these result a practical measure for the expected ambiguity on a novel view based on the recovered structure and motion is derived. As an application a viewer was built that indicates if a specific novel view can be trusted or not by changing the background color.