Critical Configurations for N-view Projective Reconstruction

In this paper we give a complete characterization of critical configurations for projective reconstruction with any number of points and views. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and the cameras uniquely, up to a projective transformation. For two views, the critical configurations are well-known. In this paper it is shown that a configuration of n 3 cameras and m points is critical if all points and cameras lie on the intersection of two distinct ruled quadrics. Contrary to the two-view case, which in general allows two ambiguous solutions, there is a family of ambiguous reconstructions for the n-view case. Conversely, it is shown that (except for minimal cases) for any critical configuration, all the points and cameras lie on the intersection of two ruled quadrics.

• Type: Conference
• Year: 2001
• Where: CVPR
• Authors: Fredrik Kahl, Kalle Åström, Richard I. Hartley
• Keywords: Ambiguous Reconstructions, Computer Vision, Critical Configurations, CVPR 2001, Distinct Ruled Quadrics, Image Points, Projective Transformation