A critical configuration for reconstruction from rectilinear motion
This paper investigates critical configurations for projective reconstruction from multiple images taken by a camera moving in a straight line. Projective reconstruction refers to a determination of the 3D (three-dimensional) geometrical configuration of a set of 3D points and cameras, given only correspondences between points in the images. A configuration of points and cameras is critical if it cannot be determined uniquely (up to a projective transform) from the image coordinates of the points. It is shown that a configuration consisting of any number of cameras lying on a straight line, and any number of points lying on a twisted cubic constitutes a critical configuration. An alternative configuration consisting of a set of points and cameras all lying on a rational quartic curve exists.