Hartley, RichardKahl, Fredrik2015-12-132015-12-13June 18 201063-6919http://hdl.handle.net/1885/86581This 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 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 can not 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.Keywords: Cameras; Image analysis; Motion compensation; Parameter estimation; Three dimensional; Critical configuration; Rectilinear compensation; Three dimensional geometrical configuration; Image reconstruction20032015-12-12