The technology described relates to reconstruction of 3-dimensional scenes from uncalibrated images, and provides a robust and systematic strategy for using cheirality in scene reconstruction and camera calibration. A general projective reconstruction is upgraded to a quasi-affine reconstruction. Cheirality constraints are deduced with regard to the cameras by statistical use of scene points in a voting procedure. The deduced cheirality constraints constrain the position of the plane at infinity. Linear programming is used to determine a tentative plane at infinity. Based on this tentative plane at infinity, the initial projective reconstruction can be transformed into a reconstruction that is quasi-affine with respect to the cameras.