Relations between the coefficients in the projective transformation equations and the orientation elements of a photograph

Abstract

The physical meaning of the 11 coefficients in the projective transformation (PT) equations between a three-dimensional (3D) object and the 2D photo plane has already been described. In this paper, the 2D PT equations which are used for rectifying a photograph are considered. The relationships between the eight coefficients of the PT equations and the nine conventional orientation elements (OES) are presented, and the method of computing the nine OES from the eight PT coefficients is shown with some numerical examples. It is also explained that the corresponding coefficients in the 3D and the 2D PT equations have the identical values.