As mentioned by Blaschke and Klein, Michel Chasles preferred the term homography to collineation. A distinction between the terms arose when the distinction was clarified between the real projective plane and the complex projective line. Since there are no non-trivial field automorphisms of the real number field, all the collineations are homographies in the real projective plane, however due to the field automorphism of complex conjugation, not all collineations of the complex projective line are homographies. In applications such as computer vision where the underlying field is the real number field, homography and collineation can be used interchangeably.
