The Fisher information and the Rao measure are obtained in closed form for a family of probability density functions parametrized by the manifold PSL(2, R) of projective transformations of the real projective line. In addition, the Fisher information and the Rao measure are obtained for the sub-manifold of affine transformations. An application of these results to computer vision is described. The Rao measure is used to obtain a closed-form approximation to the probability of misclassifying a projective transformation of the line as an affine transformation. The approximation is a function of the number of pairs of points that correspond under the projective transformation and the standard deviation of the error in locating a point.