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, <B>R</B>) 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.