The use of linear discriminant functions, and particularly a discriminant function derived from the work of Harold Hotelling, as a means of assessing image quality is reviewed. The relevant theory of ideal or Bayesian observers is briefly reviewed, and the circumstances under which this observer reduces to a linear discriminant are discussed. The Hotelling oberver is suggested as a linear discriminant in more general circumstances where the ideal observer is nonlinear and usually very difficult to calculate. Methods of calculation of the Hotelling discriminant and the associated figure of merit, the Hotelling trace, are discussed. Psychophysical studies carried out at the University of Arizona to test the predictive value of the Hotelling observer are reviewed, and it is concluded that the Hotelling model is quite useful as a predictive tool unless there are high-pass noise correlations introduced by post-processing of the images. In that case, we suggest that the Hotelling observer be modified to include spatial-frequency-selective channels analogous to those in the visual system.