This correspondence considers the problem of matching image data to a large library of objects when the image is distorted. Two types of distortions are considered: blur-type, in which a transfer function is applied to Fourier components of the image, and scale-type, in which each Fourier component is mapped into another. The objects of the library are assumed to be normally distributed in an appropriate feature space. Approximate expressions are developed for classification error rates as a function of noise. The error rates they predict are compared with those from classification of artificial data, generated by a Gaussian random number generator, and with error rates from classification of actual data. It is demonstrated that, for classification purposes, distortions can be characterized by a small number of parameters.