When objects must be identified from distorted imagery, a choice must be made between feature sets that are invariant to the distortion and those that are not. Sets of invariants almost always contain less information, resulting in classification error rates that are higher under distortion-free conditions, but which are no larger when distortion is present. The choice can be evaluated by calculating error rates as a function of the eigenvalues of the correlation matrix, noise, number of classes, and a distortion parameter. An example of this evaluation is given by comparing identification of ships by using a subtraction correlator and moment features. The distortion parameter is scale, to which the correlator is sensitive and the moment comparison is invariant.