Principal component analysis is a standard tool for decorrelating features, and has been applied to small sets of textures, faces, and many other patterns for recognition and discrimination. This study combines principal component analysis with the magnitude of the Fourier transform of the patterns instead of the typically used spatial data. This greatly improves the performance of the analysis for shifted patterns. Performance is determined by analyzing the average number of correct classifications vs. the number of false positives. This paper presents the performance of this shift-invariant principal component analysis when applied to a database of almost 1000 images, based on the entire Brodatz texture album. By ranking each pattern in the Brodatz album by its difficulty of classification, an ordering of the difficulty for all the patterns is obtained. This ranking indicates which data is best suited to this method, and should be useful for benchmarking other methods. We analyze effects due to the choice of training set, size of the feature set, and homogeneity of the data. The reported results are conservative in that a huge variety of inhomogeneous patterns were included in the choices, simulating a difficult database environment.