The thin-plate spline can unwarp a data set of landmark-labelled medical images so that their landmarks are exactly superposed over an average landmark configuration. This pixel relabeling is highly nonlinear in the original image data. Nevertheless, for most biostatistical purposes, the resulting unwarped images can be treated as if they arose from raw measurements (in this case, pixel-by-pixel gray levels) by a covariate adjustment suppressing unwanted variation. Tasks of discrimination and classification of images can benefit greatly from the augmented precision of subsequent quantitative comparisons. These `adjusted mean differences'--pixelwise group mean differences of the unwarped images--may be combined with differences of landmark shape in prescriptions for new landmark locations that further sharpen the unwarping or classification. These considerations are exemplified in a detailed analysis of some midsagittal brain images of medical students and schizophrenics.