The application of spatial filtering theory for the recognition of targets in synthetic aperture radar (SAR) imagery is proposed. Shift invariant correlation operations are used to compute distances under an optimum transform to measure similarity between an ideal reference and the input image. The transform is a filter which responds to features specifically useful for discrimination. The results demonstrate the distortion tolerance of the approach which requires only a similarity in features rather than a precise match in pixel values. Quadratic terms are unaffected by shifting of the input image while linear terms are computed using shift-invariant correlation. The system is thus non-linear but shift-invariant. Specifically, “distance” vectors are generated by filter banks which are analyzed by a rudimentary rule base to determine whether the input is a target image or clutter. An SAR automatic target recognizer (ATR) with results for 3 and 5 class problems is described. The data used is actual SAR imagery of military targets.