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A property filter is developed that is suitable for recognizing translation-rotation-dilation classes of two-dimensional images. Invariant outputs corresponding to such classes are obtained by employing two successive sampled spatial harmonic transforms. The required analyses are equivalent to taking inner products of pairs of vectors only one of which is variable in each case. Subsequently, the necessary network may be realized with fixed threshold logic, independent of the character classes to be recognized. The effectiveness of the property filter has been confirmed with printed and handwritten numerals by coupling it to a standard adaptive categorizer of a type assuming linear separability. There is further evidence to show that performance is improved by coupling a categorizer that does not assume linear separability.