Synthetic discriminant functions have been used to locate objects irrespective of distortions and to estimate the extent of the distortion. It was recognized from the beginning that accurate estimates are only possible provided the training set is constructed carefully. We obtain conditions that will ensure the accuracy of the estimates. The conditions also suggest efficient ways of constructing the training sets and the results are extended to a wide class SDF-type filters. The theoretical results are illustrated with (idealized) examples and are also applied to the more realistic problem of accurate facial location.