Point pattern matching by relaxation

Let P = P1, …, Pm and Q = Q1, …, Qn be two patterns of points. Each pairing (Pi, Qj) of a point of P with a point of Q defines a relative displacement δij of the two patterns. We can define a figure of merit for δij according to how closely other point pairs coincide under δij. If there exists a displacement δ0 for which P and Q match reasonably well, the pairings for which δij ≃ δ0 will have high merit scores, while other pairings will not. The scores can then be recomputed, giving weights to the other point pairs based on their own scores; and this process can be iterated. When this is done, the scores of pairs that correspond under δ0 remain relatively high, while those of other pairs become low. Examples of this method of point pattern matching are given, and its possible advantages relative to other methods are discussed.