In this paper, we study pattern matching of points under non-uniform distortions. First we give a natural definition for the problem. Next we present a simple polynomial time algorithm for the one-dimensional case of the problem, whereas we prove that it is NP-hard in two (or more) dimensions. Then we present a practical heuristic algorithm for finding a matching between two sets of spots obtained by the two-dimensional gel electrophoresis technique, which is a special but important case of the problem.