In this paper, a new invariant feature of two-dimensional contours is reported: the Invariance Signature. The Invariance Signature is a measure of the degree to which a contour is invariant under a variety of transformations, derived from the theory of Lie transformation groups. It is shown that the Invariance Signature is itself invariant under shift, rotation and scaling of the contour. Since it is derived from local properties of the contour, it is well-suited to a neural network implementation. It is shown that a Model-Based Neural Network (MBNN) can be constructed which computes the Invariance Signature of a contour, and classifies patterns on this basis. Experiments demonstrate that Invariance Signature networks can be employed successfully for shift-, rotation- and scale-invariant optical character recognition.