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Invariant pattern recognition is an important problem in many areas of computer vision. In this chapter, a new invariant feature of two-dimensional contours is introduced: the Invariance Signature (IS). The IS 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 a Model-Based Neural Network (MBNN) can be constructed which computes the IS of a contour, and classifies patterns on this basis. MBNNs, whilst retaining the structure and advantages of traditional neural networks (TNNs), enable explicit modeling of the target system. This can result in greatly improved generalization, and representation in lower-dimensional state spaces. MBNNs can be trained with much smaller training sets than are required by TNNs. This means that MBNNs are much less computationally-expensive to train than TNNs. Experiments demonstrate that such Invariance Signature networks can be employed successfully for shift-, rotation- and scale-invariant optical character recognition.