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Optimal image interpolation schemes, based on partial differential equation (PDE) models for the image signal, are presented. These schemes use the generalized spline interpolation approach. Minimum mean square error (MMSE) is achieved given an image PDE model and a finite set of the image data samples. Two new types of two-dimensional (2-D) interpolation techniques are presented for the implementation of these schemes. These are the generalized cardinal spline digital filter and the generalized B-spline interpolator. Computer simulations are described. In addition to possessing a meaningful theoretical basis, the results show a practical improvement of the approach presented over the existing schemes.