One of the main image representations in mathematical morphology is the shape decomposition representation, useful for image compression and pattern recognition. The morphological shape decomposition representation can be generalized to extend the scope of its algebraic characteristics as much as possible. With these generalizations, the morphological shape decomposition (MSD) role to serve as an efficient image decomposition tool is extended to interpolation of images. We address the binary and grayscale interframe interpolation by means of generalized morphological shape decomposition. Computer simulations illustrate the results.