Harmonic models of shape transformations in digital images and patterns

A harmonic model of shape transformations is presented. In this model, harmonic functions are governed by the Laplace equation. This model can convert all image or a pattern to another with arbitrary shapes. The transformation process is harmonic, without abruptness and discontinuity. This model can be used to generate and recognize handwritten Roman letters and Chinese characters, fingerprints, and other types of digitized images and patterns. The algorithms of the harmonic models involve partial differential equations and their numerical solutions. Therefore, an intrinsic link between pattern images and numerical methods is presented