A novel method for harmonic geometric transformation model based on wavelet collocation

Geometric distortion may occur in the data acquisition phase in information systems, and it can be characterized by some geometric transformation models. Once the distorted image is approximated by a certain geometric transformation model, we can apply its inverse transformation for the geometric restoration to remove the distortion. The harmonic model is a very important one, which can cover other linear and nonlinear geometric models. However, its implementation is very complicated, because it cannot be described by any fixed functions in mathematics. In fact, it is represented by a partial differential equation with a given boundary condition. In the paper a wavelet-based method is presented to handle the harmonic model. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performances are evaluated by experiments.