Integral Equation-Wavelet Collocation Method for Geometric Transformation and Application to Image Processing

摘要

Geometric (or shape) distortion may occur in the data acquisition phase in information systems, and it can be characterized by geometric transformation model. Once the distortedimage is approximated by a certain geometric transformation model, we can apply its inversetransformation to remove the distortion for the geometric restoration. Consequently, findinga mathematical form to approximate the distorted image plays a key role in the restoration. A harmonic transformation cannot be described by anyfixed functions in mathematics. In fact, it is represented by partial differential equation (PDE)with boundary conditions. Therefore, to develop an efficient method to solve such a PDE isextremely significant in the geometric restoration. In this paper, a novel wavelet-based methodis presented, which consists of three phases. In phase 1, the partial differential equation isconverted into boundary integral equation and representation by an indirect method. In phase2, the boundary integral equation and representation are changed to plane integral equationand representation by boundary measure formula. In phase 3, the plane integral equation andrepresentation are then solved by a method we call wavelet collocation. The performance of our method is evaluated by numerical experiments.