The mean curvature flow problem numerical solution and applications to image processing.

摘要

The motion of a curve or a surface by curvature occurs in a wide variety of settings including but not limited to image noise removal, minimal surfaces, soap bubbles, and grid generation. The goal of this work is to present a model for noise removal from images based on diffusion by mean curvature. The first chapter is a very superficial review of motion by mean curvature. It also goes over some of the applications mentioned above with emphasis on noise removal. Chapter two reviews some existing methods for noise removal and introduces the models discussed in this dissertation. Chapter three presents in great detail discrete algorithms corresponding to the models introduced in Chapter two. We look in particular at several variations of the algorithm to improve noise removal from images. Chapter four presents experimental results of the model introduced in chapter two and the corresponding algorithms studied in Chapter three. Chapter four also attempts to give a “recipe” to remove noise from images based on experiments. Chapter four can be thought of as the driving force behind chapters two and three. Chapter five shows how the algorithm described in Chapter three can be extended for parallel computers and applications requiring non uniform grids.