The Study Of Image Processing By The PDE Method

The Partial Differential Equation (PDE) Method on Digital Image Processing has developed rapidly in recent years. The PDE method aims to build mathematical model of partial differential equation and make the image change following the partial differential equation. Finally the image will achieve our goal. The image processing by the traditional method will never reach the effect using the PDE method. According to domestic and overseas studied conditions, we discuss four kinds of PDE models including image de-noising, image imprinting, image segmentation and image enhancement. We also analyze the establishment of partial differential equations, the solution of partial different equations and the implementation of partial differential equations. This paper will analyse the model of GAC in detail.The innovative work in this paper is as followings:1In the GAC model, the stop function plays a very important role in the segmentation of the image. This paper will study the selection of different decreasing functions. Numerous references indicate that the stop function should be decreasing function. In fact, not all of the decreasing functions can segment the image well. This paper selected three different forms of the decreasing functions as stop function to segment the image as followings:We can observe the result of the image segmentation and make the conclusion. The conclusion is that the stop function must have the characteristic of deeply stopped to zero instead of having a long tail.2This paper select three different initial curves (roundness, oval, square) to do the experiments. The result is the three different curves can finish the image segmentation well. The conclusion is that the GAC model has a good adaptation for initial curve.3In the process of the image smoothing, this paper choose as the characteristic of the image instead of|▽u|in the process of smoothing. The result indicates that has better smoothing characteristic and high efficiency of the algorithm.