Application Of Partial Differential Equations In Image Processing

This thesis focuses on some basic definitions of Partial Differential Equations method in image processing and builds the bridge between the image and mathematical models. According the analysis of some PDEs’ characters, we can finally give the good result of related image processing. It will divide in parts to introduce the PDEs’ method in image processing. Image denosing and image segmentation are the most important part of this thesis. At the last, this thesis will also give the detail application of PDE based image processing in facial recognition.In first chapter, we briefly give the research background and motivation of this dis-sertation, and some other methods, applications in the areas of image processing.In Chapter2, we show some basic definitions and mathematical preliminaries, in-cluding the definition of image model, some image processing functional. We will also give an important mathematical method, the level set method, at the last of this chapter. This method will solve the numerical calculation of Partial Differential Equations by give the evolution of curve. Furthermore, a variation level set method and its applications are also given in this chapter.During the Chapter3, we begin to introduce the restoration models of PDEs’image processing. By elicitation of energy method, giving the affect of Heat Equation, we state the PM model, which can overcome the side effects of Heat Equation denosing. At the end of this chapter, we show the Shock Filter and its results in image deblurring.Some classical PDEs’image segmentation models are given in fourth chapter. By introducing the Mumford-Shah functional, we get the GAC model and CV model with their segmentation results. It is also give some idea of how to modify the Mumford-Shah segmentation model.At last, combined with the models given in previous chapters, we will show some applications of these models in facial recognition and the advantages and disadvantages of PDEs based method in facial recognition.