The Research On Image Inpainting Based On Variational Partial Differential Equation

With the rapid development of computer and digital technology,the digital image processing technology has been applied in various fields widely.And the combination of digital image processing technology and hardware equipment makes tremendous contributions to the human society.The image restoration is an important research field in digital image processing,including image transformation,image filtering,image inpainting and so on.Image inpainting is a research content not merely in digital image processing,but in other fields such as computer,mathematics,signal theory and various kinds of teleinformatics as well.Image inpainting is mainly used to restore loss or destruction regions of images with given law and meets the viewer's visual perception.In Renaissance,the image inpainting was firstly applied to repair works of art and protect cultural relics,while at present,as the development of the technology and the mathematical theory,it is also applied to repair old photos,remove image text or obstacles,conceal video errors and handle medical image procession.It started earlier overseas and developing vigorously,while the domestic is still in its infancy.According to the image damage degree,image inpainting technology can be divided into three types: the methods based on variation partial differential equations,texture synthesis and image decomposition currently.In this paper,we mainly study the first one and related questions.The main work includes the following aspects:(1)An overview of the production and development of image inpainting,research status at home and abroad and the relevant algorithms.(2)Introduction about the mathematical knowledge of image restoration and basis of digital image technology.Mathematical knowledge includes the best guess and Bias framework theory,energy functional,Gauss iteration,variation theory,the two-order directional derivative method and central difference method.Image knowledge includes image degradation model,bounded variation space,image diffusion method and evaluation criteria.(3)Statement on classical algorithms of image inpainting and the description improved algorithms proposed by scholars domestic and abroad in recent years.Classic algorithms include Total Variation,Driven Diffusions Curvature,P-Laplace model and harmonic model.Improved algorithms include the modified TV algorithm,the hybrid model combined with the TV and the P-Laplace model,the improved CDD model and the adaptive CDD model.Finally,the advantages and disadvantages of the above algorithms will be analyzed in the form of experimental data and image contrast.(4)To solve the problems of the classical algorithm,new improved algorithms are proposed in this paper through adjusting the diffusion coefficients of the gradient direction and erpendicular to the gradient direction.These algorithms include the methods based on adaptive P-Laplace,adaptive high order variation in eight neighbors and the adaptive hybrid model.The simulation experiment results show that the images obtained by the proposed algorithms in the paper have good evaluations compared with the image inpainting algorithms in recent years,which verifies the effectiveness and rationality of the improved algorithms.