Study On Image Inpainting Algorithm Based On Partial Differential Equation

Image inpainting is a technology that uses the known information in the image to repair the damaged area,so that the restored image can meet human visual requirements.After years of development,image inpainting technology has achieved many important research results.Among them,image inpainting algorithm based on partial differential equations(PDE)is one of the widely used image inpainting algorithms.The typical image inpainting algorithms based on partial differential equations include:Total Variation(TV)inpainting algorithm,Curvature-Driven Diffusions(CDD)inpainting algorithm and so on.The inpainting algorithm based on TV model costs more iterations and time.Moreover,the restored images have ambiguity effect and staircase effect.The inpainting algorithm based on CDD model costs more iterations and time,and failure to repair boundary damaged images.In view of the above problems in TV algorithm model and CDD algorithm model,we propose optimization algorithms based on the TV model and the CDD model in this paper.The main research contents are as follows:(1)Aiming at the problem that TV model costs more iterations and time,we propose an improved image inpainting algorithm based on TV model.Firstly,the diffusion accommodation coefficient is added into the regularization term.Secondly,a self-adaptive parameter that varies with the number of iterations is added to the diffusion accommodation coefficient.Thus,the algorithm diffuses at a faster speed in the early iteration and slows down in the later iteration,and the restored image maintains a sharp edge.Simulation results show that the improved algorithm reduces the number of iterations and running time in the scratch and text removal,and the restored image has good visual effect.(2)Aiming at the problem that TV model has ambiguity effect and staircase effect.We propose a total variation inpainting algorithm based on logarithmic operation and additional directional gradient operator.Firstly,an additional directional gradient operator is added into the regular term of the original algorithm,which reduces the total number of iterations and avoids the ambiguity effect caused by too many iterations.Secondly,the logarithmic operation is added into the regular term of the original algorithm,thus avoiding the staircase effect caused by the non-linear equation.Simulation results show that the improved algorithm improves the image quality.(3)CDD inpainting algorithm needs more iterations and time when repairing images.In addition,the algorithm cannot repair the damaged points where they are in the image boundary.Aiming at the problems of the CDD inpainting algorithm,an algorithm based on corrosion treatment and multi-parameter factors is proposed in this paper.The main steps of the algorithm are as follows:Firstly,the image mask to be repaired is corroded before the damaged image is repaired,thus avoiding the waste of time caused by oversize of mask.Secondly,in the calculation of curvature and gradient modulus,a natural logarithmic exponential factor and a linear exponential factor are introduced respectively.By adjusting the parameters of different exponential factors,the effect of unreasonable gradient modulus and curvature values on diffusion rate is avoided.In addition,a self-adaptive positive lifting parameter varying with the number of iterations is introduced to calculate the curvature and gradient modulus,so that the damaged area can be repaired better.Finally,aiming at the images with broken boundary,the corresponding boundary treatment conditions are adopted according to the locations of their boundaries,thus avoiding the problem that the broken boundary is unable to be repaired.Simulation results show that the improved algorithm reduces the repair time,and the image with broken boundary can be repaired well.