Image Denoising And Boundary Extraction Based On Game Theory

Digital image processing is a computer method and technology used for noise elimination,improvement,restoration,feature extraction and other issues.In practical problems,several tasks often occur at the same time.Due to different imaging tasks and different image processing targets,the selection of optimization targets will be affected.Image segmentation is a process of extracting target objects from images and is one of the most important problems in image processing.It has been widely used in the fields of target recognition,image analysis,motion detection and so on.In most cases,the image to be segmented is polluted by noise,which will affect the subsequent image fusion and edge detection.Therefore,while maintaining the integrity of image features as much as possible,noise on the image should be reduced and useless information in the image should be removed.On the one hand,for denoising,discontinuous noise details in the image need to be eliminated;On the other hand,for boundary extraction,it is necessary to keep the discontinuity of the image.Therefore,for the same image,we need to make two opposing decisions of denoising and edge detection.Under such circumstances,it is very appropriate to use game theory to solve this problem.Game theory is a mathematical theory and method,which is used to analyze the mutual influence of decision-making among multiple participants and has been widely applied in the field of image processing.In this paper,the game theory is used to denoise the image and extract the boundary simultaneously.We have defined two participants,one is the image denoising method based on image intensity and the other is the boundary extraction method based on image gradient.This problem is expressed as a static non-cooperative game problem with complete information.By selecting appropriate image denoising and boundary extraction methods,two game models are established.In order to ensure the theoretical correlation of the two games,the regularization term of image denoising method is reconstructed.In the first task we completed,the cost functions we selected were the classical half-quadratic regularization function and the global sparse gradient model,which are relatively novel boundary extraction functions.Since the auxiliary variable in the half-quadratic regularization model represents the contour of the image,we substitute the gradient obtained from the global sparse gradient model for this auxiliary variable to further optimize the obtained boundary.Considering that natural images carry a large amount of information,the human visual system will interpret the information.The image processor we design needs to consider the influence of human visual psychology.In the second task,we still select the global gradient sparse model in the boundary extraction part,while the image denoising model selects the Weberized TV model.The Weberized TV model takes into account the human visual problems,and expresses the regular term as Weber constant.In our game model,the regular term of the Weberized TV model is improved again to complete the game with the global sparse gradient model.The two participants,image denoising and boundary extraction,iterate alternately in a game process,and their convergence points serve as Nash equilibrium points.The proposed model is applied to various types of images and the numerical experiments show the effectiveness and robustness of the algorithm.