Image Fusion Based On Calculus Of Variations And Partial Differential Equations

Image fusion is to fuse the information of two or more images into a new image through appropriate rules and means,which makes the fused image more reliable,more comprehensive and less redundant,so as to improve the ability of subsequent image detection,classification,recognition and understanding.At present,image fusion technology is widely used in remote sensing observation,military reconnaissance,weather forecast and digital imaging.At the same time,due to the limitations of imaging equipment,the image is often affected by noise,blur and other factors.Therefore,how to overcome these difficulties and improve the quality of fused image has always been the difficulty of image fusion.In this paper,image fusion method based on variational partial differential equation is studied:Firstly,the theory of variance maximization in image decolorization is introduced.Because the model of image decolorization based on variance maximization proposed by Jin et al uses the information of local covariance matrix and local mean vector in the numerical solution process,it is easy to lose the detail information in multi texture color image decolorization.Based on Jin model and primal dual algorithm,a new fast algorithm is designed.Experimental results show that the proposed algorithm can better retain the texture and other details of the source color image,and the effect of color removal is better.Secondly,the existing variational fusion methods are very sensitive to noise and the fusion results are prone to artifacts.In this paper,by introducing the maximum variance method,an image fusion variational model with adaptive weight is proposed,and the existence of the solution of the proposed variational model is proved.Also,the convexity of the model to each variable is analyzed.Furthermore,combined with the primal dual algorithm,a fast algorithm of the proposed model is given.The experimental results show that the proposed model can not only effectively fuse images,but also suppress noise.Finally,by introducing the definitions of pseudo saddle point and critical pseudo saddle point,it is proved that the proposed model has pseudo saddle point and the fixed point of the proposed algorithm is the critical pseudo saddle point of the proposed model.Furthermore,the results of convergence to the critical pseudo saddle point of the model are given.