Research On Image Denoising And Registration Algorithm Based On Fractional-order Calculus

Image denosing and image registration are the two core subjects in the field of computer vision. The natural images often contain weak edge and texture details which are the improtant information of the image.The existing image denosing algorithms cant’t keep edge and texture details well and the exiting image registration methods are mainly for some simple texture image.There are few methods about the complex textures up to now.This paper is based on image denoising and image registration problem,and research the texture image modeling and numerical algorithm with mathematical tools of fractional calculus,variational method and the theory of primal-dual.The main work is as follows:1.The famous total variation model proposed by Rudin,Osher and Fatemi(ROF)performs well in keeping edges while image denoising. However, the ROF model usually leads to block effect. The fractional order variation model has been proved to be capable of avoiding block effect, but the fine details such as textures are often filtered out with noise. Aiming at the problem, this paper proposed a new adaptive projection algorithm to calculate the fractional order variation model. Firstly, the proposed method uses Grünwald-Letnikov fractional order differential in the regularization term instead of the first order derivative, and projects the image on a total variation ball. Then, the image is divided into texture area and non-texture one according to the image local information, thus the soft threshold value can be calculated adaptively. The experimental results show that the proposed method can not only eliminate the block effect but also preserve the texture details effectively while removing noise.2.TV-L~1 optical flow model has been proved to be an effective way to solve the non-rigid registration problem,it can solve the problem of fuzzy edge caused by the smooth displacement fields of Horn-Schunck,but its first order derivative in regularization term leads to fuzzy texture information with weak derivative property.Aiming at the problem,this paper introduces G-L(Grünwald-Letnikov)fractional differentiation to TV-L~1 optical flow model,and proposes a new TV-L~1 optical flow model based on fractional differentiation,then applies primal-dual algorithm for the solution of the model.In this paper we use Grünwald-Letnikov fractional order differential instead of the first order derivative in the regularization term for its better ability of detail descripton than first order’s.Then we can purposefully control to retain or inhibit the texture information with weak derivative nature,thus registration accuracy is improved.The experimental results show that the proposed method has better registration accuracy in the registration of texture information with characteristics of weak derivative,and it can be seen generalization of TV-L~1 optical flow modes.