Research On Nonconvex Image Restoration And Multiscale Image Segmentation Based On The Variation Method

Digital image is the most important carrier for humans to obtain information.Among the information obtained by human beings,the image information accounts for about 75%and transmits faster.Therefore,digital images play an important role in life.However,the digital image often be degraded by the aged imaging equipment and multivariate external environment,which may affects the result of subsequent image processing.In order to analyse the information effectively,the image should be processed by using the computer technology.The image retoration and segmentation are the preliminary works that affect on the results of image analysis and understanding.In recent years,the image processing technique that based the variation method attracts extensive attention with the excellent theoretical basis and effective experiment results.In general,the image processing model that based the variation method constructs the energy functional according to the priori knowledge of image,and then minimizes the energy to get the image processing results by the optimization technique.In this thesis,we analyse and research the advantages and disadvantages of some existing variational model,and do some improvements that are summarized as following:1.The third charpter presents a nonconvex and nonsmooth total generalized variation?TGV?model for image restoriation.Compared to the convex ₁l norm of traditional TGV,our model can measure the variation better and provide a more sparse representation of image function by using the potential function that is nonconvex and nonsmooth,which can preserve the edges and eliminate the staircase effects simultaneously by combining the merits of TGV model and nonconvex model.And the new model introduces two iteratively reweighed algorithms to solve the nonconvex and nonsmooth model effectively.In the experiment,the recovery results obtained by the two kinds of solving algorithms are compared firstly,the experimental results and evaluation indicators of comparison experiments illustrate that our model can effectively preserve the edges and eliminate the staircase effects.2.The forth charpter proposes a variational level set model for multiscale image segmentation.By introducing the multiscale representation of image,our model can extract the different objects from the background under different scales.In the energy functional of our novel model,there are three energies for different purpose,i.e.,boundary extraction term,regularization term,multiscale representation term.The boundary extraction term that based on the region-based image segmentation model is utilized to extract the boundaries of multiscale representing image.The regularization term consists of the length term and level set regularization term that are used for ensuring the smoothness and stabilization of evolution contour respectively.The multiscale representation term that based on the total variation model in image restoration is used for representing the giving image with different scales.And then,we introduce the alternating iterative algorithm and gradient descent algorithm to minimize the energy,and use the alternating direction method of multipliers?ADMM?to solve the multiscale representing of image.Finally,the experimental results demonstrate that our model can effectively get the multiscale segmentation results and can be applied for the image denoising.