Research On Image Processing Based On A Class Of Fourth Order Partial Diffusion Equations

Image denoising has always been an important and challenging task in the field of image processing.The image denoising method based on partial differential equation(PDE)has gradually become a kind of efficient mainstream method in the past few decades.For additive noise denoising,it is divided into two categories: variational PDE method and diffusion PDE method.However,the second-order PDE approximates the original image by the piecewise plane,so the second-order denoising model has a "staircase" effect,which creates false edge in the flat region.The fourth-order equation approximates the original image by a piecewise planner,which can avoid the "staircase" effect in essence.However,the existing fourth-order denoising model does not preserve the edge of the image.In PDE image segmentation,the natural extension embedding function does not guarantee the distance function remains signed in evolution by traditional level set method.So it is necessary to re-initialize the level set function.This has an impact on the efficiency and accuracy of the segmentation.In response to the above problems we have done the following work:By comparing the advantages and disadvantages of the classical Y-K model and the LLT model,we construct a new fourth-order PDE from the perspective of the diffusion PDE for the properties of the fourth-order diffusion equation directly.Under the above ideas.In this paper,a class of four-order PDE denoising models based on image feature is proposed.We introduce the diffusion coefficient under the framework of the LLT model.The proposed models can adapt to the degree of diffusion according to the characteristics of the image.The fourth-order PDE diffusion coefficient is chosen for the second-order edge detection operator.We select the gradient operator as the diffusion coefficient.Gradient operator e dge detection is stronger and less affected by noise.A fourth-order regularization level set method is proposed by applying the proposed fourth-order term to the variational level set segmentation model.Directly from the evolution equation of the embedded function,the fourth order term is coupled to avoid reinitialization.For the numerical realization of the model,this paper first gives the finite difference explicit scheme of the equation.After that time step for the issue seriously hampered the efficiency of the algorithm,designs a semi-implicit scheme,and introduces the addition operator splitting algorithm(AOS),the step size can be increased to achieve a compromise in efficiency and accuracy.Finally,the effect of the fourth-order denoising model is tested on different additive noise images and compared with the classical second-order and fourth-order models.The experimental results show that the new algorithm has a significant improvement in denoising and efficiency.In this paper,the fourth-order regularization level set method is compared with the classical method of regularized level set.It is found that this model allows a larger range of initial values and avoids the over-smoothness of geodesic active contours model.