The total variation-based Rudin-Osher-Fatemi model is an effective and popular prior model in the image processing problem. Different to frequently using the splitting scheme to directly solve this model, we propose the primal dual method to solve the smoothing total variation-based Rudin-Osher-Fatemi model and give some convergence analysis of proposed method. Numerical implements show that our proposed model and method can efficiently improve the numerical results compared with the Rudin-Osher-Fatemi model.

Image segmentation is a fundamental problem in both image processing and computer vision with numerous applications. In this paper, we propose a two-stage image segmentation scheme based on inexact alternating direction method. Specifically, we first solve the convex variant of the Mumford-Shah model to get the smooth solution, the segmentation are then obtained by apply the K-means clustering method to the solution. Some numerical comparisons are arranged to show the effectiveness of our proposed schemes by segmenting many kinds of images such as artificial images, natural images, and brain MRI images.

Recently, variational and partial differential equation (PDE)-based algorithms have become very important for image restoration. In this study, we propose a new second order hyperbolic PDE model based on directional diffusion for image restoration. This hyperbolic PDE restoration model can simply diffuse along the edge's tangential direction in the observed image, thereby removing noise while preserving the image edges and fine details, which avoids the staircase effect in the restored image. An effective numerical scheme is proposed for handling the computation of our approach using the finite difference method. Successful image restoration experiments demonstrated that the proposed second order hyperbolic PDE-based model obtains superior performance compared with other models at preserving edges and it avoids the staircase effect. INDEX TERMSHyperbolic partial differential equation, Direction diffusion, Image restoration.

Image inpainting is an active research area in the image processing field. The essential idea of image inpainting algorithm is to fill in the missing or damaged regions with available information from their surroundings. In this paper, we propose two image inpainting models based on the variational method. We show that the diffusion performance of the proposed models for image inpainting are superior to classical total variation (TV) inpainting model according to the physical characteristics in local coordinates. To show the effective performance of the proposed models, we apply it to restoring of scratched photos, text removal and even removal of entire objects from images.