Image Smoothing Via Gradient Sparsity and Surface Area Minimization

Image smoothing is a very important topic in image processing. Among these image smoothing methods, the L0 gradient minimization method is one of the most popular ones. However, the L0 gradient minimization method suffers from the staircasing effect and over-sharpening issue, which highly degrade the quality of the smoothed image. To overcome these issues, we use not only the L0 gradient term for finding edges, but also a surface area based term for the purpose of smoothing the inside of each region. An alternating minimization algorithm is suggested to efficiently solve the proposed model, where each subproblem has a closed-form solution. Leveraging the introduced surface area term, the proposed method can effectively alleviate the staircasing effect and the over-sharpening issue. The superiority of our method over the state-of-the-art methods is demonstrated by a series of experiments.