Total Bending Method for Piecewise Smoothing Image Denoising

Abstract

Since the seminar work by Rudin, Osher, and Fatami for total variation (TV) model, piecewise smoothing image is favored in a diversity of related fields. To recover a piecewise smoothing image, we propose a high order anisotropic geometrical model which we name total bending (TB) in a multiplicative strategy. TB model measures the bending degree of the image surface by approximating its second fundamental form. The analysis shows that TB is a rotation version of TV model in moving Frenet–Serret frame: TB norm measures the jumps along the normal direction in an adaptive local coordinate while TV measures the jumps along the vertical direction in a fixed Cartesian coordinate. TB reduces undesired staircase effect by recovering the horizontal and slope surface. The evolution diffusion of TB model inherits TV’s edge preserving ability. The experimental results show the performance of the proposed model quantitatively and visually.