Minimizing Discrete Total Curvature for Image Processing

The curvature regularities have received growing attention with the advantage of providing strong priors in the continuity of edges in image processing applications. However, owing to the non-convex and non-smooth properties of the high-order regularizer, the numerical solution becomes challenging in real-time tasks. In this paper, we propose a novel curvature regularity, the total curvature (TC), by minimizing the normal curvatures along different directions. We estimate the normal curvatures discretely in the local neighborhood according to differential geometry theory. The resulting curvature regularity can be regarded as a re-weighted total variation (TV) minimization problem, which can be efficiently solved by the alternating direction method of multipliers (ADMM) based algorithm. By comparing with TV and Euler's elastica energy, we demonstrate the effectiveness and superiority of the total curvature regularity for various image processing applications.