  The curvature regularities are well-known for providing strong priors in the
continuity of edges, which have been applied to a wide range of applications in
image processing and computer vision. However, these models are usually
non-convex, non-smooth and highly non-linear, the first-order optimal condition
of which are high-order partial differential equations. Thus, the numerical
computation are extremely challenging. In this paper, we propose to estimate
the discrete curvatures, i.e., mean curvature and Gaussian curvature, in the
local neighborhood according to differential geometry theory. By minimizing
certain functions of curvatures on all level curves of an image, it yields a
kind of weighted total variation minimization problem, which can be efficiently
solved by the proximal alternating direction method of multipliers (ADMM).
Numerical experiments are implemented to demonstrate the effectiveness and
superiority of our proposed variational models for different image
reconstruction tasks.
