  Gaussian curvature is an important geometric property of surfaces, which has
been used broadly in mathematical modeling. Due to the full nonlinearity of the
Gaussian curvature, efficient numerical methods for models based on it are
uncommon in literature. In this article, we propose an operator-splitting
method for a general Gaussian curvature model. In our method, we decouple the
full nonlinearity of Gaussian curvature from differential operators by
introducing two matrix- and vector-valued functions. The optimization problem
is then converted into the search for the steady state solution of a time
dependent PDE system. The above PDE system is well-suited to time
discretization by operator splitting, the sub-problems encountered at each
fractional step having either a closed form solution or being solvable by
efficient algorithms. The proposed method is not sensitive to the choice of
parameters, its efficiency and performances being demonstrated via systematic
experiments on surface smoothing and image denoising.
