  Total Generalized Variation (TGV) has recently been proven certainly
successful in image processing for preserving sharp features as well as smooth
transition variations. However, none of the existing works aims at numerically
calculating TGV over triangular meshes. In this paper, we develop a novel
numerical framework to discretize the second-order TGV over triangular meshes.
Further, we propose a TGV-based variational model to restore the face normal
field for mesh denoising. The TGV regularization in the proposed model is
represented by a combination of a first- and second-order term, which can be
automatically balanced. This TGV regularization is able to locate sharp
features and preserve them via the first-order term, while recognize smoothly
curved regions and recover them via the second-order term. To solve the
optimization problem, we introduce an efficient iterative algorithm based on
variable-splitting and augmented Lagrangian method. Extensive results and
comparisons on synthetic and real scanning data validate that the proposed
method outperforms the state-of-the-art methods visually and numerically.
