  Recovering high quality surfaces from noisy triangulated surfaces is a
fundamental important problem in geometry processing.
  Sharp features including edges and corners can not be well preserved in most
existing denoising methods except the recent total variation (TV) and $\ell_0$
regularization methods.
  However, these two methods have suffered producing staircase artifacts in
smooth regions.
  In this paper, we first introduce a second order regularization method for
restoring a surface normal vector field, and then propose a new vertex updating
scheme to recover the desired surface according to the restored surface normal
field.
  The proposed model can preserve sharp features and simultaneously suppress
the staircase effects in smooth regions which overcomes the drawback of the
first order models.
  In addition, the new vertex updating scheme can prevent ambiguities
introduced in existing vertex updating methods.
  Numerically, the proposed high order model is solved by the augmented
Lagrangian method with a dynamic weighting strategy.
  Intensive numerical experiments on a variety of surfaces demonstrate the
superiority of our method by visually and quantitatively.
