  During a surface acquisition process using 3D scanners, noise is inevitable
and an important step in geometry processing is to remove these noise
components from these surfaces (given as points-set or triangulated mesh). The
noise-removal process (denoising) can be performed by filtering the surface
normals first and by adjusting the vertex positions according to filtered
normals afterwards. Therefore, in many available denoising algorithms, the
computation of noise-free normals is a key factor. A variety of filters have
been introduced for noise-removal from normals, with different focus points
like robustness against outliers or large amplitude of noise. Although these
filters are performing well in different aspects, a unified framework is
missing to establish the relation between them and to provide a theoretical
analysis beyond the performance of each method.
  In this paper, we introduce such a framework to establish relations between a
number of widely-used nonlinear filters for face normals in mesh denoising and
vertex normals in point set denoising. We cover robust statistical estimation
with M-smoothers and their application to linear and non-linear normal
filtering. Although these methods originate in different mathematical theories
- which include diffusion-, bilateral-, and directional curvature-based
algorithms - we demonstrate that all of them can be cast into a unified
framework of robust statistics using robust error norms and their corresponding
influence functions. This unification contributes to a better understanding of
the individual methods and their relations with each other. Furthermore, the
presented framework provides a platform for new techniques to combine the
advantages of known filters and to compare them with available methods.
