  In this paper, we define and evaluate a weighting scheme for neighborhoods in
point sets. Our weighting takes the shape of the geometry, i.e., the normal
information, into account. This causes the obtained neighborhoods to be more
reliable in the sense that connectivity also depends on the orientation of the
point set. We utilize a sigmoid to define the weights based on the normal
variation. For an evaluation of the weighting scheme, we turn to a Shannon
entropy model for feature classification that can be proven to be
non-degenerate for our family of weights. Based on this model, we evaluate our
weighting terms on a large scale of both clean and real-world models. This
evaluation provides results regarding the choice of optimal parameters within
our weighting scheme. Furthermore, the large-scale evaluation also reveals that
neighborhood sizes should not be fixed globally when processing models.
Finally, we highlight the applicability of our weighting scheme withing the
application context of denoising.
