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Abstract:
In this paper, we develop a method for generating
a high-quality approximation of a noisy set of points sampled
from a smooth surface by a sparse triangle mesh. The main
idea of the method consists of defining an appropriate set
of approximation centers and use them as the vertices
of a mesh approximating given scattered data.
To choose the approximation centers, a clustering
procedure is used. With every point of the input data
we associate a local uncertainty
measure which is used to estimate the importance of
the point contribution to the reconstructed surface.
Then a global uncertainty measure is constructed from local ones.
The approximation centers are chosen as the points where
the global uncertainty measure attains its local minima.
It allows us to achieve a high-quality approximation of uncertain and
noisy point data by a sparse mesh. An interesting feature of our
approach
is that the uncertainty measures take into account the normal
directions
estimated at the scattered points.
In particular it results in accurate reconstruction of high-curvature
regions.
