Sparse meshing of uncertain and noisy surface scattered data

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