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2007

Voronoi-based variational reconstruction of unoriented point sets

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Voronoi-based variational reconstruction of unoriented point sets
We introduce an algorithm for reconstructing watertight surfaces from unoriented point sets. Using the Voronoi diagram of the input point set, we deduce a tensor field whose principal axes and eccentricities locally represent respectively the most likely direction of the normal to the surface, and the confidence in this direction estimation. An implicit function is then computed by solving a generalized eigenvalue problem such that its gradient is most aligned with the principal axes of the tensor field, providing a best-fitting isosurface reconstruction. Our approach possesses a number of distinguishing features. In particular, the implicit function optimization provides resilience to noise, adjustable fitting to the data, and controllable smoothness of the reconstructed surface. Finally, the use of simplicial meshes (possibly restricted to a thin crust around the input data) and (an)isotropic Laplace operators renders the numerical treatment simple and robust. Categories and Subject...
Pierre Alliez, David Cohen-Steiner, Yiying Tong, M
Added 30 Sep 2010
Updated 30 Sep 2010
Type Conference
Year 2007
Where SGP
Authors Pierre Alliez, David Cohen-Steiner, Yiying Tong, Mathieu Desbrun
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