# Wednesday 18th June 2008

## Pierre ALLIEZ (INRIA GEOMETRICA, Sophia-Antipolis, France)

## Surface Reconstruction from Unoriented Point Sets

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Slides: presentation.pdf

*Abstract*

I will present 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.
This 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.