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Abstract:
Point samples of a surface in $\R^3$ are the dominant output of a
multitude of 3D scanning devices. The usefulness of these devices rests on
being able to extract properties of the surface from the sample. We show that, under
certain sampling conditions, the minimum cycle basis of a nearest neighbor graph of
the sample encodes topological information about the surface and yields bases for the
trivial and non-trivial loops of the surface. We validate our results by experiments.
