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キーワード:
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要旨:
In this paper, we investigate the problem of statistical reconstruction of
piecewise linear manifold topology. Given a noisy, probably undersampled point
cloud from a one- or two-manifold, the algorithm reconstructs an approximated
most likely mesh in a Bayesian sense from which the sample might have been
taken. We incorporate statistical priors on the object geometry to improve the
reconstruction quality if additional knowledge about the class of original
shapes is available. The priors can be formulated analytically or learned from
example geometry with known manifold tessellation. The statistical objective
function is approximated by a linear programming / integer programming problem,
for which a globally optimal solution is found. We apply the algorithm to a set
of 2D and 3D reconstruction examples, demon-strating that a statistics-based
manifold reconstruction is feasible, and still yields plausible results in
situations where sampling conditions are violated.
