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A Bayesian approach to manifold topology reconstruction

Tevs, Art and Wand, Michael and Ihrke, Ivo and Seidel, Hans-Peter

MPI-I-2009-4-002. January 2010, 23 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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, demonstrating
that a statistics-based manifold reconstruction is feasible, and still
yields plausible results in situations where sampling conditions are
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  AUTHOR = {Tevs, Art and Wand, Michael and Ihrke, Ivo and Seidel, Hans-Peter},
  TITLE = {A Bayesian approach to manifold topology reconstruction},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2009-4-002},
  MONTH = {January},
  YEAR = {2010},
  ISSN = {0946-011X},