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A Bayesian Approach to Manifold Topology Reconstruction

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45604

Tevs,  Art
Computer Graphics, MPI for Informatics, Max Planck Society;
International Max Planck Research School, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45695

Wand,  Michael
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44670

Ihrke,  Ivo
Graphics - Optics - Vision, MPI for Informatics, Max Planck Society;
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Volltexte (frei zugänglich)

technicalReport.pdf
(beliebiger Volltext), 668KB

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Zitation

Tevs, A., Wand, M., Ihrke, I., & Seidel, H.-P.(2010). A Bayesian Approach to Manifold Topology Reconstruction (MPI-I-2009-4-002). Saarbrücken: Max-Planck-Institut für Informatik.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-1722-7
Zusammenfassung
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.