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  A Bayesian Approach to Manifold Topology Reconstruction

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.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-1722-7 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-2D8D-2
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 Creators:
Tevs, Art1, 2, Author           
Wand, Michael1, Author           
Ihrke, Ivo1, 3, Author           
Seidel, Hans-Peter1, Author                 
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              
2International Max Planck Research School, MPI for Informatics, Max Planck Society, ou_1116551              
3Graphics - Optics - Vision, MPI for Informatics, Max Planck Society, ou_1116549              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2011-01-272010
 Publication Status: Issued
 Pages: 23 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 537282
ISSN: 0946-011X
BibTex Citekey: TevsTechReport2009
Report Nr.: MPI-I-2009-4-002
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