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  Weighted Minimal Hypersurface Reconstruction

Goldlücke, B., Ihrke, I., Linz, C., & Magnor, M. (2007). Weighted Minimal Hypersurface Reconstruction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(7), 1194-1208. doi:10.1109/TPAMI.2007.1146.

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Goldluecke2006_WeightedMinimalSurfaces.pdf (Publisher version), 2MB
 
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 Creators:
Goldlücke, Bastian1, Author           
Ihrke, Ivo1, 2, Author           
Linz, Christian3, Author           
Magnor, Marcus3, Author           
Affiliations:
1Graphics - Optics - Vision, MPI for Informatics, Max Planck Society, ou_1116549              
2Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              
3External Organizations, ou_persistent22              

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 Abstract: Many problems in computer vision can be formulated as a minimization problem for an energy functional. If this functional is given as an integral of a scalar-valued weight function over an unknown hypersurface, then the sought-after minimal surface can be determined as a solution of the functional's Euler-Lagrange equation. This paper deals with a general class of weight functions that may depend on surface point coordinates as well as surface orientation. We derive the Euler-Lagrange equation in arbitrary dimensional space without the need for any surface parameterization, generalizing existing proofs. Our work opens up the possibility of solving problems involving minimal hypersurfaces in a dimension higher than three, which were previously impossible to solve in practice. We also introduce two applications of our new framework: We show how to reconstruct temporally coherent geometry from multiple video streams, and we use the same framework for the volumetric reconstruction of refractive and transparent natural phenomena, here bodies of flowing water.

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Language(s): eng - English
 Dates: 2007-07-1120072007
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 520722
BibTex Citekey: Goldluecke2006_WeightedMinimalSurfaces
DOI: 10.1109/TPAMI.2007.1146
URI: http://csdl.computer.org/dl/trans/tp/2007/07/i1194.pdf
Other: Local-ID: C1256BDE005F57A8-6E53AE509D99514CC125722D00791979-Goldluecke2006_WeightedMinimalSurfaces
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Title: IEEE Transactions on Pattern Analysis and Machine Intelligence
Source Genre: Journal
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Publ. Info: Piscataway, NJ : IEEE
Pages: - Volume / Issue: 29 (7) Sequence Number: - Start / End Page: 1194 - 1208 Identifier: -