research-article

Weighted Minimal Hypersurface Reconstruction

Authors:

Bastian Goldlucke,

Christian Linz,

Marcus MagnorAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 29, Issue 7

Pages 1194 - 1208

https://doi.org/10.1109/TPAMI.2007.1146

Published: 01 July 2007 Publication History

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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Cited By

Weinmann MKlein R(2015)Advances in geometry and reflectance acquisition (course notes)SIGGRAPH Asia 2015 Courses10.1145/2818143.2818165(1-71)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2818143.2818165
Li ZWang KJia WChen HZuo WMeng DSun M(2015)Multiview stereo and silhouette fusion via minimizing generalized reprojection errorImage and Vision Computing10.1016/j.imavis.2014.10.00833:C(1-14)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.imavis.2014.10.008
Balzer J(2012)A Gauss-Newton Method for the Integration of Spatial Normal Fields in Shape SpaceJournal of Mathematical Imaging and Vision10.1007/s10851-011-0311-144:1(65-79)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.1007/s10851-011-0311-1
Show More Cited By

Index Terms

Weighted Minimal Hypersurface Reconstruction
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
        Reconstruction
  2. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Information

Published In

cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 29, Issue 7

July 2007

193 pages

ISSN:0162-8828

Issue’s Table of Contents

Copyright © 2007.

Publisher

IEEE Computer Society

United States

Publication History

Published: 01 July 2007

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Cited By

Weinmann MKlein R(2015)Advances in geometry and reflectance acquisition (course notes)SIGGRAPH Asia 2015 Courses10.1145/2818143.2818165(1-71)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2818143.2818165
Li ZWang KJia WChen HZuo WMeng DSun M(2015)Multiview stereo and silhouette fusion via minimizing generalized reprojection errorImage and Vision Computing10.1016/j.imavis.2014.10.00833:C(1-14)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.imavis.2014.10.008
Balzer J(2012)A Gauss-Newton Method for the Integration of Spatial Normal Fields in Shape SpaceJournal of Mathematical Imaging and Vision10.1007/s10851-011-0311-144:1(65-79)Online publication date: 1-Sep-2012
https://dl.acm.org/doi/10.1007/s10851-011-0311-1
Delaunoy APrados E(2011)Gradient Flows for Optimizing Triangular Mesh-based SurfacesInternational Journal of Computer Vision10.1007/s11263-010-0408-995:2(100-123)Online publication date: 1-Nov-2011
https://dl.acm.org/doi/10.1007/s11263-010-0408-9
Taneja ABallan LPollefeys M(2010)Modeling dynamic scenes recorded with freely moving camerasProceedings of the 10th Asian conference on Computer vision - Volume Part III10.5555/1966049.1966098(613-626)Online publication date: 8-Nov-2010
https://dl.acm.org/doi/10.5555/1966049.1966098
Balzer JHöfer SWerling SBeyerer J(2010)Optimization on shape curves with application to specular stereoProceedings of the 32nd DAGM conference on Pattern recognition10.5555/1926258.1926265(41-50)Online publication date: 22-Sep-2010
https://dl.acm.org/doi/10.5555/1926258.1926265
Sharf AAlcantara DLewiner TGreif CSheffer AAmenta NCohen-Or D(2008)Space-time surface reconstruction using incompressible flowACM SIGGRAPH Asia 2008 papers10.1145/1457515.1409063(1-10)Online publication date: 10-Dec-2008
https://dl.acm.org/doi/10.1145/1457515.1409063
Sharf AAlcantara DLewiner TGreif CSheffer AAmenta NCohen-Or D(2008)Space-time surface reconstruction using incompressible flowACM Transactions on Graphics10.1145/1409060.140906327:5(1-10)Online publication date: 1-Dec-2008
https://dl.acm.org/doi/10.1145/1409060.1409063
Vlasic DBaran IMatusik WPopović J(2008)Articulated mesh animation from multi-view silhouettesACM SIGGRAPH 2008 papers10.1145/1399504.1360696(1-9)Online publication date: 11-Aug-2008
https://dl.acm.org/doi/10.1145/1399504.1360696
Vlasic DBaran IMatusik WPopović J(2008)Articulated mesh animation from multi-view silhouettesACM Transactions on Graphics10.1145/1360612.136069627:3(1-9)Online publication date: 1-Aug-2008
https://dl.acm.org/doi/10.1145/1360612.1360696

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