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Journal of Mathematical Imaging and Vision

, Volume 51, Issue 1, pp 98–105 | Cite as

2-Manifold Tests for 3D Delaunay Triangulation-Based Surface Reconstruction

  • Maxime Lhuillier
Article

Abstract

This is a companion paper of a previous work on the surface reconstruction from a sparse cloud of points, which are estimated by Structure-from-Motion. The surface is a 2-manifold sub-complex of the 3D Delaunay triangulation of the points. It is computed as the boundary of a list of tetrahedra, which grows in the set of Delaunay tetrahedra. Here we detail the proofs for the 2-manifold tests that are used during the growing: we show that the tetrahedron-based test and the test for adding (or subtracting) one tetrahedron to (or from) the list are equivalent to standard tests based on triangles.

Keywords

Reconstruction Volumetric models  Geometric topology Duality and planar graphs 

Supplementary material

10851_2014_508_MOESM1_ESM.pdf (176 kb)
ESM 1 (PDF 176 kb)

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut PascalAubière cedexFrance

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