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

Lhuillier, Maxime

doi:10.1007/s10851-014-0508-1

Cited by 8 publications

(15 citation statements)

References 12 publications

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“…Every triangle in c(T ) is included in exactly two tetrahedra in c(T ), except those in ∂T (we have ∂T = ∅). These exceptions are removed as in [2,14] to make easier proofs. Let v ∞ be an abstract vertex that is different to those in c(T ).…”

Section: Abstract Simplicial Complexesmentioning

confidence: 99%

“…According to [21,1,14], X is a 2-manifold iff for every vertex v ∈ c(X), there is a cycle a * such that X v = v×a * . Thus there are distinct vertices a i ∈ c(X v ) such that a * = a 1 -· · · -a m -a 1 .…”

Section: -Manifold Criterion For Simplicial Complexesmentioning

confidence: 99%

“…The two following lemmas are needed in its proof (the former is Lemma 3 in [14]. Proof We find a homeomorphism ϕ such that ϕ(|∂O|) = |∂(O ∪ {∆})|.…”

Section: Topology Of Surfaces ∂O Imentioning

confidence: 99%

“…Note that Appendix B of [14] provides a first version of the proof of Lemma 3 without details on steps 2 and 4. (Fig.…”

Section: Topology Of Surfaces ∂O Imentioning

confidence: 99%

“…Lemma 18 Proof This is Lemma 1 in [14] by replacing the set B by a single tetrahedron. The proof is very similar as the proof in Appendix A.1 of [14].…”

Section: Proof Of Theorem 10mentioning

confidence: 99%

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Overview of Shelling for 2-Manifold Surface Reconstruction Based on 3D Delaunay Triangulation

Lhuillier

2017

J Math Imaging Vis

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Recently, methods have been proposed to reconstruct a 2-manifold surface from a sparse cloud of points estimated from an image sequence. Once a 3D Delaunay triangulation is computed from the points, the surface is searched by growing a set of tetrahedra whose boundary is maintained 2-manifold. Shelling is a step that adds one tetrahedron at once to the growing set. This paper surveys properties that helps to understand the shelling performances: shelling provides most tetrahedra enclosed by the final surface but it can "get stuck" or block in unexpected cases.

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Section: Abstract Simplicial Complexesmentioning

confidence: 99%

Section: -Manifold Criterion For Simplicial Complexesmentioning

confidence: 99%

“…The two following lemmas are needed in its proof (the former is Lemma 3 in [14]. Proof We find a homeomorphism ϕ such that ϕ(|∂O|) = |∂(O ∪ {∆})|.…”

Section: Topology Of Surfaces ∂O Imentioning

confidence: 99%

“…Note that Appendix B of [14] provides a first version of the proof of Lemma 3 without details on steps 2 and 4. (Fig.…”

Section: Topology Of Surfaces ∂O Imentioning

confidence: 99%

“…Lemma 18 Proof This is Lemma 1 in [14] by replacing the set B by a single tetrahedron. The proof is very similar as the proof in Appendix A.1 of [14].…”

Section: Proof Of Theorem 10mentioning

confidence: 99%

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Overview of Shelling for 2-Manifold Surface Reconstruction Based on 3D Delaunay Triangulation

Lhuillier

2017

J Math Imaging Vis

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Efficient Moving Point Handling for Incremental 3D Manifold Reconstruction

Romanoni

Matteucci

2015

Image Analysis and Processing — ICIAP 2015

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Abstract. As incremental Structure from Motion algorithms become effective, a good sparse point cloud representing the map of the scene becomes available frame-by-frame. From the 3D Delaunay triangulation of these points, state-of-the-art algorithms build a manifold rough model of the scene. These algorithms integrate incrementally new points to the 3D reconstruction only if their position estimate does not change. Indeed, whenever a point moves in a 3D Delaunay triangulation, for instance because its estimation gets refined, a set of tetrahedra have to be removed and replaced with new ones to maintain the Delaunay property; the management of the manifold reconstruction becomes thus complex and it entails a potentially big overhead. In this paper we investigate different approaches and we propose an efficient policy to deal with moving points in the manifold estimation process. We tested our approach with four sequences of the KITTI dataset and we show the effectiveness of our proposal in comparison with state-of-the-art approaches.

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On Volumetric Shape Reconstruction from Implicit Forms

Wang

Hétroy-Wheeler

Boyer

2016

Computer Vision – ECCV 2016

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International audienceIn this paper we report on the evaluation of volumetric shape reconstruction methods that consider as input implicit forms in 3D. Many visual applications build implicit representations of shapes that are converted into explicit shape representations using geometric tools such as the Marching Cubes algorithm. This is the case with image based reconstructions that produce point clouds from which implicit functions are computed, with for instance a Poisson reconstruction approach. While the Marching Cubes method is a versatile solution with proven efficiency, alternative solutions exist with different and complementary properties that are of interest for shape modeling. In this paper, we propose a novel strategy that builds on Centroidal Voronoi Tessellations (CVTs). These tessellations provide volumetric and surface representations with strong regularities in addition to provably more accurate approximations of the implicit forms considered. In order to compare the existing strategies, we present an extensive evaluation that analyzes various properties of the main strategies for implicit to explicit volumetric conversions: Marching cubes, Delaunay refinement and CVTs, including accuracy and shape quality of the resulting shape mesh

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

Cited by 8 publications

References 12 publications

Overview of Shelling for 2-Manifold Surface Reconstruction Based on 3D Delaunay Triangulation

Overview of Shelling for 2-Manifold Surface Reconstruction Based on 3D Delaunay Triangulation

Efficient Moving Point Handling for Incremental 3D Manifold Reconstruction

On Volumetric Shape Reconstruction from Implicit Forms

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