Surface Reconstruction S. Ohrhallinger, S. Mudur and M. Wimmer 2 - - PowerPoint PPT Presentation

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Surface Reconstruction S. Ohrhallinger, S. Mudur and M. Wimmer 2 - - PowerPoint PPT Presentation

Aug 31, 2022 322 likes •1.08k views

Minimizing Edge Length to Connect Sparsely Sampled Unstructured Point Sets in 3D S. Ohrhallinger 1,2 , S. Mudur 2 and M. Wimmer 1 1 Vienna University of Technology, 2 Concordia University, Montral Surface Reconstruction S. Ohrhallinger, S.

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Minimizing Edge Length to Connect Sparsely Sampled Unstructured Point Sets in 3D

  • S. Ohrhallinger1,2, S. Mudur2 and M. Wimmer1

1Vienna University of Technology, 2Concordia University, Montréal

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Surface Reconstruction

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Sparse is hard Sparse is hard Dense is easy Dense is easy

Surface Reconstruction

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Ours Ours Shrink Shrink Tight Cocone Tight Cocone Wrap Wrap

State of the Art

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Interpolating Interpolating

Problem Domain

Fitting

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Interpolating Interpolating

Problem Domain

Fitting Too smooth

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Interpolating Interpolating

Problem Domain

Closed Mesh Closed Mesh Fitting Too smooth Bound Holes

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Interpolating Interpolating

Problem Domain

Parameter Parameter Closed Mesh Closed Mesh Fitting Too smooth Bound Holes

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Connect points with polyhedron B in DT, close to smooth surface S Connect points with polyhedron B in DT, close to smooth surface S Interpolating Interpolating

Problem Domain

Parameter Parameter Closed Mesh Closed Mesh Fitting Too smooth Bound Holes

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Related Work

α-Shapes [4,5]

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Related Work

Local Tangent Planes [8,9,10,11] α-Shapes [4,5]

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Related Work

Umbrella Matching [12,13] Local Tangent Planes [8,9,10,11] α-Shapes [4,5]

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Related Work

Sculpturing [8,14,15,18] Sculpturing [8,14,15,18] Umbrella Matching [12,13] Local Tangent Planes [8,9,10,11] α-Shapes [4,5]

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Related Work

Sculpturing [8,14,15,18] Sculpturing [8,14,15,18] Umbrella Matching [12,13] Local Tangent Planes [8,9,10,11] Voronoi Filtering [3,16,17] α-Shapes [4,5]

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Related Work

Sculpturing [8,14,15,18] Sculpturing [8,14,15,18] Umbrella Matching [12,13] Local Tangent Planes [8,9,10,11] Voronoi Filtering [3,16,17] Optimization [26,27,28] Optimization [26,27,28] α-Shapes [4,5]

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Related Work

Sculpturing [8,14,15,18] Sculpturing [8,14,15,18] Umbrella Matching [12,13] Local Tangent Planes [8,9,10,11] Voronoi Filtering [3,16,17] Optimization [26,27,28] Optimization [26,27,28] α-Shapes [4,5] Flow [20,21,22,23,24,25]

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Related Work

Sculpturing [8,14,15,18] Sculpturing [8,14,15,18] Umbrella Matching [12,13] Local Tangent Planes [8,9,10,11] Voronoi Filtering [3,16,17] Optimization [26,27,28] Optimization [26,27,28] Ours Ours α-Shapes [4,5] Flow [20,21,22,23,24,25]

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sculpture sculpture inflate inflate

We extend our 2D Method

[OM13] [OM13] create create

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sculpture sculpture inflate inflate

We extend our 2D Method

[OM13] [OM13] create create

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Minimization Objective

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Circumradius Circumradius

Minimization Objective

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Aspect ratio Aspect ratio Circumradius Circumradius

Minimization Objective

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Aspect ratio Aspect ratio Area Area Circumradius Circumradius

Minimization Objective

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Aspect ratio Aspect ratio Area Area Longest edge in triangle Longest edge in triangle Circumradius Circumradius

Minimization Objective

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Aspect ratio Aspect ratio Area Area Longest edge in triangle Longest edge in triangle Circumradius Circumradius

Minimization Objective

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A fast Approximation

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A fast Approximation

NP-hard NP-hard

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A fast Approximation

NP-hard NP-hard

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A fast Approximation

NP-hard NP-hard

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A fast Approximation

NP-hard NP-hard Still NP-hard? Still NP-hard? Still NP-hard?

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A fast Approximation

NP-hard NP-hard Still NP-hard? Still NP-hard? Still NP-hard?

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A fast Approximation

NP-hard NP-hard ? Still NP-hard? Still NP-hard? Still NP-hard?

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Bound artifacts Bound artifacts

Artifact Removal

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Cover hull holes Cover hull holes Bound artifacts Bound artifacts

Artifact Removal

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Sculpture slivers Sculpture slivers Cover hull holes Cover hull holes Bound artifacts Bound artifacts

Artifact Removal

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Our Method: Overview

Sliver sets manifold Slivers @holes

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Our Method: Overview

Close hull holes Sliver sets manifold Slivers @holes

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Our Method: Overview

Close hull holes Inflate Sliver sets manifold Slivers @holes

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Our Method: Overview

Close hull holes Inflate Sliver sets manifold Slivers @holes

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Our Method: Overview

Close hull holes Inflate Sculpture Sliver sets manifold Slivers @holes

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Our Method: Overview

Close hull holes Inflate Sculpture Sliver sets manifold Slivers @holes

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Dual Dual

Our Method: Overview

Close hull holes Inflate Sculpture Sliver sets manifold Slivers @holes

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Dual Dual

Our Method: Overview

Inflating exploits Closure to reconstruct very sparse sampling Inflating exploits Closure to reconstruct very sparse sampling Close hull holes Inflate Sculpture Sliver sets manifold Slivers @holes

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Input Input

Results (1): Improves sparse sampling

Wrap Shrink TCocone Ours

Results (1): Very Sparse Sampling

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Input Input Empty Set Empty Set

Results (1): Improves sparse sampling

Wrap Shrink TCocone Ours

Results (1): Very Sparse Sampling

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Input Input Empty Set Empty Set

Results (1): Improves sparse sampling

Wrap Shrink TCocone Ours

Results (1): Very Sparse Sampling

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Input Input Empty Set Empty Set

Results (1): Improves sparse sampling

Wrap Shrink TCocone Ours

Results (1): Very Sparse Sampling

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33 vertices 33 vertices 35k vertices 35k vertices

Results (2): Robust to sub-sampling

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RCocone RCocone Ours Ours

Results (3): Noise tolerant

0% 1% Perturbation of z-extent Perturbation of z-extent

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Results (4): Runtime

Our unoptimized algorithm is competitive for global approach Our unoptimized algorithm is competitive for global approach TCocone Ours Shrink seconds x1000 vertices

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Results(5): Guarantees of Bout

Watertight Manifold Watertight Manifold

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Results(5): Guarantees of Bout

Watertight Manifold Watertight Manifold 1 Connected Component 1 Connected Component

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Results(5): Guarantees of Bout

Watertight Manifold Watertight Manifold 1 Connected Component 1 Connected Component contains P (or in interior) contains P (or in interior)

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Results(5): Guarantees of Bout

Watertight Manifold Watertight Manifold 1 Connected Component 1 Connected Component Conjecture: ε<0.5 Conjecture: ε<0.5 contains P (or in interior) contains P (or in interior)

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Limitation

Bottom hole Bottom hole

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Limitation

Bottom hole Bottom hole Convoluted boundary Convoluted boundary

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Limitation

Bottom hole Bottom hole Convoluted boundary Convoluted boundary inflate

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Limitation

Bottom hole Bottom hole Convoluted boundary Convoluted boundary Far from Bmin Far from Bmin inflate

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Future work

Close Convoluted Holes Close Convoluted Holes

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Future work

Close Convoluted Holes Close Convoluted Holes Bounded Surfaces Bounded Surfaces Bounded Surfaces Bounded Surfaces

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Future work

Close Convoluted Holes Close Convoluted Holes Bounded Surfaces Bounded Surfaces Bounded Surfaces Bounded Surfaces Multiple Components Multiple Components

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Future work

Close Convoluted Holes Close Convoluted Holes Bounded Surfaces Bounded Surfaces Bounded Surfaces Bounded Surfaces Multiple Components Multiple Components Local Reconstruction Local Reconstruction

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Future work

Close Convoluted Holes Close Convoluted Holes Bounded Surfaces Bounded Surfaces Bounded Surfaces Bounded Surfaces Multiple Components Multiple Components Proof: ε<0.5 Proof: ε<0.5 Local Reconstruction Local Reconstruction

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Future work

Close Convoluted Holes Close Convoluted Holes Bounded Surfaces Bounded Surfaces Bounded Surfaces Bounded Surfaces Multiple Components Multiple Components Proof: ε<0.5 Proof: ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Local Reconstruction Local Reconstruction

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Future work

Close Convoluted Holes Close Convoluted Holes Bounded Surfaces Bounded Surfaces Bounded Surfaces Bounded Surfaces Multiple Components Multiple Components Proof: ε<0.5 Proof: ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Local Reconstruction Local Reconstruction Noisy Samples Noisy Samples

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Future work

Close Convoluted Holes Close Convoluted Holes Bounded Surfaces Bounded Surfaces Bounded Surfaces Bounded Surfaces Multiple Components Multiple Components Proof: ε<0.5 Proof: ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Exact Bmin for ε<0.5 Local Reconstruction Local Reconstruction Noisy Samples Noisy Samples Use Prior Knowledge Use Prior Knowledge

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Contributions

Source: http://sf.net/p/connect3d/

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Contributions

Source: http://sf.net/p/connect3d/

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Contributions

Source: http://sf.net/p/connect3d/ → Visualizes shape

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Contributions

Source: http://sf.net/p/connect3d/

  • Topolog. operations →
  • Topolog. operations →

→ Visualizes shape

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Contributions

Source: http://sf.net/p/connect3d/ Closure → Sparse features Closure → Sparse features

  • Topolog. operations →
  • Topolog. operations →

→ Visualizes shape

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Contributions

Noise tolerant Source: http://sf.net/p/connect3d/ Closure → Sparse features Closure → Sparse features

  • Topolog. operations →
  • Topolog. operations →

→ Visualizes shape

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Contributions

Robust to down-sampling Noise tolerant Source: http://sf.net/p/connect3d/ Closure → Sparse features Closure → Sparse features

  • Topolog. operations →
  • Topolog. operations →

→ Visualizes shape

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Contributions

Robust to down-sampling Noise tolerant Source: http://sf.net/p/connect3d/ +MeshLab plug-in +MeshLab plug-in Closure → Sparse features Closure → Sparse features

  • Topolog. operations →
  • Topolog. operations →

→ Visualizes shape