feature-preserving reconstruction of singular surfaces
DESCRIPTION
with Tamal Dey , Qichao Que , Issam Safa , Lei Wang, Yusu Wang Computer science and Engineering The Ohio State University. Feature-Preserving Reconstruction of Singular Surfaces. Xiaoyin Ge. Problem statement. Surface reconstruction of singular surface. input. output. - PowerPoint PPT PresentationTRANSCRIPT
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Feature-Preserving Reconstruction of Singular Surfaces
with Tamal Dey, Qichao Que, Issam Safa, Lei Wang, Yusu WangComputer science and Engineering
The Ohio State University
Xiaoyin Ge
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Problem statement
Surface reconstruction of singular surface
input output
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Problem statement
Singular surface
A collection of smooth surface patches with boundaries.
glueintersectboundary
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Motivation and Previous work
2D manifold reconstruction
[AB99] Surface reconstruction by Voronoi filtering. AMENTA N., BERN M.
[ACDL02] A simple algorithm for homeomorphic surface reconstruction. AMENTA N., et. al.
[BC02] Smooth surface reconstruction via natural neighbor interpolation of distance functions. BOISSONNAT et. Al
[ABCO01] Point set surfaces. ALEXA et. al. …
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Motivation and Previous work
Feature aware method
[LCOL07] Data dependent MLS for faithful surface approximation. LIPMAN , et. al.
[ÖGG09] Feature preserving point set surfaces based on non-linear kernel regression, ÖZTIRELI, et.al
[CG06] Delaunay triangulation based surface reconstruction, CAZALS, et.al [FCOS05] Robust moving least-squares fitting with sharp features,
FLEISHMAN, et.al …
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Motivation
Need a simple yet effective reconstruction algorithm for all three singular surfaces.
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Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
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Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
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(I) Identify feature point
Gaussian-weighted graph Laplacian ( [BN02], Belkin-Niyogi, 2002)
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(I) Identify feature point
Gaussian-weighted graph Laplacian ([BQWZ12])
Gaussian kernel
Position difference
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(I) Identify feature point
Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
boundarylow high
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(I) Identify feature point
surf B
surf A
intersectionlow high
Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
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(I) Identify feature point
surf
A
surf B
glue (sharp feature)low high
Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
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(I) Identify feature point
surf
A
surf B
Gaussian-weighted graph Laplacian (scaling, [BQWZ12])
boundary
surf B
surf A
intersection sharp feature
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Gaussian-weighted graph Laplacian
(I) Identify feature point
highlow
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(I) Identify feature point
Gaussian-weighted graph Laplacian Advantage:
Simple Unified approach Robust to noise
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Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
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(II) reconstruct feature curve
Graph method proposed by [GSBW11]
[ Data skeletonization via reeb graphs, Ge, et.al , 2011]
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(II) reconstruct feature curve
Reeb graph ( from Rips-complex [DW11] )
Rips complexReeb graph(abstract)
Reeb graph(augmented)
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(II) reconstruct feature curve
Reeb graph a noisy graph
feature points Reeb graph
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(II) reconstruct feature curve
Graph simplification(denoise)
a zigzag graph
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Graph smoothening [KWT88] Use snake to smooth out the graph
(II) reconstruct feature curve
graph energy
graph Laplacian
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Graph smoothening Use snake to smoothen graph
graph Laplacian
(II) reconstruct feature curve
graph energy
align along feature
min( )
smoothen graph
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(II) reconstruct feature curve
Graph smoothening Use snake to smooth out the graph
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Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
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(III) Reconstruct singular surface
Reconstruction [CDR07][CDL07]
[CDL07] A Practical Delaunay Meshing Algorithm for a Large Class of Domains, Cheng, et.al
[CDR07] Delaunay Refinement for Piecewise Smooth Complexes, Cheng-Dey-Ramos, 2007
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(III) Reconstruct singular surface
Weighted cocone
cocone weighted Delaunay[ACDL00] A simple algorithm for homeomorphic surface reconstruction, Amenta,-Choi-Dey -Leekha
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(III) Reconstruct singular surface
Weighted cocone
un-weighted point
weighted point
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(III) Reconstruct singular surface
Reconstruction Voronoi cell size weight∝ Give higher weight to points on the feature curve
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Experiment results
ab
cd
a. Octaflower 107K
b. Fandisk 114K
c. SphCube 65K
d. Beetle 63K
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Experiment results
Robust to noise
input with 1% noise result
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Experiment results
Perform much better than un-weighted cocone
Cocone Our method
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Conclusion and Future work
Conclusion Unified and simple method to handle all three
types of singular surfaces Robust to noise
Future work More robust system for real data Concave corner
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Acknowledgement
We thank all people who have helped us to demonstrate this method !
Most of the models used in this paper are courtesy of
AIM@SHAPE Shape Repository. The authors acknowledge the support of NSF under grants CCF-1048983, CCF-1116258 and CCF-0915996.
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Thank you!
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Conclusion and Future work
Real scanned data