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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 Presentation
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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
Problem statement
Surface reconstruction of singular surface
input output
Problem statement
Singular surface
A collection of smooth surface patches with boundaries.
glueintersectboundary
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. …
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 …
Motivation
Need a simple yet effective reconstruction algorithm for all three singular surfaces.
Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
(I) Identify feature point
Gaussian-weighted graph Laplacian ( [BN02], Belkin-Niyogi, 2002)
(I) Identify feature point
Gaussian-weighted graph Laplacian ([BQWZ12])
Gaussian kernel
Position difference
(I) Identify feature point
Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
boundarylow high
(I) Identify feature point
surf B
surf A
intersectionlow high
Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
(I) Identify feature point
surf
A
surf B
glue (sharp feature)low high
Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
(I) Identify feature point
surf
A
surf B
Gaussian-weighted graph Laplacian (scaling, [BQWZ12])
boundary
surf B
surf A
intersection sharp feature
Gaussian-weighted graph Laplacian
(I) Identify feature point
highlow
(I) Identify feature point
Gaussian-weighted graph Laplacian Advantage:
Simple Unified approach Robust to noise
Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
(II) reconstruct feature curve
Graph method proposed by [GSBW11]
[ Data skeletonization via reeb graphs, Ge, et.al , 2011]
(II) reconstruct feature curve
Reeb graph ( from Rips-complex [DW11] )
Rips complexReeb graph(abstract)
Reeb graph(augmented)
(II) reconstruct feature curve
Reeb graph a noisy graph
feature points Reeb graph
(II) reconstruct feature curve
Graph simplification(denoise)
a zigzag graph
Graph smoothening [KWT88] Use snake to smooth out the graph
(II) reconstruct feature curve
graph energy
graph Laplacian
Graph smoothening Use snake to smoothen graph
graph Laplacian
(II) reconstruct feature curve
graph energy
align along feature
min( )
smoothen graph
(II) reconstruct feature curve
Graph smoothening Use snake to smooth out the graph
Our method: outline
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
(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
(III) Reconstruct singular surface
Weighted cocone
cocone weighted Delaunay[ACDL00] A simple algorithm for homeomorphic surface reconstruction, Amenta,-Choi-Dey -Leekha
(III) Reconstruct singular surface
Weighted cocone
un-weighted point
weighted point
(III) Reconstruct singular surface
Reconstruction Voronoi cell size weight∝ Give higher weight to points on the feature curve
Experiment results
ab
cd
a. Octaflower 107K
b. Fandisk 114K
c. SphCube 65K
d. Beetle 63K
Experiment results
Robust to noise
input with 1% noise result
Experiment results
Perform much better than un-weighted cocone
Cocone Our method
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
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.
Thank you!
Conclusion and Future work
Real scanned data