Transcript Xiaoyin Ge with Tamal Dey, Qichao Que, Issam Safa, Lei Wang, Yusu Wang Computer science and Engineering The Ohio State University.

Xiaoyin Ge
with Tamal Dey, Qichao Que, Issam Safa, Lei Wang, Yusu Wang
Computer science and Engineering
The Ohio State University
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Surface reconstruction of singular
surface
input
output
Singular surface
A collection of smooth surface patches with
boundaries.
boundary
glue
intersect
2D manifold reconstruction
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[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.
…
Feature aware method
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[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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Need a simple yet effective reconstruction
algorithm for all three singular surfaces.
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
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Gaussian-weighted graph Laplacian
( [BN02], Belkin-Niyogi, 2002)
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Gaussian-weighted graph Laplacian
([BQWZ12])
Position difference
Gaussian kernel
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Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
low
high
boundary
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Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
surf A
surf B
low
high
intersection
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Gaussian-weighted graph Laplacian, scaling ([BQWZ12])
surf B
low
high
glue (sharp feature)
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Gaussian-weighted graph Laplacian (scaling,
[BQWZ12])
surf A
surf B
boundary
intersection
surf B
sharp feature
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low
Gaussian-weighted graph Laplacian
high
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Gaussian-weighted graph Laplacian
Advantage:
 Simple
 Unified approach
 Robust to noise
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
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Graph method proposed by [GSBW11]
[ Data skeletonization via reeb graphs, Ge, et.al , 2011]
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Reeb graph ( from Rips-complex [DW11] )
Rips complex
Reeb graph
(abstract)
Reeb graph
(augmented)
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Reeb graph
a noisy graph
feature points
Reeb graph
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Graph simplification(denoise)
a zigzag graph
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Graph smoothening [KWT88]
 Use snake to smooth out the graph
graph Laplacian
graph energy
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Graph smoothening
 Use snake to smoothen graph
align
along
feature
graph
Laplacian
min(
)
graph energy
smoothen
graph
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Graph smoothening
 Use snake to smooth out the graph
Identify feature points
Reconstruct feature curves
Reconstruct singular surface
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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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Weighted cocone
cocone
[ACDL00] A simple algorithm for homeomorphic
surface reconstruction, Amenta,-Choi-Dey -Leekha
weighted Delaunay
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Weighted cocone
weighted point
un-weighted point
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Reconstruction
 Voronoi cell size ∝ weight
 Give higher weight to points on the feature curve
a. Octaflower
107K
b. Fandisk
114K
a
c
b
d
c. SphCube
65K
d. Beetle
63K
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Robust to noise
input with 1% noise
result
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Perform much better than un-weighted
cocone
Cocone
Our method
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Conclusion
 Unified and simple method to handle all three
types of singular surfaces
 Robust to noise
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Future work
 More robust system for real data
 Concave corner
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, CCF1116258 and CCF-0915996.
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Real scanned data