Consolidation of Unorganized Point
Clouds for Surface Reconstruction
Hui Huang1
1 University
Dan Li1
Hao Zhang2
Uri Ascher1
2 Simon
Fraser University
of British Columbia
Daniel Cohen-Or3
3 Tel-Aviv
University
1
Raw Scan Data
2
Data Consolidation
3
Surface Reconstruction
• Delaunay techniques
[Amenta & Bern 1998], Power-crust [Amenda et
al. 2001], Cocone [Dey & Giesen 2001], [Cazals &
Giesen 2006] ……
• Approximate reconstructions
[Hoppe et al. 1992], RBF [Carr et al. 2001],
Poisson [Kazhdan et al. 2006] ……
4
Raw Scan Data
5
RBF Reconstruction
6
Difficulties
• Direct surface reconstruction may fail on
challenging datasets
 noise
 outliers
 close-by surface sheets
 missing normal information
• Normals are crucial for surface reconstruction
 not always available
 not always reliable
7
Unsigned Directions by PCA
Thick cloud
Non-uniform distribution
Close-by surface sheets
8
Normal Consistency
[Hoppe et al. 1992]
• Based on angles between unsigned normals
• May produce errors on close-by surface sheets
9
Point Cloud Consolidation
Input
Output
Input
Unorganized
Noisy
Thick
Outliers
Non-uniform
Un-oriented
Output
Consolidated
Clean
Thin
Outlier-free
Uniform
Oriented
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Contributions
To consolidate point clouds:
• Weighted locally optimal
projection operator (WLOP)
• Robust normal estimation
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Locally Optimal Projection
LOP operator [Lipman et al. 2007] defines a point set by
a fixed point iteration where, for each point x, given the
current iterate, the next iterate is to minimize
The repulsion function here is
12
New Repulsion Function
• More locally regular point distribution
13
New Repulsion Function
• Better convergence behavior
14
Non-uniformity
The first term of LOP, an L1 median, tends to follow the
trend of non-uniformity if input is highly non-uniform.
σ = 0.24
Raw scan
LOP (old η)
σ = 0.18
LOP (new η)
15
Improved Weighted LOP
Define the weighted local densities for each point in the
input set and projection set as
Then the projection becomes
16
WLOP vs. LOP
• More globally regular point distribution
σ = 0.24
Raw Scan
LOP (old η)
σ = 0.18
LOP (new η)
σ = 0.09
WLOP
17
WLOP vs. LOP
• Better convergence
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Normal Propagation
Select a source
Detect thin surface features
Propagate
Normal flipping
19
Source Selection


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Distance Measure
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Thin Features and Normal Flipping
Outside the convex hull
Limitation: cannot distinguish between
flat and concave
Remedy: normal flipping
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Orientation-aware PCA
Predictor
PCA
Propagate
OPCA
Corrector Loop
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One Example
Noisy input Traditional result
Without flip
With flip
After correction
24
Up-sampling
Raw scan
Without consolidation
With consolidation
25
Surface Generation
RBF
LOP
WLOP
RBF
26
RBF
Poisson
27
NormFet+AMLS+Cocone [Dey et al.] Traditional
Our
28
Traditional
Without iteration
With OPCA
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Limitations
30
Sparse set
Front-culling
Back-culling
Poisson surface
31
Future Work
• Theoretical guarantee for the correctness of
normal estimation under sampling
• Rigorous theoretical analysis of the predictorcorrector iteration
• Better handling of missing data
• Recovery and enhancement of sharp features
32
Acknowledgements
Federico Ponchio
Anonymous Reviewers
AIM@SHAPE
NSERC (No. 84306 and No. 611370)
The Israel Science Foundation
33
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