Consolidation of Unorganized Point Clouds for Surface Reconstruction

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Consolidation of Unorganized Point Clouds for
Surface Reconstruction

• Hui Huang1 Dan Li1 Hao Zhang2
  Uri Ascher1 Daniel Cohen-Or3
• 1 University of British Columbia 2 Simon
  Fraser University 3 Tel-Aviv University

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Raw Scan Data
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Data Consolidation
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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

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Raw Scan Data
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RBF Reconstruction
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Difficulties

• Direct surface reconstruction may fail on
  challenging datasets
• Normals are crucial for surface reconstruction

• noise
• outliers
• close-by surface sheets
• missing normal information

• not always available
• not always reliable

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Unsigned Directions by PCA
Thick cloud
Non-uniform distribution
Close-by surface sheets
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Normal Consistency

• Hoppe et al. 1992
• Based on angles between unsigned normals
• May produce errors on close-by surface sheets

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Point Cloud Consolidation
Input
Output
Input
Output
Unorganized Noisy Thick Outliers Non-uniform Un-or
iented
Consolidated Clean Thin Outlier-free Uniform Orien
ted
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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
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New Repulsion Function

• More locally regular point distribution

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New Repulsion Function

• Better convergence behavior

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Non-uniformity
The first term of LOP, an L1 median, tends to
follow the trend of non-uniformity if input is
highly non-uniform.
s 0.18
s 0.24
LOP (old ?)
LOP (new ?)
Raw scan
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Improved Weighted LOP
Define the weighted local densities for each
point in the input set and projection set as
Then the projection becomes
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WLOP vs. LOP

• More globally regular point distribution

s 0.18
s 0.24
s 0.09
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WLOP vs. LOP

• Better convergence

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Normal Propagation
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Source Selection
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Distance Measure
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Thin Features and Normal Flipping
Outside the convex hull
Remedy normal flipping
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Orientation-aware PCA
Predictor
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One Example
Without flip
After correction
Noisy input
Traditional result
With flip
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Up-sampling
Raw scan
With consolidation
Without consolidation
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Surface Generation
RBF
LOP
WLOP
RBF
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(No Transcript)
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Traditional
Our
NormFetAMLSCocone Dey et al.
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Traditional
With OPCA
Without iteration
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Limitations
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Back-culling
Front-culling
Sparse set
Poisson surface
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Future Work

• Theoretical guarantee for the correctness of
  normal estimation under sampling
• Rigorous theoretical analysis of the
  predictor-corrector iteration
• Better handling of missing data
• Recovery and enhancement of sharp features

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Acknowledgements
Federico Ponchio Anonymous Reviewers AIM_at_SHAPE
NSERC (No. 84306 and No. 611370) The Israel
Science Foundation
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Point-Consolidation API is available http//people
.cs.ubc.ca/hhzhiyan/consolidation.html