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Consolidation of Unorganized Point Clouds for Surface Reconstruction Hui Huang 1 Dan Li 1 Hao Zhang 2 Uri Ascher 1 Daniel Cohen-Or 3 1 University of British Columbia 2 Simon Fraser University 3 Tel-Aviv University 1
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2 Raw Scan Data
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3 Data Consolidation
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4 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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5 Raw Scan Data
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6 RBF Reconstruction
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7 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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8 Unsigned Directions by PCA Thick cloudNon-uniform distribution Close-by surface sheets
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9 Normal Consistency [Hoppe et al. 1992] Based on angles between unsigned normals May produce errors on close-by surface sheets
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10 Point Cloud Consolidation Unorganized Noisy Thick Outliers Non-uniform Un-oriented Input Consolidated Clean Thin Outlier-free Uniform Oriented Output InputOutput
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11 Contributions Weighted locally optimal projection operator (WLOP) To consolidate point clouds: Robust normal estimation
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12 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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13 New Repulsion Function More locally regular point distribution
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14 New Repulsion Function Better convergence behavior
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15 Non-uniformity The first term of LOP, an L 1 median, tends to follow the trend of non-uniformity if input is highly non-uniform. Raw scan LOP (old η)LOP (new η) σ = 0.24 σ = 0.18
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16 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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17 WLOP vs. LOP More globally regular point distribution Raw ScanLOP (old η)LOP (new η)WLOP σ = 0.24 σ = 0.18 σ = 0.09
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18 WLOP vs. LOP Better convergence
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19 Normal Propagation Select a source Detect thin surface features Normal flipping Propagate
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20 Source Selection
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21 Distance Measure
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22 Thin Features and Normal Flipping Outside the convex hull Limitation: cannot distinguish between flat and concave Remedy: normal flipping
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23 Orientation-aware PCA Propagate Predictor Corrector Loop OPCA PCA
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24 Noisy inputTraditional result Without flip With flip After correction One Example
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25 Up-sampling Raw scanWith consolidationWithout consolidation
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26 Surface Generation LOP WLOP RBF
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27 RBFPoisson
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28 NormFet+AMLS+Cocone [Dey et al.] TraditionalOur
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29 TraditionalWith OPCAWithout iteration
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30 Limitations
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31 Back-cullingFront-cullingSparse setPoisson surface
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32 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 Future Work
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33 Federico Ponchio Anonymous Reviewers AIM@SHAPE NSERC (No. 84306 and No. 611370) The Israel Science Foundation Acknowledgements
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34 Point-Consolidation API is available http://people.cs.ubc.ca/~hhzhiyan/consolidation.html
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