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Consolidation of Unorganized Point Clouds for Surface Reconstruction

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. Raw Scan Data.

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Consolidation of Unorganized Point Clouds for Surface Reconstruction

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  1. 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

  2. Raw Scan Data

  3. Data Consolidation

  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] ……

  5. Raw Scan Data

  6. RBF Reconstruction

  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

  8. Unsigned Directions by PCA Thick cloud Non-uniform distribution Close-by surface sheets

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

  10. Point Cloud Consolidation Input Output Input Output Unorganized Noisy Thick Outliers Non-uniform Un-oriented Consolidated Clean Thin Outlier-free Uniform Oriented

  11. Contributions To consolidate point clouds: • Weighted locally optimal projection operator (WLOP) • Robust normal estimation

  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

  13. New Repulsion Function • More locally regular point distribution

  14. New Repulsion Function • Better convergence behavior

  15. 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 = 0.18 σ = 0.24 LOP (old η) LOP (new η) Raw scan

  16. Improved Weighted LOP Define the weighted local densities for each point in the input set and projection set as Then the projection becomes

  17. Raw Scan LOP (old η) LOP (new η) WLOP WLOP vs. LOP • More globally regular point distribution σ = 0.18 σ = 0.24 σ = 0.09

  18. WLOP vs. LOP • Better convergence

  19. Select a source Propagate Detect thin surface features Normal flipping Normal Propagation

  20.  Source Selection

  21. Distance Measure

  22. Limitation: cannot distinguish between flat and concave Thin Features and Normal Flipping Outside the convex hull Remedy: normal flipping

  23. PCA OPCA Propagate Corrector Loop Orientation-aware PCA Predictor

  24. One Example Without flip After correction Noisy input Traditional result With flip

  25. Up-sampling Raw scan Without consolidation With consolidation

  26. Surface Generation RBF LOP WLOP RBF

  27. RBF Poisson

  28. Traditional Our NormFet+AMLS+Cocone [Dey et al.]

  29. Traditional Without iteration With OPCA

  30. Limitations

  31. Sparse set Front-culling Back-culling Poisson surface

  32. 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

  33. Acknowledgements Federico Ponchio Anonymous Reviewers AIM@SHAPE NSERC (No. 84306 and No. 611370) The Israel Science Foundation

  34. Point-Consolidation APIis available http://people.cs.ubc.ca/~hhzhiyan/consolidation.html

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