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Feature-Preserving Reconstruction of Singular Surfaces

with Tamal Dey , Qichao Que , Issam Safa , Lei Wang, Yusu Wang Computer science and Engineering The Ohio State University. Feature-Preserving Reconstruction of Singular Surfaces. Xiaoyin Ge. Problem statement. Surface reconstruction of singular surface. input. output.

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Feature-Preserving Reconstruction of Singular Surfaces

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  1. with TamalDey, QichaoQue, IssamSafa, Lei Wang, Yusu Wang Computer science and Engineering The Ohio State University Feature-Preserving Reconstruction of Singular Surfaces XiaoyinGe

  2. Problem statement • Surface reconstruction of singular surface input output

  3. Problem statement Singular surface A collection of smooth surface patches with boundaries. boundary glue intersect

  4. Motivation and Previous work 2D manifold reconstruction • [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. • …

  5. Motivation and Previous work Feature aware method • [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 • …

  6. Motivation Need a simple yet effective reconstruction algorithm for all three singular surfaces.

  7. Our method: outline Identify feature points Reconstruct feature curves Reconstruct singular surface

  8. Our method: outline Identify feature points Reconstruct feature curves Reconstruct singular surface

  9. (I) Identify feature point • Gaussian-weighted graph Laplacian ( [BN02], Belkin-Niyogi, 2002)

  10. (I) Identify feature point • Gaussian-weighted graph Laplacian([BQWZ12]) Position difference Gaussian kernel

  11. (I) Identify feature point • Gaussian-weighted graph Laplacian, scaling ([BQWZ12]) boundary low high

  12. (I) Identify feature point • Gaussian-weighted graph Laplacian, scaling ([BQWZ12]) surf A surf B intersection low high

  13. (I) Identify feature point • Gaussian-weighted graph Laplacian, scaling ([BQWZ12]) surf B surf A glue (sharp feature) low high

  14. (I) Identify feature point • Gaussian-weighted graph Laplacian (scaling, [BQWZ12]) surf A surf B surf B surf A boundary intersection sharp feature

  15. (I) Identify feature point • Gaussian-weighted graph Laplacian low high

  16. (I) Identify feature point • Gaussian-weighted graph Laplacian • Advantage: • Simple • Unified approach • Robust to noise

  17. Our method: outline Identify feature points Reconstructfeaturecurves Reconstruct singular surface

  18. (II) reconstruct feature curve • Graph method proposed by [GSBW11] [ Data skeletonization via reeb graphs, Ge, et.al , 2011]

  19. (II) reconstruct feature curve • Reeb graph ( from Rips-complex [DW11] ) Reeb graph (abstract) Reeb graph (augmented) Rips complex

  20. (II) reconstruct feature curve • Reeb graph a noisy graph feature points Reeb graph

  21. (II) reconstruct feature curve • Graph simplification(denoise) a zigzag graph

  22. (II) reconstruct feature curve • Graph smoothening [KWT88] • Use snake to smooth out the graph graph Laplacian graph energy

  23. (II) reconstruct feature curve • Graph smoothening • Use snake to smoothen graph align along feature graph Laplacian min( ) graph energy smoothen graph

  24. (II) reconstruct feature curve • Graph smoothening • Use snake to smooth out the graph

  25. Our method: outline Identify feature points Reconstruct feature curves Reconstruct singular surface

  26. (III) Reconstruct singular surface • 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

  27. (III) Reconstruct singular surface • Weighted cocone weighted Delaunay cocone [ACDL00] A simple algorithm for homeomorphic surface reconstruction, Amenta,-Choi-Dey -Leekha

  28. (III) Reconstruct singular surface • Weighted cocone weighted point un-weighted point

  29. (III) Reconstruct singular surface • Reconstruction • Voronoi cell size ∝ weight • Give higher weight to points on the feature curve

  30. Experiment results a. Octaflower 107K b. Fandisk 114K c. SphCube 65K a b c d. Beetle 63K d

  31. Experiment results • Robust to noise input with 1% noise result

  32. Experiment results • Perform much better than un-weighted cocone Our method Cocone

  33. Conclusion and Future work • Conclusion • Unified and simple method to handle all three types of singular surfaces • Robust to noise • Future work • More robust system for real data • Concave corner

  34. Acknowledgement 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, CCF-1116258 and CCF-0915996.

  35. Thank you!

  36. Conclusion and Future work • Real scanned data

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