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Delaunay Based Shape Reconstruction from Large Data

Delaunay Based Shape Reconstruction from Large Data. Tamal K. Dey, Joachim Giesen and James Hudson Ohio State University. Surface Reconstruction. Reconstruction. A sample. Local feature size and sampling Amenta-Bern-Eppstein. Medial axis Local feature size f(p).  -sampling

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Delaunay Based Shape Reconstruction from Large Data

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  1. Delaunay Based Shape Reconstruction from Large Data Tamal K. Dey, Joachim Giesen and James Hudson Ohio State University

  2. Surface Reconstruction Reconstruction A sample

  3. Local feature size and samplingAmenta-Bern-Eppstein • Medial axis • Local feature size f(p) • -sampling •   d(p)/f(p)

  4. Reconstruction • Functional approach • Tangent plane [HDeDDMS92] • Natural Neighbors [BC00] • Voronoi/Delaunay filtering • Alpha shapes [EM94] • Crust [AB98] • Cocone [ACDL00]

  5. Surface and Voronoi Diagram • Restricted Voronoi • Restricted Delaunay • Poles • Cocone Space spanned by vectors making angle q /8 with horizontal

  6. Cocone Algorithm • Compute VP • Compute Boundary samples (Dey-Giesen 2001) • Filter triangles whose duals intersect cocones • Extract a manifold using prune and walk

  7. Why manifold extraction works? • Candidate triangles are dual to Voronoi edges intersected by cocones. • Each candidate triangle is small w.r.t. feature size. • All restricted Delaunay triangles is in the set of candidate triangles.

  8. Large Data • Octree subdivision

  9. Cracks • Cracks appear in surface computed from octree boxes

  10. Padding • Include a fraction from the neighbors to form the extended box

  11. Boundary sample detection

  12. Supercocone(P,D,l) • Compute octree for P with D and extended box with l th subdivision • For each box perform all steps of cocone on the extended set • Extract a manifold

  13. Theoretical Justification • Because of padding restricted Voronoi neighbors are included • Normals are approximated • Cocone computes the candidate triangles with two necessary properties • Manifold extraction takes care of matching • Even a local manifold extraction works in practice due to padding

  14. Surface matching

  15. Experiments • 733 MHz Pentium III, 512 MB RAM, 10GB disk • C++, CGAL code for Voronoi/Delaunay

  16. Dragon data (time)

  17. Dragon data (memory)

  18. Dragon

  19. Blade data (time)

  20. Blade data(memory)

  21. Blade

  22. Lucy25 data(time)

  23. Lucy Data (memory)

  24. Lucy25 3.5 million points, 198 mints

  25. Experimental data

  26. David’s Head 2 mil points, 93 minutes

  27. St. Mathew’s Head 3.4 mil points, 150 minutes

  28. Parallel • 10x2 450MHz Pentium II Xeon • 512MB, 1GB swap • one 733 MHz Pentium III, 512MB, 1.5 GB • MPI, 10Mbit ethernet 14 mil points, 67 minutes

  29. Conclusions • Introduced Reconstruction by local Voronoi computations. • Large sample in the range of million points is doable. • Parallel implementation. • Softwares: • www.cis.ohio-state.edu/~tamaldey/cocone.html

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