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Surface Reconstruction S. Ohrhallinger, S. Mudur and M. Wimmer 2 - PowerPoint PPT Presentation

Aug 31, 2022 •322 likes •1.08k views

Minimizing Edge Length to Connect Sparsely Sampled Unstructured Point Sets in 3D S. Ohrhallinger 1,2 , S. Mudur 2 and M. Wimmer 1 1 Vienna University of Technology, 2 Concordia University, Montral Surface Reconstruction S. Ohrhallinger, S.

  1. Minimizing Edge Length to Connect Sparsely Sampled Unstructured Point Sets in 3D S. Ohrhallinger 1,2 , S. Mudur 2 and M. Wimmer 1 1 Vienna University of Technology, 2 Concordia University, Montréal

  2. Surface Reconstruction S. Ohrhallinger, S. Mudur and M. Wimmer 2

  3. Surface Reconstruction Dense is easy Sparse is hard Dense is easy Sparse is hard S. Ohrhallinger, S. Mudur and M. Wimmer 3

  4. State of the Art Tight Wrap Wrap Tight Cocone Cocone Shrink Ours Shrink Ours S. Ohrhallinger, S. Mudur and M. Wimmer 4

  5. Problem Domain Interpolating Fitting Interpolating S. Ohrhallinger, S. Mudur and M. Wimmer 5

  6. Problem Domain Interpolating Fitting Interpolating Too smooth S. Ohrhallinger, S. Mudur and M. Wimmer 6

  7. Problem Domain Interpolating Fitting Interpolating Too smooth Closed Mesh Bound Holes Closed Mesh S. Ohrhallinger, S. Mudur and M. Wimmer 7

  8. Problem Domain Interpolating Fitting Interpolating Too smooth Closed Mesh Bound Holes Closed Mesh Parameter Parameter S. Ohrhallinger, S. Mudur and M. Wimmer 8

  9. Problem Domain Interpolating Fitting Interpolating Too smooth Closed Mesh Bound Holes Closed Mesh Parameter Parameter Connect points with polyhedron B in DT , close to smooth surface S Connect points with polyhedron B in DT , close to smooth surface S S. Ohrhallinger, S. Mudur and M. Wimmer 9

  10. Related Work α-Shapes [4,5] S. Ohrhallinger, S. Mudur and M. Wimmer 10

  11. Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] S. Ohrhallinger, S. Mudur and M. Wimmer 11

  12. Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] S. Ohrhallinger, S. Mudur and M. Wimmer 12

  13. Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Sculpturing Sculpturing [8,14,15,18] [8,14,15,18] S. Ohrhallinger, S. Mudur and M. Wimmer 13

  14. Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] S. Ohrhallinger, S. Mudur and M. Wimmer 14

  15. Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] Optimization Optimization [26,27,28] [26,27,28] S. Ohrhallinger, S. Mudur and M. Wimmer 15

  16. Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] Optimization Optimization Flow [26,27,28] [26,27,28] [20,21,22,23,24,25] S. Ohrhallinger, S. Mudur and M. Wimmer 16

  17. Related Work α-Shapes Local Tangent Planes [4,5] [8,9,10,11] Umbrella Matching [12,13] Voronoi Filtering Sculpturing Sculpturing [3,16,17] [8,14,15,18] [8,14,15,18] Ours Ours Optimization Optimization Flow [26,27,28] [26,27,28] [20,21,22,23,24,25] S. Ohrhallinger, S. Mudur and M. Wimmer 17

  18. We extend our 2D Method create inflate sculpture create inflate sculpture [OM13] [OM13] S. Ohrhallinger, S. Mudur and M. Wimmer 18

  19. We extend our 2D Method create inflate sculpture create inflate sculpture [OM13] [OM13] S. Ohrhallinger, S. Mudur and M. Wimmer 19

  20. Minimization Objective S. Ohrhallinger, S. Mudur and M. Wimmer 20

  21. Minimization Objective Circumradius Circumradius S. Ohrhallinger, S. Mudur and M. Wimmer 21

  22. Minimization Objective Circumradius Aspect ratio Circumradius Aspect ratio S. Ohrhallinger, S. Mudur and M. Wimmer 22

  23. Minimization Objective Circumradius Aspect ratio Area Circumradius Aspect ratio Area S. Ohrhallinger, S. Mudur and M. Wimmer 23

  24. Minimization Objective Longest edge Circumradius Aspect ratio Area Longest edge Circumradius Aspect ratio Area in triangle in triangle S. Ohrhallinger, S. Mudur and M. Wimmer 24

  25. Minimization Objective Longest edge Circumradius Aspect ratio Area Longest edge Circumradius Aspect ratio Area in triangle in triangle S. Ohrhallinger, S. Mudur and M. Wimmer 25

  26. A fast Approximation S. Ohrhallinger, S. Mudur and M. Wimmer 26

  27. A fast Approximation NP-hard NP-hard S. Ohrhallinger, S. Mudur and M. Wimmer 27

  28. A fast Approximation NP-hard NP-hard S. Ohrhallinger, S. Mudur and M. Wimmer 28

  29. A fast Approximation NP-hard NP-hard S. Ohrhallinger, S. Mudur and M. Wimmer 29

  30. A fast Approximation NP-hard NP-hard Still NP-hard? Still NP-hard? Still NP-hard? S. Ohrhallinger, S. Mudur and M. Wimmer 30

  31. A fast Approximation NP-hard NP-hard Still NP-hard? Still NP-hard? Still NP-hard? S. Ohrhallinger, S. Mudur and M. Wimmer 31

  32. A fast Approximation NP-hard NP-hard ? Still NP-hard? Still NP-hard? Still NP-hard? S. Ohrhallinger, S. Mudur and M. Wimmer 32

  33. Artifact Removal Bound artifacts Bound artifacts S. Ohrhallinger, S. Mudur and M. Wimmer 33

  34. Artifact Removal Bound artifacts Cover hull holes Bound artifacts Cover hull holes S. Ohrhallinger, S. Mudur and M. Wimmer 34

  35. Artifact Removal Bound artifacts Cover hull holes Sculpture slivers Bound artifacts Cover hull holes Sculpture slivers S. Ohrhallinger, S. Mudur and M. Wimmer 35

  36. Our Method: Overview Slivers @holes Sliver sets manifold S. Ohrhallinger, S. Mudur and M. Wimmer 36

  37. Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes S. Ohrhallinger, S. Mudur and M. Wimmer 37

  38. Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 38

  39. Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 39

  40. Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 40

  41. Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate S. Ohrhallinger, S. Mudur and M. Wimmer 41

  42. Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate Dual Dual S. Ohrhallinger, S. Mudur and M. Wimmer 42

  43. Our Method: Overview Slivers @holes Sliver sets manifold Close hull holes Sculpture Inflate Dual Dual Inflating exploits Closure to reconstruct very sparse sampling Inflating exploits Closure to reconstruct very sparse sampling S. Ohrhallinger, S. Mudur and M. Wimmer 43

  44. Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 44

  45. Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Empty Set Empty Set Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 45

  46. Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Empty Set Empty Set Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 46

  47. Results (1): Very Sparse Sampling Results (1): Improves sparse sampling Empty Set Empty Set Wrap Shrink TCocone Ours Input Input S. Ohrhallinger, S. Mudur and M. Wimmer 47

  48. Results (2): Robust to sub-sampling 35k vertices 35k vertices 33 vertices 33 vertices S. Ohrhallinger, S. Mudur and M. Wimmer 48

  49. Results (3): Noise tolerant RCocone RCocone Ours Ours 0% 1% Perturbation of z-extent Perturbation of z-extent S. Ohrhallinger, S. Mudur and M. Wimmer 49

  50. Results (4): Runtime Ours TCocone Shrink seconds x1000 vertices Our unoptimized algorithm is competitive for global approach Our unoptimized algorithm is competitive for global approach S. Ohrhallinger, S. Mudur and M. Wimmer 50

  51. Results(5): Guarantees of B out Watertight Manifold Watertight Manifold S. Ohrhallinger, S. Mudur and M. Wimmer 51

  52. Results(5): Guarantees of B out Watertight Manifold Watertight Manifold 1 Connected Component 1 Connected Component S. Ohrhallinger, S. Mudur and M. Wimmer 52

  53. Results(5): Guarantees of B out Watertight Manifold contains P (or in interior) Watertight Manifold contains P (or in interior) 1 Connected Component 1 Connected Component S. Ohrhallinger, S. Mudur and M. Wimmer 53

  54. Results(5): Guarantees of B out Watertight Manifold contains P (or in interior) Watertight Manifold contains P (or in interior) 1 Connected Component Conjecture: ε<0.5 1 Connected Component Conjecture: ε<0.5 S. Ohrhallinger, S. Mudur and M. Wimmer 54

  55. Limitation Bottom hole Bottom hole S. Ohrhallinger, S. Mudur and M. Wimmer 55

  56. Limitation Bottom hole Convoluted boundary Bottom hole Convoluted boundary S. Ohrhallinger, S. Mudur and M. Wimmer 56

  57. Limitation inflate Bottom hole Convoluted boundary Bottom hole Convoluted boundary S. Ohrhallinger, S. Mudur and M. Wimmer 57

  58. Limitation inflate Far from B min Bottom hole Convoluted boundary Far from B min Bottom hole Convoluted boundary S. Ohrhallinger, S. Mudur and M. Wimmer 58

  59. Future work Close Convoluted Holes Close Convoluted Holes S. Ohrhallinger, S. Mudur and M. Wimmer 59

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