1. Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly Sampled Point Clouds Without Normal Information

2. Computer Graphics Group Alexander Hornung Point Cloud Reconstruction

3. Computer Graphics Group Alexander Hornung Point Cloud Reconstruction Non-uniform sampling Holes Noise Bad scan alignment No (reliable) normals

4. Computer Graphics Group Alexander Hornung Point Cloud Reconstruction Smooth watertight manifold No topological artifacts (low genus) Detail preservation Robustness to Non-uniform sampling Holes Bad registration and noise From 3D points only

5. Computer Graphics Group Alexander Hornung Outline Introduction Surface confidence estimation Graph-based surface extraction Hole filling and detail preservation Mesh extraction Results

6. Computer Graphics Group Alexander Hornung Related Work Wrapping and Voronoi-based Amenta et al., Bernardini et al., Boissonat and Cazals, Dey and Goswami, Mederos et al., Scheidegger et al., … Deformable models Esteve et al., Sharf et al., … Volumetric reconstruction Hoppe et al., Curless and Levoy, Carr et al., Ohtake et al., Fleishman et al., Kazhdan, …

7. Computer Graphics Group Alexander Hornung Related Work Wrapping and Voronoi-based Amenta et al., Bernardini et al., Boissonat and Cazals, Dey and Goswami, Mederos et al., Scheidegger et al., … Deformable models Esteve et al., Sharf et al., … Volumetric reconstruction Hoppe et al., Curless and Levoy, Carr et al., Ohtake et al., Fleishman et al., Kazhdan, … Graph-based energy minimization and surface reconstruction Boykov and Kolmogorov, Vogiatzis et al., Hornung and Kobbelt

8. Computer Graphics Group Alexander Hornung Signed vs. Unsigned Distance

9. Computer Graphics Group Alexander Hornung Signed vs. Unsigned Distance

10. Computer Graphics Group Alexander Hornung Signed vs. Unsigned Distance

11. Computer Graphics Group Alexander Hornung Signed vs. Unsigned Distance

12. Computer Graphics Group Alexander Hornung Overview Point cloud P

13. Computer Graphics Group Alexander Hornung Overview Point cloud P Surface confidence (unsigned distance)

14. Computer Graphics Group Alexander Hornung Overview Point cloud P Surface confidence (unsigned distance) Embed weighted graph structure G

15. Computer Graphics Group Alexander Hornung Overview Point cloud P Surface confidence (unsigned distance) Embed weighted graph structure Min-Cut of G yields unknown surface

16. Computer Graphics Group Alexander Hornung Outline Introduction Surface confidence estimation Graph-based surface extraction Hole filling and detail preservation Mesh extraction Results

17. Computer Graphics Group Alexander Hornung Surface Confidence Insert 3D samples into volumetric grid Sparse set of occupied voxels Compute a confidence map  “Probability” that surface intersects a voxel v

18. Computer Graphics Group Alexander Hornung Surface Confidence Insert 3D samples into volumetric grid Sparse set of occupied voxels Compute a confidence map  “Probability” that surface intersects a voxel v Compute “crust” containing the surface Morphological dilation Medial axis approximation

19. Computer Graphics Group Alexander Hornung Surface Confidence Insert 3D samples into volumetric grid Sparse set of occupied voxels Compute a confidence map  “Probability” that surface intersects a voxel v Compute “crust” containing the surface Morphological dilation Medial axis approximation Estimate by volumetric diffusion

20. Computer Graphics Group Alexander Hornung Outline Introduction Surface confidence estimation Graph-based surface extraction Hole filling and detail preservation Mesh extraction Results

21. Computer Graphics Group Alexander Hornung Find Optimal Surface Minimize energy Min-Cut of an embedded graph Global optimum Highly efficient Graph structure?

22. Computer Graphics Group Alexander Hornung Dual Graph Embedding : Probability that v is intersected by surface s Intersected voxels are split into 2 components Interior faces Exterior faces

23. Computer Graphics Group Alexander Hornung Dual Graph Embedding : Probability that v is intersected by surface s Intersected voxels are split into 2 components Interior faces Exterior faces  Split along a sequence of edges Octahedral graph structure Voxel split-edges Graph cut-edges

24. Computer Graphics Group Alexander Hornung Min-Cut Surface Extraction Embed graph into a crust containing the surface

25. Computer Graphics Group Alexander Hornung Min-Cut Surface Extraction Embed graph into a crust containing the surface Edge weights defined per voxel

26. Computer Graphics Group Alexander Hornung Embed graph into a crust containing the surface Edge weights defined per voxel Min-cut yields set of intersected surface voxels Min-Cut Surface Extraction

27. Computer Graphics Group Alexander Hornung Embed graph into a crust containing the surface Edge weights defined per voxel Min-cut yields set of intersected surface voxels Parameter s to emphasize strong/weak maxima Min-Cut Surface Extraction

28. Computer Graphics Group Alexander Hornung Outline Introduction Surface confidence estimation Graph-based surface extraction Hole filling and detail preservation Mesh extraction Results

29. Computer Graphics Group Alexander Hornung Hierarchical Approach Single resolution impractical High volumetric resolutions Non-uniform sampling / large holes Hierarchical framework Adaptive volumetric grid (Octree) Proper initial crust at low resolutions Simple narrow-band approach insufficient Loss of fine details not contained within crust

30. Computer Graphics Group Alexander Hornung Hierarchical Approach Single resolution impractical High volumetric resolutions Non-uniform sampling / large holes Hierarchical framework Adaptive volumetric grid (Octree) Proper initial crust at low resolutions Simple narrow-band approach insufficient Loss of fine details not contained within crust  Re-insertion of data samples Merge samples with crust

31. Computer Graphics Group Alexander Hornung Hierarchical Approach 1)Surface confidence estimation (Re-)Insert point samples Dilate and compute 2)Graph-based surface extraction Generate octahedral graph Compute min-cut 3)Volumetric refinement Narrow band 64 3

32. Computer Graphics Group Alexander Hornung Hierarchical Approach 1)Surface confidence estimation (Re-)Insert point samples Dilate and compute 2)Graph-based surface extraction Generate octahedral graph Compute min-cut 3)Volumetric refinement Narrow band 128 3

33. Computer Graphics Group Alexander Hornung Hierarchical Approach 1)Surface confidence estimation (Re-)Insert point samples Dilate and compute 2)Graph-based surface extraction Generate octahedral graph Compute min-cut 3)Volumetric refinement Narrow band 128 3

34. Computer Graphics Group Alexander Hornung Hierarchical Approach 1)Surface confidence estimation (Re-)Insert point samples Dilate and compute 2)Graph-based surface extraction Generate octahedral graph Compute min-cut 3)Volumetric refinement Narrow band 256 3

35. Computer Graphics Group Alexander Hornung Hierarchical Approach 1)Surface confidence estimation (Re-)Insert point samples Dilate and compute 2)Graph-based surface extraction Generate octahedral graph Compute min-cut 3)Volumetric refinement Narrow band 256 3

36. Computer Graphics Group Alexander Hornung Hierarchical Approach 1)Surface confidence estimation (Re-)Insert point samples Dilate and compute 2)Graph-based surface extraction Generate octahedral graph Compute min-cut 3)Volumetric refinement Narrow band 512 3

37. Computer Graphics Group Alexander Hornung Hierarchical Approach 1)Surface confidence estimation (Re-)Insert point samples Dilate and compute 2)Graph-based surface extraction Generate octahedral graph Compute min-cut 3)Volumetric refinement Narrow band 512 3

38. Computer Graphics Group Alexander Hornung Outline Introduction Surface confidence estimation Graph-based surface extraction Hole filling and detail preservation Mesh extraction Results

39. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Loop of voxel split-edgesGraph cut-edges

40. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Loops define non-planar polygonal faces Mesh vertices at voxel corners

41. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Loops define non-planar polygonal faces Mesh vertices at voxel corners Cycle along split-edges

42. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Loops define non-planar polygonal faces Mesh vertices at voxel corners Cycle along split-edges

43. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Loops define non-planar polygonal faces Mesh vertices at voxel corners Cycle along split-edges

44. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Loops define non-planar polygonal faces Mesh vertices at voxel corners Cycle along split-edges

45. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Loops define non-planar polygonal faces Mesh vertices at voxel corners Cycle along split-edges

46. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers

47. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers

48. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers Voxel corners correspond to non-planar faces Cycle over shared split-edges

49. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers Voxel corners correspond to non-planar faces Cycle over shared split-edges

50. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers Voxel corners correspond to non-planar faces Cycle over shared split-edges

51. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers Voxel corners correspond to non-planar faces Cycle over shared split-edges

52. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers Voxel corners correspond to non-planar faces Cycle over shared split-edges

53. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh estimated per voxel  Mesh vertices at voxel centers Voxel corners correspond to non-planar faces Cycle over shared split-edges

54. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh

55. Computer Graphics Group Alexander Hornung Cut Manifold to Triangle Mesh Elimination of grid artifacts  Error controlled Bi-Laplacian smoothing Based on surface confidence Stop smoothing if

56. Computer Graphics Group Alexander Hornung Outline Introduction Surface confidence estimation Graph-based surface extraction Hole filling and detail preservation Mesh extraction Results

57. Computer Graphics Group Alexander Hornung Max Planck ResolutionTimeGenusVertices 512 3 199s0320K

58. Computer Graphics Group Alexander Hornung Statue ResolutionTimeGenusVertices 1024 3 269s0448K

59. Computer Graphics Group Alexander Hornung Rings ResolutionTimeGenusVertices 256 3 45s491K

60. Computer Graphics Group Alexander Hornung Rings ResolutionTimeGenusVertices 256 3 45s491K

61. Computer Graphics Group Alexander Hornung Leo ResolutionTimeGenusVertices 256 3 48s147K

62. Computer Graphics Group Alexander Hornung Monkey ResolutionTimeGenusVertices 256 3 82s072K

63. Computer Graphics Group Alexander Hornung Dragon ResolutionTimeGenusVertices 512 3 150s1 (>400)318K

64. Computer Graphics Group Alexander Hornung Conclusions New algorithm for point cloud reconstruction Surface confidence map and graph cuts No normals required Guaranteed watertight surface No topological artifacts Hierarchical approach Handles non-uniform sampling and large gaps Preserves fine details Reduces number of computed voxels  Efficiency Conversion of min-cut into triangle mesh

65. Computer Graphics Group Alexander Hornung Future Work Voxel representative Slow smoothing convergence Subvoxel precision using input samples Performance No explicit graph generation Flow from previous levels Graph structure for thin-plate surfaces Flux for preferred cut directions

66. Computer Graphics Group Alexander Hornung Thank You