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Alexander Hornung and Leif Kobbelt RWTH Aachen

Alexander Hornung and Leif Kobbelt RWTH Aachen

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Alexander Hornung and Leif Kobbelt RWTH Aachen

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

  2. Point Cloud Reconstruction

  3. Point Cloud Reconstruction • Non-uniform sampling • Holes • Noise • Bad scan alignment • No (reliable) normals

  4. 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. Outline • Introduction • Surface confidence estimation • Graph-based surface extraction • Hole filling and detail preservation • Mesh extraction • Results

  6. 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. 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. Signed vs. Unsigned Distance

  9. Signed vs. Unsigned Distance

  10. Signed vs. Unsigned Distance

  11. Signed vs. Unsigned Distance

  12. Overview • Point cloud P

  13. Overview • Point cloud P • Surface confidence (unsigned distance)

  14. Overview • Point cloud P • Surface confidence (unsigned distance) • Embed weighted graph structure G

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

  16. Outline • Introduction • Surface confidence estimation • Graph-based surface extraction • Hole filling and detail preservation • Mesh extraction • Results

  17. 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. 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. 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. Outline • Introduction • Surface confidence estimation • Graph-based surface extraction • Hole filling and detail preservation • Mesh extraction • Results

  21. Find Optimal Surface • Minimize energy • Min-Cut of an embedded graph • Global optimum • Highly efficient • Graph structure?

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

  23. Dual Graph Embedding Voxel split-edges Graph cut-edges • : 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

  24. Min-Cut Surface Extraction • Embed graph into a crust containing the surface

  25. Min-Cut Surface Extraction • Embed graph into a crust containing the surface • Edge weights defined per voxel

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

  27. Min-Cut Surface Extraction • 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

  28. Outline • Introduction • Surface confidence estimation • Graph-based surface extraction • Hole filling and detail preservation • Mesh extraction • Results

  29. 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. 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. Hierarchical Approach • Surface confidence estimation • (Re-)Insert point samples • Dilate and compute • Graph-based surface extraction • Generate octahedral graph • Compute min-cut • Volumetric refinement • Narrow band 643

  32. Hierarchical Approach • Surface confidence estimation • (Re-)Insert point samples • Dilate and compute • Graph-based surface extraction • Generate octahedral graph • Compute min-cut • Volumetric refinement • Narrow band 1283

  33. Hierarchical Approach • Surface confidence estimation • (Re-)Insert point samples • Dilate and compute • Graph-based surface extraction • Generate octahedral graph • Compute min-cut • Volumetric refinement • Narrow band 1283

  34. Hierarchical Approach • Surface confidence estimation • (Re-)Insert point samples • Dilate and compute • Graph-based surface extraction • Generate octahedral graph • Compute min-cut • Volumetric refinement • Narrow band 2563

  35. Hierarchical Approach • Surface confidence estimation • (Re-)Insert point samples • Dilate and compute • Graph-based surface extraction • Generate octahedral graph • Compute min-cut • Volumetric refinement • Narrow band 2563

  36. Hierarchical Approach • Surface confidence estimation • (Re-)Insert point samples • Dilate and compute • Graph-based surface extraction • Generate octahedral graph • Compute min-cut • Volumetric refinement • Narrow band 5123

  37. Hierarchical Approach • Surface confidence estimation • (Re-)Insert point samples • Dilate and compute • Graph-based surface extraction • Generate octahedral graph • Compute min-cut • Volumetric refinement • Narrow band 5123

  38. Outline • Introduction • Surface confidence estimation • Graph-based surface extraction • Hole filling and detail preservation • Mesh extraction • Results

  39. Cut Manifold to Triangle Mesh Graph cut-edges Loop of voxel split-edges

  40. Cut Manifold to Triangle Mesh • Loops define non-planar polygonal faces • Mesh vertices at voxel corners

  41. Cut Manifold to Triangle Mesh • Loops define non-planar polygonal faces • Mesh vertices at voxel corners • Cycle along split-edges

  42. Cut Manifold to Triangle Mesh • Loops define non-planar polygonal faces • Mesh vertices at voxel corners • Cycle along split-edges

  43. Cut Manifold to Triangle Mesh • Loops define non-planar polygonal faces • Mesh vertices at voxel corners • Cycle along split-edges

  44. Cut Manifold to Triangle Mesh • Loops define non-planar polygonal faces • Mesh vertices at voxel corners • Cycle along split-edges

  45. Cut Manifold to Triangle Mesh • Loops define non-planar polygonal faces • Mesh vertices at voxel corners • Cycle along split-edges

  46. Cut Manifold to Triangle Mesh • estimated per voxel  Mesh vertices at voxel centers

  47. Cut Manifold to Triangle Mesh • estimated per voxel  Mesh vertices at voxel centers

  48. 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. 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. 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