Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust...
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![Page 1: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/1.jpg)
Computer Graphics GroupAlexander Hornung
Alexander Hornung and Leif KobbeltRWTH Aachen
Robust Reconstruction of Watertight 3D Models from
Non-uniformly Sampled Point Clouds Without Normal Information
![Page 2: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/2.jpg)
Computer Graphics GroupAlexander Hornung
Point Cloud Reconstruction
![Page 3: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/3.jpg)
Computer Graphics GroupAlexander Hornung
Point Cloud Reconstruction
• Non-uniform sampling
• Holes
• Noise
• Bad scan alignment
• No (reliable) normals
![Page 4: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/4.jpg)
Computer Graphics GroupAlexander 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
![Page 5: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/5.jpg)
Computer Graphics GroupAlexander Hornung
Outline
• Introduction
• Surface confidence estimation
• Graph-based surface extraction
• Hole filling and detail preservation
• Mesh extraction
• Results
![Page 6: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/6.jpg)
Computer Graphics GroupAlexander 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, …
![Page 7: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/7.jpg)
Computer Graphics GroupAlexander 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
![Page 8: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/8.jpg)
Computer Graphics GroupAlexander Hornung
Signed vs. Unsigned Distance
![Page 9: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/9.jpg)
Computer Graphics GroupAlexander Hornung
Signed vs. Unsigned Distance
![Page 10: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/10.jpg)
Computer Graphics GroupAlexander Hornung
Signed vs. Unsigned Distance
![Page 11: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/11.jpg)
Computer Graphics GroupAlexander Hornung
Signed vs. Unsigned Distance
![Page 12: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/12.jpg)
Computer Graphics GroupAlexander Hornung
Overview
• Point cloud P
![Page 13: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/13.jpg)
Computer Graphics GroupAlexander Hornung
Overview
• Point cloud P
• Surface confidence (unsigned distance)
)(v
![Page 14: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/14.jpg)
Computer Graphics GroupAlexander Hornung
Overview
• Point cloud P
• Surface confidence (unsigned distance)
• Embed weighted graph structure G
)(v
![Page 15: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/15.jpg)
Computer Graphics GroupAlexander Hornung
Overview
• Point cloud P
• Surface confidence (unsigned distance)
• Embed weighted graph structure
• Min-Cut of G yields unknown surface
)(v
![Page 16: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/16.jpg)
Computer Graphics GroupAlexander Hornung
Outline
• Introduction
• Surface confidence estimation
• Graph-based surface extraction
• Hole filling and detail preservation
• Mesh extraction
• Results
![Page 17: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/17.jpg)
Computer Graphics GroupAlexander 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
)(v
![Page 18: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/18.jpg)
Computer Graphics GroupAlexander 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
)(v
![Page 19: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/19.jpg)
Computer Graphics GroupAlexander 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
)(v
)(v
![Page 20: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/20.jpg)
Computer Graphics GroupAlexander Hornung
Outline
• Introduction
• Surface confidence estimation
• Graph-based surface extraction
• Hole filling and detail preservation
• Mesh extraction
• Results
![Page 21: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/21.jpg)
Computer Graphics GroupAlexander Hornung
Find Optimal Surface
• Minimize energy
• Min-Cut of an embedded graph• Global optimum
• Highly efficient
• Graph structure?
S S
dSadxxSE )()(
![Page 22: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/22.jpg)
Computer Graphics GroupAlexander Hornung
Dual Graph Embedding
• : Probability that v is intersected by surface s
• Intersected voxels are split into 2 components• Interior faces
• Exterior faces
)(v
![Page 23: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/23.jpg)
Computer Graphics GroupAlexander 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
)(v
Voxel split-edges
Graph cut-edges
![Page 24: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/24.jpg)
Computer Graphics GroupAlexander Hornung
Min-Cut Surface Extraction
• Embed graph into a crust containing the surface
![Page 25: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/25.jpg)
Computer Graphics GroupAlexander Hornung
Min-Cut Surface Extraction
• Embed graph into a crust containing the surface
• Edge weights defined per voxel avvw s )()(
![Page 26: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/26.jpg)
Computer Graphics GroupAlexander 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
avvw s )()(
![Page 27: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/27.jpg)
Computer Graphics GroupAlexander 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
avvw s )()(
![Page 28: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/28.jpg)
Computer Graphics GroupAlexander Hornung
Outline
• Introduction
• Surface confidence estimation
• Graph-based surface extraction
• Hole filling and detail preservation
• Mesh extraction
• Results
![Page 29: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/29.jpg)
Computer Graphics GroupAlexander 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
![Page 30: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/30.jpg)
Computer Graphics GroupAlexander 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
![Page 31: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/31.jpg)
Computer Graphics GroupAlexander 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
)(v
643
![Page 32: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/32.jpg)
Computer Graphics GroupAlexander 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
)(v
1283
![Page 33: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/33.jpg)
Computer Graphics GroupAlexander 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
)(v
1283
![Page 34: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/34.jpg)
Computer Graphics GroupAlexander 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
)(v
2563
![Page 35: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/35.jpg)
Computer Graphics GroupAlexander 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
)(v
2563
![Page 36: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/36.jpg)
Computer Graphics GroupAlexander 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
)(v
5123
![Page 37: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/37.jpg)
Computer Graphics GroupAlexander 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
)(v
5123
![Page 38: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/38.jpg)
Computer Graphics GroupAlexander Hornung
Outline
• Introduction
• Surface confidence estimation
• Graph-based surface extraction
• Hole filling and detail preservation
• Mesh extraction
• Results
![Page 39: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/39.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
Loop of voxel split-edgesGraph cut-edges
![Page 40: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/40.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• Loops define non-planar polygonal faces
• Mesh vertices at voxel corners
![Page 41: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/41.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• Loops define non-planar polygonal faces
• Mesh vertices at voxel corners
• Cycle along split-edges
![Page 42: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/42.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• Loops define non-planar polygonal faces
• Mesh vertices at voxel corners
• Cycle along split-edges
![Page 43: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/43.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• Loops define non-planar polygonal faces
• Mesh vertices at voxel corners
• Cycle along split-edges
![Page 44: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/44.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• Loops define non-planar polygonal faces
• Mesh vertices at voxel corners
• Cycle along split-edges
![Page 45: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/45.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• Loops define non-planar polygonal faces
• Mesh vertices at voxel corners
• Cycle along split-edges
![Page 46: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/46.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• estimated per voxel
Mesh vertices at voxel centers
![Page 47: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/47.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• estimated per voxel
Mesh vertices at voxel centers
![Page 48: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/48.jpg)
Computer Graphics GroupAlexander 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
![Page 49: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/49.jpg)
Computer Graphics GroupAlexander 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
![Page 50: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/50.jpg)
Computer Graphics GroupAlexander 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
![Page 51: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/51.jpg)
Computer Graphics GroupAlexander 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
![Page 52: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/52.jpg)
Computer Graphics GroupAlexander 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
![Page 53: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/53.jpg)
Computer Graphics GroupAlexander 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
![Page 54: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/54.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
![Page 55: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/55.jpg)
Computer Graphics GroupAlexander Hornung
Cut Manifold to Triangle Mesh
• Elimination of grid artifactsError controlled Bi-Laplacian smoothing
• Based on surface confidence• Stop smoothing if
svvp )1)((
![Page 56: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/56.jpg)
Computer Graphics GroupAlexander Hornung
Outline
• Introduction
• Surface confidence estimation
• Graph-based surface extraction
• Hole filling and detail preservation
• Mesh extraction
• Results
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Computer Graphics GroupAlexander Hornung
Max Planck
Resolution Time Genus Vertices
5123 199s 0 320K
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Computer Graphics GroupAlexander Hornung
Statue
Resolution Time Genus Vertices
10243 269s 0 448K
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Computer Graphics GroupAlexander Hornung
Rings
Resolution Time Genus Vertices
2563 45s 4 91K
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Computer Graphics GroupAlexander Hornung
Rings
Resolution Time Genus Vertices
2563 45s 4 91K
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Computer Graphics GroupAlexander Hornung
Leo
Resolution Time Genus Vertices
2563 48s 1 47K
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Computer Graphics GroupAlexander Hornung
Monkey
Resolution Time Genus Vertices
2563 82s 0 72K
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Computer Graphics GroupAlexander Hornung
Dragon
Resolution Time Genus Vertices
5123 150s 1 (>400) 318K
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Computer Graphics GroupAlexander 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
![Page 65: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/65.jpg)
Computer Graphics GroupAlexander 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
![Page 66: Computer Graphics Group Alexander Hornung Alexander Hornung and Leif Kobbelt RWTH Aachen Robust Reconstruction of Watertight 3D Models from Non-uniformly.](https://reader035.fdocuments.us/reader035/viewer/2022062320/56649d0a5503460f949dc293/html5/thumbnails/66.jpg)
Computer Graphics GroupAlexander Hornung
Thank You