Robust Repair of Polygonal Models

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Robust Repair of Polygonal Models
Tao Ju Rice University
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Polygonal Models
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Closed Model

• Partitions the space into disjoint inside and
  outside volumes
• Each polygon lies between inside and outside

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Model Repair

• Close polygonal models
• Not just hole-filling
• Challenges
• Models may contain complex errors
• Models are often very big
• Geometry features need to be preserved

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Previous Work

• Mesh-based model repair
• Zippering Turk and Levoy 1994
• Stitching Barequet and Kumar 1997
• Progressive boundary decimation Borodin et al.
  2002
• Hole filling with fairing Liepa 2003
• Scattered data reconstruction
• Tangent plane estimation Hoppe et al. 1992
• Level sets Zhao and Osher 2002
• Radial basis functions Turk and OBrien 2002
• Partition-of-unity methods Ohtake et al. 2003
• Moving least squares surfaces Shen et al. 2004
• Context-based completion Sharf et al. 2004

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Previous Work

• Volumetric model repair

• How to determine signs ?
• How to generate surface ?

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Previous Work

• Volumetric model repair Sign generation
• Adaptive signed distances Frisken et al. 2000
• Flood-filling Oomes et al. 1997 Andujar et al.
  2002
• Space carving Curless and Levoy 1996
• Volumetric diffusion Davis et al. 2002
• Parity count and ray stabbing Nooruddin and Turk
  2003

• Volumetric model repair Contouring
• Marching Cubes Lorensen and Cline 1987
• Extended Marching Cubes Kobbelt et al. 2001
• Dual Contouring Ju et al. 2002

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Robust Model Repair

• Robust
• Closes arbitrary polygon soups
• Efficient
• Processes gigantic models on standard PCs
• Accurate
• Preserves surface quality
• Simple !

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Algorithm in a Nutshell
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Scan-conversion

• Octree grid

• Edges intersected with model
• Top-down creation

• Memory-less octree construction
• Reliable and fast intersection tests

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Dual Surface

• Each face dual to an intersected octree edge

Octree Edge
Dual Face
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Finding Holes

• Boundary edges
• Odd-valence edges
• Closed dual surface ? No boundary edge
• Set of boundary edges partitioned into cycles
• Each cycle encloses a hole

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Building a Patch

• Build one patch for each cycle
• Each quad dual to an octree edge
• Patch boundary is the cycle
• Divide-and-conquer!
• Using octree

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Integrating a Patch

• Add a quad
• If does not exist on the dual surface
• Remove a quad
• If already exists on the dual surface
• Key parity of edge valence

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Integrating a Patch

• Add a quad
• If not already on the dual surface
• Remove a quad
• If already on the dual surface
• Key parity of edge valence

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Sign Generation

• Sign changes across dual surface
• Flood-filling

Dual Face
Octree Signs
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Contouring

• Marching Cubes
• Edge intersections
• Rounded corners
• Dual Contouring
• Hermite data
• Sharp features

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Examples CAD Model
Input Model
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Examples CAD Model
Dual Surface
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Examples CAD Model
Closed Dual Surface
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Examples CAD Model
Output (Marching Cubes)
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Examples CAD Model
Output (Dual Contouring)
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Examples - Bunny
1. Input
2. DS
4. Output
3. DS Closed
Model Courtesy of the Stanford 3D Scanning
Repository
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Examples - Horse
1. Input
2. DS
3. DS Closed
4. Output
Model Courtesy of the Stanford 3D Scanning
Repository
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Examples David (at 1mm)
Input
Model Courtesy of the Digital Michelangelo Project
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Performance

• On PC with 1.5GHz CPU and 2GB memory

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Conclusion

• A simple, fast, and robust method to repair
  arbitrary polygon models
• Future work
• Remove topological noise
• Improve the quality of hole filling
• Repair using an adaptive grid
• Special thanks to my advisor, Prof. Joe Warren,
  for his insights and support