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Non-Manifold Medial Surface Reconstruction
from Volumetric Data
2010/6/16
Takashi Michikawa and Hiromasa Suzuki
Research Center for Advanced Science and Technology
The University of Tokyo, JAPAN
Thin-plate mechanical parts
• Made with metal plates by stamping and welding– Found in many kinds of mechanical objects
• Car bodies, electric parts etc…– In CAD, Represented by open surfaces with boundaries
• Non-manifold surfaces
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Thin-plate part(photo)
Volumetric Data CAD surfaces Car body (photo)
Goal
• Extracting medial meshes from CT images of thin-plate parts– Applications : Reverse engineering
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Boundary
Junction
Closed surfaces by Marching Cubes Medial Mesh CT images
Related work
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CT images
Volume Polygon
Isosurfaces
Marching Cubes,Dual Contouring etc.
Medial surfaces
Amenta2001Dey2002Foskey2003, Sud 2005 etc…
Sensitive to noisy bumps
Medial voxels
Prohaska2002,Fujimori2004 etc.. Sensitive to
non-manifold
Challenge
• Handling non-manifold junctions• Our method
– Polygonization using sub-sampled medial voxels
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Medial voxels Sub-sampling ofMedial voxels
Medial mesh
Example(1)
• Shock absorber (car body parts) – 400x400x640– 10 min.
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Binary volume Medial mesh Manifold decomposition
Application： Reverse Engineering
• Fitting NURBS surfaces to manifold parts
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Manifold decomposition NURBS surface Control points
Example(2) : Complex models
• Side frame of car body (after crashing)– 708x965x813 voxels– 8 hours– Application to stress analysis of crashed models
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Binary volume Medial mesh
Example (3) : High-valence junctions
• Our method “absorbs” complex junctions by sub-sampling and makes junction simple.
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Binary volume Medial voxels Intersection of the medial voxels
Medial surface By our method
Display Non-manifold edges
Junctions are spitted into
several small junctions
Procedure Outline
1. Binarize
2. Extract medial voxels
3. Sub-sampling of medial voxels
4. Voronoi diagram on medial voxels
5. Dual graph (Delaunay triangulation)
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Sub-sampling of medial voxels
• Covering medial voxels by a set of spheres [Ohtake05]– Select one medial voxel v and define sphere S centered at v– Radius is distance to boundraryscaled by α (α=2 for all examples)– Remove medial voxels in the sphere S – Repeat them until all the medial voxels are covered by spheres
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medial voxels Sub-sampled medial voxels and their support spheres
Removed
Sampled
Topology-based sub-sampling
• Problem : Which point is sampled first?– Random sampling makes small cavities.
• Priority sampling by voxel topology [Malandain97]– ordering voxels by
1. Topology : junction boundary surfaces
2. Distance to the boundary surfaces : voxels with larger distance are selected first
2010/6/16 12Random Priority
Polygonization
• Computing Voronoi Diagram restricted on medial voxels by using sampled voxels as sites
• Creating triangles by dual graph of the Voronoi diagram
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Mesh Cleaning
• Non-manifold exceptions– In some case, overlapped triangles are made
• c.f. Degeneration of Delaunay Triangulation
• Manifold cleaning for manifold points [Ohtake05]– Referring to topological type of voxels
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Limitation
• Too thin input volumes– Sub-sampling may be failed because it remove
nothing.
• Speed– Building Voronoi diagram
• Sharp corner– Lost by sampling order
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Summary and Future work
• Polygonization of thin-plate mechanical objects– sub-sampling simplifies non-manifold junction voxels– Handling non-manifold part
• Future work– Speed up & robustness– Simultaneous polygonization of wires, thin-plate and
solids(e.g. [Ju06]).
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Acknowledgments
• Grant– Grants-in-Aid for Scientific Research (Japanese
Government)
• Reverse engineering software– Ko-ichi Matsuzaki ( RCAST, The University of Tokyo)
• Data courtesy– Honda
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Topology of voxels [Malandain97]
• Counting the number of FG/BG clusters
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