1. Non-Manifold Medial Surface Reconstruction from Volumetric Data 12010/6/16 Takashi Michikawa and Hiromasa Suzuki Research Center for Advanced Science and Technology The University of Tokyo, JAPAN

2. 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 2010/6/162 Thin-plate part (photo) Volumetric Data CAD surfaces Car body (photo)

3. Goal Extracting medial meshes from CT images of thin-plate parts –Applications : Reverse engineering 2010/6/163 Boundary Junction Closed surfaces by Marching Cubes Medial Mesh CT images

4. Related work 2010/6/164 CT images Volume Polygon Isosurfaces Marching Cubes, Dual Contouring etc. Medial surfaces Amenta2001 Dey2002 Foskey2003, Sud 2005 etc… Sensitive to noisy bumps Medial voxels Prohaska2002, Fujimori2004 etc.. Sensitive to non-manifold Sensitive to non-manifold

5. Challenge Handling non-manifold junctions Our method –Polygonization using sub-sampled medial voxels 2010/6/165 Medial voxels Sub-sampling of Medial voxels Medial mesh

6. Example(1) Shock absorber (car body parts) –400x400x640 –10 min. 2010/6/166 Binary volumeMedial meshManifold decomposition

7. Application ： Reverse Engineering Fitting NURBS surfaces to manifold parts 2010/6/167 Manifold decompositionNURBS surfaceControl points

8. Example(2) : Complex models Side frame of car body (after crashing) –708x965x813 voxels –8 hours –Application to stress analysis of crashed models 2010/6/168 Binary volume Medial mesh

9. Example (3) : High-valence junctions Our method “absorbs” complex junctions by sub- sampling and makes junction simple. 2010/6/169 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

10. 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) 2010/6/1610

11. 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 2010/6/1611 medial voxels Sub-sampled medial voxels and their support spheres Removed Sampled

12. 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 2010/6/1612 RandomPriority

13. Polygonization Computing Voronoi Diagram restricted on medial voxels by using sampled voxels as sites Creating triangles by dual graph of the Voronoi diagram 2010/6/1613

14. 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 2010/6/1614

15. Limitation Too thin input volumes –Sub-sampling may be failed because it remove nothing. Speed –Building Voronoi diagram Sharp corner –Lost by sampling order 2010/6/1615

16. 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]). 2010/6/1616

17. Acknowledgments Grant –Grants-in-Aid for Scientific Research (Japanese Government) Reverse engineering software –Ko-ichi Matsuzaki ( RCAST, The University of Tokyo) Data courtesy –Honda 2010/6/1617

18. The End michi@den.rcast.u-tokyo.ac.jp 2010/6/1618

19. Topology of voxels [Malandain97] Counting the number of FG/BG clusters 2010/6/1619