1. Filling Holes in Complex Surfaces using Volumetric Diffusion James Davis, Stephen Marschner, Matt Garr, Marc Levoy Stanford University First International Symposium on 3D Data Processing, Visualization, Transmission June 2002

2. 2 Scanned geometry often has complex holes

3. 3 Locate hole boundaries and triangulate?

4. 4 Triangulating boundaries sometimes fails Self intersecting surface

5. 5 Hole boundaries must be correctly connected Fill hole on blue boundary - no solution possible Fill hole between blue and red boundary - solution possible Blue boundary Red boundary

6. 6 Topological complexity

7. 7 Geometric complexity Noise at the micro scale insures complex geometry

8. 8 Desirable hole filling attributes Manifold non-self-intersecting surfaces Manifold non-self-intersecting surfaces Topological flexibility Topological flexibility Use of all available information Use of all available information Efficiency Efficiency

9. 9 Related work Simple boundary triangulation [Berg, et. al. 97] Mesh based surface reconstruction [Turk94] [Curless96] [Wheeler98] Point cloud interpolation [Edelsbrunner92] [Hoppe92] [Bajaj95] [Chen95] [Amenta98] [Whitaker98] [Bernardini99] [Dey01] [Zhao01] [Dinh01] [Carr01]

10. 10 Volumetric surface representation Surface is the zero set of a filtered sidedness function ( or equivalently a clamped signed-distance function )

11. 11 Limit the computational domain Brown is unknown or unimportant region Volume represented only near the surface Volume represented only near the surface

12. 12 Surface holes are unknown regions Brown is unknown or unimportant region

13. 13 Diffuse to fill in missing volumetric regions

14. 14 Simplified method description h  compositeonto convolve dsds dsds (1) (2)

15. 15 Examples from synthetic holes

16. 16 Examples from real meshes [ video ]

17. 17 Flexible but not always correct topology

18. 18 Scanner line of sight constraint scanner region known to be empty

19. 19 Method with line of sight constraint (1) (2) (3) h  composite onto convolve dsds dsds ontoweighted composite

20. 20 Line of sight constraint enforces correct topology

21. 21 Efficient computation possible Mesh size : 4.5 M triangles Volume size : 440 M voxels Voxels touched : 4.5% [ video ] Memory allocated : 550MB Processing time : 20 minutes

22. 22 Summary Manifold non-self-intersecting surfaces Manifold non-self-intersecting surfaces Topological flexibility Topological flexibility Use of all available information Use of all available information Efficient Efficient Simple Simple

23. 23 Algorithm’s free parameters Number of iterations Number of iterations Distance to clamp the computational domain Distance to clamp the computational domain Diffusion operator Diffusion operator Compositing percentage Compositing percentage

24. 24 Future work – choice of diffusion operator Convolution Convolution 3x3x3 box filter 7-part plus filter Anisotropic diffusion Anisotropic diffusion In direction of gradient? Morphological operators Morphological operators Opening – closing

25. 25 Future work – control of surface shape minimum curvature minimum area

26. 26 Future work – line of sight constraint What should compositing be set to? What should compositing  be set to?  low  mid  high

27. 27 END