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Filling Holes in Complex Surfaces using Volumetric Diffusion

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. Scanned geometry often has complex holes.

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Filling Holes in Complex Surfaces using Volumetric Diffusion

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  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. Scanned geometry often has complex holes

  3. Locate hole boundaries and triangulate?

  4. Self intersecting surface Triangulating boundaries sometimes fails

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

  6. Topological complexity

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

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

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

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

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

  13. Diffuse to fill in missing volumetric regions

  14. Simplified method description ds h  (1) convolve ds composite onto (2)

  15. Examples from synthetic holes

  16. Examples from real meshes [ video ]

  17. Flexible but not always correct topology

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

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

  20. Line of sight constraint enforces correct topology

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

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

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

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

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

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

  27. END

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