1. Reporter: Zhonggui Chen 2006.3.29
Surface Completion
Reporter: Zhonggui Chen

2. Outline Background Overview Geometric method Volumetric method
Image-based method
Reference

3. Background
Data acquisition

4. Background
Surface reconstruction

5. Surface Completion Integrated into surface reconstruction algorithm
Considered as a post-processing

6. Requirements Robustness Efficiency Accuracy
The method should always produce a watertight surface for any input model.
Efficiency
The method should be able to process huge models within reasonable time and space.
Accuracy
The method should preserve the geometry of the input model whenever possible.
Boundary condition
Context condition

7. Classifications Geometric method Volumetric method Image-based
Operate directly on the polygons in the model
Volumetric method
Convert a polygonal model into a volume representation
Image-based
Convert a polygonal model into a geometry
image

8. Radial Basis Functions
J.C.Carr et al. Siggraph 2001

9. Signed-distance Function

10. Interpolation Problem
Given:
and
Output: ？

11. Radial Basis Function General form e.g.
is a polynomial of low degree
the basic function is a real valued function

12. Evaluation

13. Evaluation

14. Greed algorithm Procedure
Choose a subset from the interpolation nodes X and fit an RBF only to these.
Evaluate the residual, , at all nodes.
If then stop.
Else append new centers where is large.
Re-fit RBF and goto 2.

15. Results

16. Summary Repair holes with arbitrary topology Holes are smoothly filled
Approximate original surface

17. Filling Holes in Meshes
Peter Liepa. Eurographics Symposium on Geometry Prosessing 2003

18. Pipeline Hole identification Hole triangulation Mesh refinement
Mesh fairing

19. Triangulation of 3D Polygons
Minimum area triangulation
Min-max dihedral angel triangulation

20. Mesh Refinement
1. Subdivision
2. Edge Relaxation

21. Fairing
Weighted umbrella-operator
Uniform :
Scale-dependent :

22. Summary Easy to implement Focus algorithm on holes
Triangulation may self-intersect
Can’t fill holes with islands
Fairing weaken original surface feature

23. Robust Repair of Polygonal Models
Tao Ju, Rice University, Siggraph 2004

24. Pipeline
Scan-conversion
Sign generation
Surface reconstruction

25. Sign Generation
Cell faces containing an odd number of intersection edges

26. Patch Boundary Circles
Patching dual surface
Edges intersected with the model and the corresponding dual surface

27. Marching Cubes
Cube with signs at eight corners

28. Marching Cubes

29. Results

30. Results

31. Summary Employ a space-efficient octree grid
Produce closed, manifold surface for any input model
创新点:1. 文章做得很细, 对怎样充分利用八叉树性质提高算法效率有很详细的讨论. 2. 对每个空间点作标记时, 先使对偶曲面封闭, 然后对每个空间点作inside还是outside标记. 3. 利用自己发表的曲面重建的新方法.

32. Atomic Volumes for Mesh Completion
J. Podolak and S. Rusinkiewicz, SGP’05
A volume is atomic if
it doesn’t intersect
the polygons of the
mesh.

33. Spatial Partitioning

34. Pipeline
Hole Cube
Out Cube
In Cube

35. Pipeline

36. Pipeline
Sink
(outside)
Source
(inside)

37. Pipeline

38. User Constraints

39. Results

40. Summary
Avoid changing, approximating or re-sampling the original mesh data
Incorporate user constraints
Can’t process holes with islands

41. Geometry Completion and Detail Generation by Texture Synthesis
Minh X. Nguyen, Xiaoru Yan, Baoquan Chen. Pacific Graphics 2005

42. Geometry Image

43. Basic idea
cut
Gu et al. Siggraph 02
parametrize

44. Basic idea
cut
sample

45. Basic idea
cut
store
render
[r,g,b] = [x,y,z]

47. References
Curless B., Levoy M.: A volumetric method for building complex models from range images. In SIGGRAPH'96
Davis J., Marschner S., Garr M., Levoy M.: Filling holes in complex surfaces using volumetric diffusion, 2002.
Fakir S. N., Greg T.: Simplification an repair of polygonal models using volumetic techniques, TVCG. 9, 3(2003)
J. C. Carr et al.: Reconstruction and representation of 3D objects with radial basis functions. Siggraph’01.
Joshua P., Szymon R., Atomic volumes for mesh completion. Eurographics Symposium on Geometry Processing (2005)
Ju T.: Robust repair of polygonal models. ACM Trans. Graph. 23, 3 (2004),

48. References
Kolluri R. K.: Spectral watertight surface reconstruction, 2003.
Liepa P.: Filling holes in meshes. In Proceedings of the Eurographics/ACM SIGGRAPH symposium on Geometry processing (2003)
Minh X. N., Xiaoru Y., Baoqun C.: Geometry completion and detail generation by texture synthesis. PG’05.
Sharf A., Alexa M., Cohen-or D.: Context-based surface completion. ACM Trans. Graph. 23, 3 (2004),
Verdera, J., Caselles, V., Bertalmio, M., , Sapiro, G.: In-painting surface holes. In: Proceedings of International Conference on Image Processing, pp. 903–906 (2003)

49. Thank you !