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• 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 .

### Transcript

• 1. Surface Completion Reporter: Zhonggui Chen 2006.3.29
• 2. Outline
• Background
• Overview
• Geometric method
• Volumetric method
• Image-based method
• Reference
• 3.
• Data acquisition
Background
• 4. Background
• Surface reconstruction
• 5. Surface Completion
• Integrated into surface reconstruction algorithm
• Considered as a post-processing
• 6. Requirements
• Robustness
• 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
• 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
• J.C.Carr et al. Siggraph 2001
• 9. Signed-distance Function
• 10. Interpolation Problem Given: and ？ Output:
• 11.
• General form
• e.g.
Radial Basis Function 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 2. Edge Relaxation 1. Subdivision
• 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
• 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 In Cube Out Cube Hole 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. Gu et al. Siggraph 02 cut parametrize Basic idea
• 44. Basic idea cut sample
• 45. Basic idea cut [ r , g , b ] = [ x , y , z ] render store
• 46.
• 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), 888-895.
• 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), 878-887.
• 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 !