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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
  • 8. Radial Basis Functions
    • 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 !