1. zl1 A sharpness dependent filter for mesh smoothing Chun-Yen Chen Kuo-Young Cheng available in CAGD Vol.22. 5(2005) 376-391

2. zl2 Outline  Introduction about authors  Introduction about works  Sharpness dependent filter  Sharpness dependent weighting function  Comparison  Conclusion

3. zl3 Introduction about authors  Chun-Yen Chen, Kuo-Young Cheng Institute of Information Science, Academia Sinica, Nankang, Taipei Department of Computer Science and Information Engineering, National Taiwan University Computer Graphics, Chinese Processing

4. zl4 Outline  Introduction about authors  Introduction about works  Sharpness dependent filter  Sharpness dependent weighting function  Comparison  Conclusion

5. zl5 Introduction about works  Mesh straight-line graph embedded in R³ a pair (K, V), where K is a simplicial complex representing the connectivity of vertices, edges, and faces and V=( ) describes the geo- metric positions of the vertices in R³ … …

6. zl6 Introduction about works  Mesh

7. zl7 Introduction about works  Mesh smoothing problem arising creating high-fidelity computer graphics objects using imperfectly-measured data from the real world

8. zl8 Introduction about works  Mesh smoothing main task adjusting the position of mesh vertex the to remove undesirable noise and uneven edges while retaining desirable geometric features

9. zl9 Introduction about works  Mesh smoothing regarded as a filter design problem, to remove high-frequency tiny part on surfaces filter : a function or a procedure which remove unwanted parts of a signal Taubin, G., 1995. A signal processing approach to fair surface design. Siggraph ’ 95. Taubin, G., 1996. Optimal surface smoothing as filter design. Research Report RC-20404. IBM Thomas J.Watson Research Center.

10. zl10 Introduction about works  Mesh smoothing dilemma how can one get rid of the noise by smoothing the surface, while preserving sharp edge to keep the underlying geometry intact or feature?

11. zl11 Introduction about works  Related works Notations mesh S={V, F}, where V and F are the sets of vertices and faces, respectively vertex element, face element collection of neighboring vertices of vertex Laplacian operator

12. zl12 Introduction about works  Laplacian smoothing (Taubin, 1995, 2000) adjust vertex for smoothingCompensate shrinkage

13. zl13 Introduction about works  Laplacian smoothing (Taubin, 1995, 2000) iterative process anti-shrinkage good overall smoothing, bad feature preserving 200 smoothing steps100 smoothing steps

14. zl14 Introduction about works  MCF (Mean Curvature Flow) isotropic filter design (Desbrun et al., 1999) mean curvature, discrete mean curvature operator

15. zl15 Introduction about works  MCF (Mean Curvature Flow) isotropic filter design (Desbrun et al., 1999) new vertex position

16. zl16 Introduction about works  MCF (Mean Curvature Flow) anisotropic filter design (Meyer et al., 2002)

17. zl17 Introduction about works  MCF (Mean Curvature Flow) isotropic filter feature non-preserving anisotropic filter feature preserving

18. zl18 Introduction about works  Bilateral Filter (Fleishman, et al., 2003; Jones et al., 2003)

19. zl19 Introduction about works  Mean-filter design (Ohtake et al., 2001) surface normal based  compute weighted average normal

20. zl20 Introduction about works  Mean-filter design (Ohtake et al., 2001) surface normal based  update each vertex

21. zl21 Introduction about works  Mean-filter design (Ohtake et al., 2001) feature non-preserving

22. zl22 Introduction about works  Median-filter design (Yagou et al., 2002) surface normal based  compute weighted average normal

23. zl23 Introduction about works  Median-filter design (Yagou et al., 2002) surface normal based  adjust normal choose as media angle in N(T) replace m(T) by m( )

24. zl24 Introduction about works  Median-filter design (Yagou et al., 2002) surface normal based  update each vertex

25. zl25 Introduction about works  Median-filter design (Yagou et al., 2002) feature preserving

26. zl26 Introduction about works  Remark mean-filter flat region median-filteredge min-filtercorner (Gonzalez, Woods, 2002) to smooth mesh appropriately, combine filters above together

27. zl27 Introduction about works  This paper propose a sharpness dependent filter design based on the fairing of surface normal, selecting a mean-filter for flat region and a min-filter for sharp region automatically

28. zl28 Introduction about works  This paper

29. zl29 Outline  Introduction about authors  Introduction about works  Sharpness dependent filter  Sharpness dependent weighting function  Comparison  Conclusion

30. zl30 Sharpness dependent filter  Basic concepts sharpness a measure of the distribution of the included angles between polygon face normals

31. zl31 Sharpness dependent filter  Basic concepts sharpness dependent weighting function defined as the distribution of sharpness cutoff value of sharp criteria for sharp and non-sharp, derived by Bayesian classification (Chen, et al., 2004)

32. zl32 Sharpness dependent filter  Algorithm 1. compute mean normal for each polygon face is the No. of neighboring faces of

33. zl33 Sharpness dependent filter  Algorithm 2. determine the closet face normal,, for each as follows  calculate the angle between normals normalized in a range [0,1]

34. zl34 Sharpness dependent filter  Algorithm 2. determine the closet face normal,, for each as follows  find the minimum value of

35. zl35 Sharpness dependent filter  Algorithm 3. Calculate the local sharpness

36. zl36 Sharpness dependent filter  Algorithm 4. compute a new face normal user-defined sharpness dependent weighting functon

37. zl37 Sharpness dependent filter  Algorithm 5. update each vertex position area weight contributed by

38. zl38 Sharpness dependent filter  Algorithm 6. proceed to next iteration step until a steady state, i.e., is a preset tolerance

39. zl39 Sharpness dependent filter  Remark we ’ ve got a filter design for mesh smoothing based on the weighting function defined by sharpness mean-filter min-filer

40. zl40 Sharpness dependent filter  Remark how to select weighing function ?

41. zl41 Outline  Introduction about authors  Introduction about works  Sharpness dependent filter  Sharpness dependent weighting function  Comparison  Conclusion

42. zl42 Sharpness dependent weighting function  Selection principle experiment to compare sharpness distribution of most noisy models Fandisk

43. zl43 Sharpness dependent weighting function  Selection principle experiment to compare sharpness distribution of most noisy models Two-hole structure

44. zl44 Sharpness dependent weighting function  Selection principle experiment to compare sharpness distribution of most noisy models Golf driver head

45. zl45 Sharpness dependent weighting function  Selection principle monotonic decreasing function, vanishing beyond the cutoff of sharpness Gaussian function Laplacian function El Fallah Ford function

46. zl46 Sharpness dependent weighting function  Selection principle monotonic decreasing function, vanishing beyond the cutoff of sharpness

47. zl47 Sharpness dependent weighting function  selection user-defined, chosen such that for large sharpness and for small sharpness Remember cutoff value of sharpness for sharp and non-sharp obtained by applying Bayesian classification?

48. zl48 Sharpness dependent weighting function  selection user-defined, chosen such that for large sharpness and for small sharpness obtain the best cutoff,, should be small when Gaussian weighting function

49. zl49 Sharpness dependent weighting function  selection sharpness factor to control degree of sharpness for feature preserving

50. zl50 Sharpness dependent weighting function  Remark sharpness factor controls the degress of sharpness for feature preserving, non-feature preserving the larger, the stronger the feature preserving

51. zl51 Outline  Introduction about authors  Introduction about works  Sharpness dependent filter  Sharpness dependent weighting function  Comparison  Conclusion

52. zl52 Comparison  Different sharpness factor sf=0, 10, 15, 20

53. zl53 Comparison  With other feature preserving filter Like anisotropic MCF bilateral filter median filter

54. zl54 Comparison  With other feature preserving filter Fandisk model A MCFBilateralMedian Sharpness Gaussian, sh=23.4, 16 steps

55. zl55 Comparison  With other feature preserving filter Two hole structure Laplacian, sh=32, 97 steps

56. zl56 Comparison  With other feature preserving filter Golf driver head Bilateral

57. zl57 Comparison  With other feature preserving filter Golf driver head A MCF

58. zl58 Comparison  With other feature preserving filter Golf driver head Sharpness

59. zl59 Comparison  With other feature preserving filter Guardian lion Bilateral

60. zl60 Comparison  With other feature preserving filter Guardian lion A MFC

61. zl61 Comparison  With other feature preserving filter Guardian lion Sharpness

62. zl62 Comparison  How about shrinkage? Little volume shrinkage, nearly intact

63. zl63 Comparison  How about execution time? 2.8 GHz Pentium 4 processor with 1 GB RAM

64. zl64 Outline  Introduction about authors  Introduction about works  Sharpness dependent filter  Sharpness dependent weighting function  Comparison  Conclusion

65. zl65 Conclusion  Highlights Define sharpness to measure feature areas of models Use sharpness dependent weighting function to automatically select filter to smooth for different feature Experiments to evaluate weighting function

66. zl66 ThankU