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Evaluation of the Robustness of Surface Characterisation of Carbon Fibre Composites Using Wavelet Texture Analysis

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Sp120709 slideshare

  1. 1. Evaluation of the Robustness of SurfaceCharacterisation of Carbon Fibre CompositesUsing Wavelet Texture Analysis Associate Professor Stuart Palmer Faculty of Science and Technology Deakin University, Australia Dr Wayne Hall Griffith School of Engineering Griffith University, Australia 1
  2. 2. IntroductionThe mechanical properties of composites are importantfor their structural performanceBut, quality of finish on visible surfaces is also importantfor customer satisfactionCurrently, surface finish assessment is often based onhuman observation, which is time consuming, subjectiveand not appropriate for automationThe wavelet transform has the ability to effectivelycharacterise many engineering surfaces 2
  3. 3. The 2D discrete wavelet transform (2DDWT)Produces a nearly orthogonal decomposition of animage into coefficients that separately represent theinformation in the image in:• 3 orientations (horizontal, vertical and diagonal);• and, different scales (scale=characteristic dimension)The 2DDWT is an iterative decomposition where thescale doubles each step, until the limit of the imageresolution is reached 3
  4. 4. The 2D discrete wavelet transform (2DDWT)Original image 4
  5. 5. The 2D discrete wavelet transform (2DDWT)Original imageDecomposition cD1v cD1d cA1 cD1h level 1 5
  6. 6. The 2D discrete wavelet transform (2DDWT)Original imageDecomposition cD1v cD1d cA1 cD1h level 1Decomposition cA2 h cD2 v cD2 cD2d level 2 6
  7. 7. The 2D discrete wavelet transform (2DDWT)Original imageDecomposition cD1v cD1d cA1 cD1h level 1Decomposition cA2 h cD2 v cD2 cD2d level 2Decomposition cAJ cD Jh v cD J cDJd level J 7
  8. 8. The 2D discrete wavelet transform (2DDWT)Original imageDecomposition cD1v cD1d cA1 cD1h level 1Decomposition cA2 h cD2 v cD2 cD2d level 2Decomposition cAJ cD Jh v cD J cDJd level J 8
  9. 9. The 2D discrete wavelet transform (2DDWT) It is possible to selectively re-assemble images:Detail coefficients from Detail coefficients from Original image levels 2-4 levels 5-6 9
  10. 10. Wavelet texture analysis (WTA)Energy measure computed for detail coefficient sets: cD1h cD1v cD1d h cD2 v cD2 cD2d cAJ cD Jh v cD J cDJd 10
  11. 11. Wavelet texture analysis (WTA) Energy measure computed for detail coefficient sets: 1 k 2E jk cD j F J j 1; k h, v , d E1h E1v E1d M Nwhere:j is the wavelet analysis scale/levelk is the wavelet detail coefficient set E 2h v E2 E2d orientation (horiz., vert. or diagon.)J is the maximum analysis scale/levelM×N is the size of the coefficient setand: 2 2 A a ij v E Jd F i, j cAJ E Jh EJ 11
  12. 12. Wavelet texture analysis (WTA)A texture feature vector is created from the energy setfor each sample image:[E1h, E1v, E1d, E2h, E2v, E2d, … EJh, EJv, EJd]The texture feature vectors for all samples are used asthe inputs for principal components analysis (PCA)PCA uses linear algebra to transform a set of correlatedvariables into a smaller set of uncorrelated variablescalled ‘principal components’PC1=l1E1h+l2E1v+l3E1d+l4E2h+l5E2v+l6E2d… 12
  13. 13. MethodTypical clear resin sample images for the three grades ofsurface finishGrade 1 Grade 2 Grade 3 13
  14. 14. Results 200 100 6 12 Principal Component 2 score 3 1 11 8 0 2 57 -100 4 10 -200 -300 9 -400 -800 -600 -400 -200 0 200 400 600 800 1000 1200 1400 Principal Component 1 score ◊ Grade 1 ∆ Grade 2 O Grade 3 14
  15. 15. Results db7 wavelet / 3 levels of decomposition 200 100 6 12 Principal Component 2 score 3 1 11 8 0 2 57 -100 4 10 -200 -300 9 -400 -800 -600 -400 -200 0 200 400 600 800 1000 1200 1400 Principal Component 1 score ◊ Grade 1 ∆ Grade 2 O Grade 3 15
  16. 16. Robustness of the WTA methodGiven these promising results, the following workpresents an evaluation of the robustness of the WTAmethod to common process errors that can occur in theimaging of material samples; those being:• horizontal and/or vertical translation;• rotation; and• dilation 16
  17. 17. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 17
  18. 18. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 18
  19. 19. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 19
  20. 20. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 20
  21. 21. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 21
  22. 22. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 22
  23. 23. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 23
  24. 24. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 24
  25. 25. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 25
  26. 26. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 26
  27. 27. Robustness to translation Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 1 2 3 4 5 6 7 8 9 Sample number 27
  28. 28. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 28
  29. 29. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 29
  30. 30. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 30
  31. 31. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 31
  32. 32. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 32
  33. 33. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 33
  34. 34. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 34
  35. 35. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 35
  36. 36. Robustness to rotation - small Grade 1 Grade 2 Grade 3 1200 Principal component 1 score 800 400 0 -400 -800 -8 -6 -4 -2 0 2 4 6 8 Angle of rotation 36
  37. 37. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 37
  38. 38. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 38
  39. 39. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 39
  40. 40. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 40
  41. 41. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 41
  42. 42. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 42
  43. 43. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 43
  44. 44. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 44
  45. 45. Robustness to rotation - gross Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 -1500 Angle of rotation 45
  46. 46. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 46
  47. 47. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 47
  48. 48. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 48
  49. 49. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 49
  50. 50. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 50
  51. 51. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 51
  52. 52. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 52
  53. 53. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 53
  54. 54. Robustness to dilation - small Grade 1 Grade 2 Grade 3 1500 Principal component 1 score 1000 500 0 -500 -1000 92 94 96 98 100 102 104 106 108 Percentage dilation 54
  55. 55. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 55
  56. 56. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 56
  57. 57. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 57
  58. 58. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 58
  59. 59. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 59
  60. 60. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 60
  61. 61. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 61
  62. 62. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 62
  63. 63. Robustness to dilation - gross Grade 1 Grade 2 Grade 3 2000 Principal component 1 score 1600 1200 800 400 0 -400 -800 -1200 60 70 80 90 100 110 120 130 140 Percentage dilation 63
  64. 64. ConclusionsThe results obtained indicate that the WTA method isrobust to:• significant horizontal and/or vertical translations of the sample being imaged;• significant rotation of the sample being imaged; and• significant dilation of the sample being imagedGross rotation and/or dilation of the sample beingimaged can impact of the repeatability of the WTAmethod 64
  65. 65. Thank you for your timePresentation: http://ow.ly/diQxn (~40 MB) 65

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