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Stuart Palmer

The document evaluates the robustness of wavelet texture analysis (WTA) for characterizing carbon fibre composite surfaces. WTA uses the discrete wavelet transform to decompose images into orientation and scale-based detail coefficients, from which texture features are extracted. Principal component analysis is applied to classify samples by surface finish grade. The study examines WTA's sensitivity to common imaging errors like translation, rotation, and dilation. Results show the method maintains good discrimination between grades despite such errors, demonstrating it is a robust automated approach to surface assessment.

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Evaluation of the Robustness of Surface Characterisation of Carbon Fibre Composites Using 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
Introduction The mechanical properties of composites are important for their structural performance But, quality of finish on visible surfaces is also important for customer satisfaction Currently, surface finish assessment is often based on human observation, which is time consuming, subjective and not appropriate for automation The wavelet transform has the ability to effectively characterise many engineering surfaces 2
The 2D discrete wavelet transform (2DDWT) Produces a nearly orthogonal decomposition of an image into coefficients that separately represent the information in the image in: • 3 orientations (horizontal, vertical and diagonal); • and, different scales (scale=characteristic dimension) The 2DDWT is an iterative decomposition where the scale doubles each step, until the limit of the image resolution is reached 3
The 2D discrete wavelet transform (2DDWT) Original image 4
The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 5
The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 Decomposition cA2 h cD2 v cD2 cD2d level 2 6
The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 Decomposition cA2 h cD2 v cD2 cD2d level 2 Decomposition cAJ cD Jh v cD J cDJd level J 7
The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 Decomposition cA2 h cD2 v cD2 cD2d level 2 Decomposition cAJ cD Jh v cD J cDJd level J 8
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
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
Wavelet texture analysis (WTA) Energy measure computed for detail coefficient sets: 1 k 2 E jk cD j F J j 1; k h, v , d E1h E1v E1d M N where: j is the wavelet analysis scale/level k is the wavelet detail coefficient set E 2h v E2 E2d orientation (horiz., vert. or diagon.) J is the maximum analysis scale/level M×N is the size of the coefficient set and: 2 2 A a ij v E Jd F i, j cAJ E Jh EJ 11
Wavelet texture analysis (WTA) A texture feature vector is created from the energy set for each sample image: [E1h, E1v, E1d, E2h, E2v, E2d, … EJh, EJv, EJd] The texture feature vectors for all samples are used as the inputs for principal components analysis (PCA) PCA uses linear algebra to transform a set of correlated variables into a smaller set of uncorrelated variables called ‘principal components’ PC1=l1E1h+l2E1v+l3E1d+l4E2h+l5E2v+l6E2d… 12
Method Typical clear resin sample images for the three grades of surface finish Grade 1 Grade 2 Grade 3 13
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
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
Robustness of the WTA method Given these promising results, the following work presents an evaluation of the robustness of the WTA method to common process errors that can occur in the imaging of material samples; those being: • horizontal and/or vertical translation; • rotation; and • dilation 16
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Conclusions The results obtained indicate that the WTA method is robust 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 imaged Gross rotation and/or dilation of the sample being imaged can impact of the repeatability of the WTA method 64
Thank you for your time Presentation: http://ow.ly/diQxn (~40 MB) 65

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Sp120709 slideshare

  • 1. Evaluation of the Robustness of Surface Characterisation of Carbon Fibre Composites Using 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. Introduction The mechanical properties of composites are important for their structural performance But, quality of finish on visible surfaces is also important for customer satisfaction Currently, surface finish assessment is often based on human observation, which is time consuming, subjective and not appropriate for automation The wavelet transform has the ability to effectively characterise many engineering surfaces 2
  • 3. The 2D discrete wavelet transform (2DDWT) Produces a nearly orthogonal decomposition of an image into coefficients that separately represent the information in the image in: • 3 orientations (horizontal, vertical and diagonal); • and, different scales (scale=characteristic dimension) The 2DDWT is an iterative decomposition where the scale doubles each step, until the limit of the image resolution is reached 3
  • 4. The 2D discrete wavelet transform (2DDWT) Original image 4
  • 5. The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 5
  • 6. The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 Decomposition cA2 h cD2 v cD2 cD2d level 2 6
  • 7. The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 Decomposition cA2 h cD2 v cD2 cD2d level 2 Decomposition cAJ cD Jh v cD J cDJd level J 7
  • 8. The 2D discrete wavelet transform (2DDWT) Original image Decomposition cD1v cD1d cA1 cD1h level 1 Decomposition cA2 h cD2 v cD2 cD2d level 2 Decomposition cAJ cD Jh v cD J cDJd level J 8
  • 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. 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. Wavelet texture analysis (WTA) Energy measure computed for detail coefficient sets: 1 k 2 E jk cD j F J j 1; k h, v , d E1h E1v E1d M N where: j is the wavelet analysis scale/level k is the wavelet detail coefficient set E 2h v E2 E2d orientation (horiz., vert. or diagon.) J is the maximum analysis scale/level M×N is the size of the coefficient set and: 2 2 A a ij v E Jd F i, j cAJ E Jh EJ 11
  • 12. Wavelet texture analysis (WTA) A texture feature vector is created from the energy set for each sample image: [E1h, E1v, E1d, E2h, E2v, E2d, … EJh, EJv, EJd] The texture feature vectors for all samples are used as the inputs for principal components analysis (PCA) PCA uses linear algebra to transform a set of correlated variables into a smaller set of uncorrelated variables called ‘principal components’ PC1=l1E1h+l2E1v+l3E1d+l4E2h+l5E2v+l6E2d… 12
  • 13. Method Typical clear resin sample images for the three grades of surface finish Grade 1 Grade 2 Grade 3 13
  • 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. 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. Robustness of the WTA method Given these promising results, the following work presents an evaluation of the robustness of the WTA method to common process errors that can occur in the imaging of material samples; those being: • horizontal and/or vertical translation; • rotation; and • dilation 16
  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Conclusions The results obtained indicate that the WTA method is robust 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 imaged Gross rotation and/or dilation of the sample being imaged can impact of the repeatability of the WTA method 64
  • 65. Thank you for your time Presentation: http://ow.ly/diQxn (~40 MB) 65

Notas del editor

  1. For each of the 3 grades,[CLICK] a 1st sample was windowed from the centre of the sample panel. Here we show grade 3.[CLICK] the window was then translated to the left/west[CLICK] the window was then translated up/north-west[CLICK] the window was then translated right/north[CLICK…] and so on for 9 samplesThe PC1 scores are computed using the previously established calibrationVariation in the PC1 scores between the translated images is observed within each grade; however there is no over-lap between the grades, indicating that the WTA method is robust to significant horizontal and/or vertical translation of the sample being imaged