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1
Evaluation of the Robustness of Surface Characterisation of Carbon Fibre Composites Using Wavelet Texture Analysis
Associate Professor Stuart PalmerFaculty of Science and Technology
Deakin University, AustraliaDr Wayne Hall
Griffith School of EngineeringGriffith University, Australia
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
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
4
The 2D discrete wavelet transform (2DDWT)
Original image
5
The 2D discrete wavelet transform (2DDWT)
Original image
hcD1vcD1
dcD11cADecomposition
level 1
6
The 2D discrete wavelet transform (2DDWT)
Original image
hcD1vcD1
dcD11cA
2cAhcD2
vcD2dcD2
Decompositionlevel 1
Decompositionlevel 2
7
The 2D discrete wavelet transform (2DDWT)
Original image
hcD1vcD1
dcD11cA
2cAhcD2
vcD2dcD2
JcAhJcD v
JcD dJcD
Decompositionlevel 1
Decompositionlevel 2
Decompositionlevel J
8
The 2D discrete wavelet transform (2DDWT)
Original image
hcD1vcD1
dcD11cA
2cAhcD2
vcD2dcD2
JcAhJcD v
JcD dJcD
Decompositionlevel 1
Decompositionlevel 2
Decompositionlevel J
9
The 2D discrete wavelet transform (2DDWT)
It is possible to selectively re-assemble images:
Detail coefficients fromlevels 2-4
Detail coefficients fromlevels 5-6
Original image
10
hcD1vcD1
dcD1
hcD2vcD2
dcD2
JcAhJcD v
JcD dJcD
Wavelet texture analysis (WTA)
Energy measure computed for detail coefficient sets:
11
JcA
Wavelet texture analysis (WTA)
dvhkjJNM FcDE
k
jjk,,;1
1 2
2
,
2
A ji
ijaF
Energy measure computed for detail coefficient sets:
hE1vE1
dE1
dE2vE2
hE2
hJE
vJE
dJE
where:j is the wavelet analysis scale/levelk is the wavelet detail coefficient set orientation (horiz., vert. or diagon.)J is the maximum analysis scale/levelM×N is the size of the coefficient set
and:
12
Wavelet texture analysis (WTA)
A texture feature vector is created from the energy set for each sample image:[E1
h, E1v, E1
d, E2h, E2
v, E2d, … EJ
h, EJv, EJ
d]
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+l2E1
v+l3E1d+l4E2
h+l5E2v+l6E2
d…
13
Typical clear resin sample images for the three grades of surface finish
Grade 1 Grade 2 Grade 3
Method
14
Results
12
3
45
6
7
8
9
10
11
12
-400
-300
-200
-100
0
100
200
-800 -600 -400 -200 0 200 400 600 800 1000 1200 1400
Prin
cipa
l Com
pone
nt 2
sco
re
Principal Component 1 score
◊ Grade 1 ∆ Grade 2 O Grade 3
15
Results
db7 wavelet / 3 levels of decomposition
12
3
45
6
7
8
9
10
11
12
-400
-300
-200
-100
0
100
200
-800 -600 -400 -200 0 200 400 600 800 1000 1200 1400
Prin
cipa
l Com
pone
nt 2
sco
re
Principal Component 1 score
◊ Grade 1 ∆ Grade 2 O Grade 3
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
17
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
18
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
19
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
20
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
21
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
22
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
23
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
24
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
25
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
26
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
27
Robustness to translation
-1000
-500
0
500
1000
1500
1 2 3 4 5 6 7 8 9
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Sample number
Grade 1 Grade 2 Grade 3
28
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
29
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
30
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
31
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
32
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
33
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
34
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
35
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
36
Robustness to rotation - small
-800
-400
0
400
800
1200
-8 -6 -4 -2 0 2 4 6 8
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
37
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
38
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
39
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
40
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
41
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
42
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
43
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
44
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
45
Robustness to rotation - gross
-1500
-1000
-500
0
500
1000
1500
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Angle of rotation
Grade 1 Grade 2 Grade 3
46
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
47
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
48
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
49
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
50
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
51
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
52
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
53
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
54
Robustness to dilation - small
-1000
-500
0
500
1000
1500
92 94 96 98 100 102 104 106 108
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
55
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
56
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
57
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
58
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
59
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
60
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
61
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
62
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
63
Robustness to dilation - gross
-1200
-800
-400
0
400
800
1200
1600
2000
60 70 80 90 100 110 120 130 140
Pri
nc
ipa
l co
mp
on
en
t 1
sc
ore
Percentage dilation
Grade 1 Grade 2 Grade 3
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
65
Thank you for your time
Presentation: http://ow.ly/diQxn (~40 MB)
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