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Xi = ao + a1Xn! + a2Yn! 
Yi = bo + biXn' + b2Ya' (9) 
(i = 12,...,m) 
Xi and Yi represent the coordinates of the i!" control 
point in the reference image. Xn' and Yn' represent the 
coordinates of the i^ control point in the image which 
are to be transformed. Since there are m control points, 
then m must be greater or equal to three. Hence, using 
Equation 9, and the usual matrix notation: 
X — Aa (10) 
Y= Ab (11) 
Where: 
XT = [X1, X2,...Xm] 
YT - [Y1, Yo... Yn] 
al = [ao, a1, a2] 
bl - [bo, by, bz] 
i X v 
Aci: x? v 
$m 
If the Equations 10 and 11 are solved separately then 
the coefficients aibi are obtained. For m = 3, the 
equations 10 and 11 are valid and: 
a=AlX (12) 
-1 
b=Aly (13) 
If | A | is not equal to zero, then |A] exists. 
When m is greater than 3 the solution to Equations 10, 
and 11 are expressed as the least squares estimate of 
parameters a and b. 
— (ATA yl( ATx 14 
am A df a an 
Using the methods discussed all images from the 
differing camera stations were transformed into the 
same coordinate system. However, because of the 
approximations in the transformation to a new 512x512 
image these images can only be used for target labelling. 
Targets which are very close together could cause 
problems to the raster scanning labelling system. In the 
case of conflict a test is used to measure which target in 
the warped image is closest to the reference image. 
When all of the targets in the warped image have been 
mapped to the m image the reference image 
ETT system is applied. Figure 8, shows the location 
or the targets in from one of non-reference camera 
stations. 
x x x 
x x x x 
x x x x x 
x x x x x x 
x x 
x x x x x 
x x 
x x x x x x x 
x 
x x x x x x x x 
x x x x x 
% x x x 
x x x 
x x x x x 
x x x x x 
x x 
x 
x X x x 
x x x x x 
x x 
x 
x x x 
x 
x 
x x 
x 
x 
x x 
Figure 8. Target locations from camera station 2. 
The results of the transform and are shown in Figure 9. 
by the circular symbols and the reference image shown 
by the triangular symbols. 
e e e e v 
e 
e » v v v v v v ® v v 
e e e e 
e e e 
e 
2 v v v v v v v = ve v 
. . e e e e o 
e 
- = v v v v v v v % v 
e 
e e 
® e e P 
v v v® 
e e v v v v v v v > 
e e 
e e s - e 
vw 
e 
e e o e . e 
ve 
= = v v v v v v v ve 
9 e ° e 
e e ® 
v? 
v^ 
s at v v * * v v v 
e 
® e e e © 
e 
v v 9 « v v v v v v v 
e e 
e e e e 
e 
* v v 
v v v . e . v ." v v » 
Figure 9. Results of target transformation. 
It was found that in the case of the simple geometry of 
the turbine blade under test the targets could be 
uniquely identified in each of the images according to 
the numbering scheme of the reference image. 
5. CONCLUSION 
Using the methods described, several tests were 
performed in order to measure the 3-D coordinates of 
the targets placed on a turbine blade of a wind power 
enerator. There were 10 x 11 targets placed on the 
lade. Five images were collected in each group as 
shown in Figure 10. 
— —