A weighting factor was introduced as suggested by 
Trinder, 1989, changing Equation 6 into Equation 7. 
n m 
X=1MZ X] .gij.-Wij 
i=1j=1 
nm 
y = /ME Li £ij.Wij (7) 
i=1j=1 
Where 
nm 
M = 3 gij-Wij 
i=1j=1 
gij is the grey scale value of each pixel and n = m = 15, 
and wij — gij. 
In this case the higher intensity values of the target are 
iven a greater weight in the calculation so that the 
influence of the background is decreased. Further tests 
were performed using this equation instead of Equation 
6, with unaltered: data sets, network, camera 
calibration, method of target location, labelling, and 
bundle adjustment procedure. This resulted in an 
improvement over the simple centroid method of 25% 
giving an overall subpixel accuracy of 0.11 of a pixel. 
The benefit of the approach adopted is that an 
independent measure of accuracy achieved is used to 
assess the two methods. Furthermore, this is possible in 
a measurement situation with real problems of variable 
illumination, target orientation, and target distance. 
The results of these tests show that the location of the 
targets using these methods produces reasonable 
accuracy. À few targets exhibited residuals of up to one 
pixel in the bundle adjustment. These larger residuals 
occurred at the same image positions for each method 
but were not examined further as the primary purpose 
was to compare the two target location methode 
4. UNIQUE LABELLING OF TARGETS. 
It is has been shown that the coordinates of legitimate 
targets can be extracted with high reliability and 
accuracy. These coordinates provide the basic 
information required for the bundle adjustment 
program to calculate the 3-D coordinates of the targets. 
However, although it is possible to identify and locate 
the targets from each camera station, the differing 
camera orientations mean that: the subject may be 
distorted, some of the targets possibly occluded, or 
targets may be out of the field of view. Therefore, it is 
necessary for the targets from each view to be uniquely 
identified with respect to each other. 
Ideally, the locations of some or all of the labels of the 
targets could be mathematically modelled in 3-D space 
and a transformation performed for each varying 
camera location. However, this presupposes just the 
information which is the end product of the whole 
measurement process. Unfortunately many objects are 
complex to model accurately and so an approximation 
may be a better approach. Another method may be to 
use uniquely shaped targets. However, this has serious 
    
implications for the imaging of these targets because for 
unique identification it is likely that the targets would 
need to be larger than the small circular targets used 
and would also be non symmetric under translation. 
Fortunately the wind vane under consideration 
approximates to a flat surface and an affine 
transformation can be performed. See Figure 7. 
  
Figure 7. Image of the tip of the turbine blade. 
4.1 Choice of control points. 
The choice of parameters for the transformation of the 
image data to the same orientation is performed by 
choosing at least three, generally four, known control 
points which can be uniquely identified in each image, 
say, the corners. Then by performing the affine 
transformation the image is warped. These control 
points need to be positioned to minimise the distortion 
caused by the transformation of the 2-D image of a real 
3-D object. It was found in practice the choice of targets 
at or near to the corners gave the best results. 
4.2. Principle of the transformation. 
The basic principle of the transformation is that one of 
the images is considered to be the reference image and 
the other images are transformed to match its 
orientation. If the number of control points identified 
on the master image is m, then the equations of a 
polynomial are: 
X = Tx (Xa, Yn) 
Y = Ty (Xn, Yn) (8) 
Tx(), and Ty() are single mapping functions. Because 
the position and orientation of the cameras are 
arbitrarily placed, the mapping relationship of Tx() and 
Ty() has to be approximated. In this case, where a linear 
fine transformation is sufficient, then: