ight projection were 
m described in $3. 
d most of the area 
). This dataset was 
on against the point 
two datasets. 
  
d laser dot targets 
ication process was 
targets and a single 
> point cloud (Figure 
] in two areas of the 
ere also available for 
  
  
get triangulation for 
ht data set (2) 
ss has provided points 
points in some parts is 
problems arising from 
faces as well as the 
4.3 Bundle adjustment results 
Measurements from all three datasets have been processed 
using a self-calibrating bundle adjustment with results being 
computed for the retro targets alone and the targets and model 
points combined. The bundle adjustment solution has been set 
to use the retro targets and their associated standard deviations 
as external constraints. Each dataset was solved for the retro 
targets alone and a second time including the point cloud 
produced by the densification method described in $3. The 
summary from the bundle adjustment includes the a-posteriori 
sigma nought (ey), which in the absence of systematic error 
gives an indication of the correction of the a-priori weight 
estimate. Other results from the bundle adjustment are the RMS 
of the image measurement residuals and the RMS of the a- 
posteriori object coordinate standard deviations. 
4.3.1 Laser dot data 
The results for the target data are in general agreement with the 
expectation that the target image measurements will be affected 
by the less effective retro-target illumination required for the 
simultaneous imaging of both the retro reflective and laser dot 
targets. The poorer image measurement RMS for the laser dots 
is attributable to the fact that they deliver lower quality 
measurements due to their shape and speckle effects. This is 
also portrayed in the large a-posteriori weight estimate. 
| A'post. c, RMS image (um) RMS object (um) 
Targets 1.57 0.61 45.44 
All pnts 4.52 2.18 99.17 
Table 1: Results from bundle adjustment for laser dot projection 
dataset 
4.3.2 Pattern projection data 
The second dataset with the projected pattern produced poorer 
target image measurement results than the first dataset (Table 
2). This is attributed to the fact that the pattern projection was 
overlaid on the retro reflective targets, thus affecting the 
illumination conditions and interfering with the target images. 
| A'post. 69 RMS image (um) RMS object (um) 
Targets 2.45 0.74 61.59 
All pnts 0.56 0.25 27.42 
Table 2: Results from bundle adjustment for pattern projection 
dataset 
4.3.3 White light data 
The third data set was processed similarly to the second 
concentrating only in the areas where CMM data was available. 
The results are in general agreement with the fact that this data 
set was captured with better illumination for achieving both 
target contrast and image texture. The a-posteriori o, for the 
combined model and target data indicates the suitability of the 
a-priori weight estimation for the model measurements. 
| A'post. o; RMS image (um) RMS object (um) 
Targets 1.89 0.67 41.50 
All pnts 1.26 0.57 39.54 
Table 3: Results from bundle adjustment for white light dataset 
4.3.4 Precision summary 
The results from the bundle adjustments indicate that the laser 
dot data produced the best precision estimates for the retro 
reflective targets due to optimised illumination conditions. 
Pattern projection affected the precision of the retro reflective 
targets but produced better results for the densified point cloud 
than the white light projection data set. However, the white 
light data set results display a more balanced solution, which 
effectively displays the compromise between acquiring image 
texture and adequate retro-reflective target illumination. 
The object coordinates RMS for the two data sets with the 
texture information are in close agreement with each other and 
those from the laser solution. The results indicate the 
densification process has provided high precision 
measurements. The object coordinate standard deviations for 
the produced point clouds are in both cases approximately two 
to three times worse that those of the retro reflective targets. 
4.4 Comparison with CMM data 
The CMM point clouds as well as the point clouds derived by 
the point densification method correspond to small areas on the 
gearbox surface (Figure 7). The areas are highly complex 
surfaces that do not directly conform to a mathematical model 
description composed by geometric primitives. 
  
Figure 7: Areas of comparison on the gearbox 
The comparisons performed in this paper are based on a fixed 
datum. A best fit solution using least squares surface fitting 
algorithms would also be possible if there was sufficient 
information about the mathematical description of the object 
surfaces involved. For the analysis presented in this paper, 
reference surface models were constructed in a CAD-based 
software (MicroStation) using the CMM point cloud as posts 
for B-Spline curve-derived surfaces (Figure 8). The CMM data 
has been measured in a grid formation, at intervals ranging from 
2-5 mm. 
  
Figure 8: Reference surfaces 1 and 2 derived from CMM data. 
The point clouds that were derived from the method developed 
in this research could subsequently be compared to the 
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