ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision", Graz, 2002 
  
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Figure 2: Six of the 500 images that were used to test the recognition rate. The model was generated from the print on the IC in the top 
left image. With the proposed approach, the model was found in all images except the lower right image. 
after one and three iterations of the least-squares adjustment de- 
scribed in Section 4. Evidently, the extracted positions lie much 
closer to the three cluster centers. Furthermore, it can be seen that 
the least-squares adjustment does not introduce matching errors, 
i.e., outliers, and hence is very robust. 
To check whether the proposed approach results in an improve- 
ment over existing approaches, the original implementation by 
Rucklidge (Rucklidge, 1997) of an approach that uses the par- 
tial Hausdorff distance as a similarity measure was used for the 
same test. The parameter for the maximum object to image and 
image to object distance were set to 1. Initial tests with the for- 
ward and reverse fractions set to 0.3 resulted in run times of more 
than three hours per image. Therefore, the forward and reverse 
fractions were set to 0.5. This resulted in an average matching 
time of 2.27 s per image, i.e., more that 100 times as long as the 
proposed approach. Since the method of (Rucklidge, 1997) re- 
turns all matches that fulfill its score and distance criteria, the 
best match was selected based on the minimum forward distance. 
If more than one match had the same minimum forward distance, 
the match with the maximum forward fraction was selected as the 
best match. A match was considered correct if its distance to the 
reference point of the model was less than one pixel. With this, 
the IC was recognized in 361 images for a rate of 72.2%. If Smin 
was set to 0.5 in the proposed approach, the recognition rate was 
83.896, i.e., the proposed approach performed 11.6% better than 
a method using the Hausdorff distance. Figure 3(e) shows a plot 
of the forward fraction of the best match returned by the partial 
Hausdorff distance versus the visibility of the model in the im- 
age. The wrong matches either have a forward fraction of 0 or 
close to 0.5. Figure 3(f) displays the position errors of the best 
matches. Note that in some instances the best match was more 
than 200 pixels from the true location. 
To test the subpixel accuracy of the proposed approach, the IC 
was mounted onto an table that can be shifted with an accuracy 
of 1 um and can be rotated with an accuracy 0.7’ (0.011667°). 
In the first set of experiments, the IC was shifted in 10 um in- 
crements, which resulted in shifts of about 1/7 pixel in the im- 
age. A total of 50 shifts were performed, while 10 images were 
taken for each position of the object. The IC was not occluded 
in this experiment. The pose of the object was extracted using 
the extrapolation of Section 3 and the least-squares adjustment 
of Section 4 using one and three iterations. To assess the accu- 
racy of the extracted results, a straight line was fitted to the ex- 
tracted model positions. The residual errors of the line fit, shown 
in Figure 4(a), are an extremely good indication of the achiev- 
able accuracy. The errors using the extrapolation are never larger 
than 1/22 pixel. What may seem surprising at first glance is that 
the position actually gets worse when using the least-squares ad- 
justment. What can also be noted is that the errors show a si- 
nusoidal pattern that corresponds exactly to the pixel size. This 
happens because the IC is moved exactly vertically and because 
the fill factor of the camera (the ratio of the light-sensitive area 
of each sensor element to the total pixel area of each sensor el- 
ement) is much less than 100%. Because of this, the subpixel 
edge positions do not cause any gray value changes whenever the 
edge falls on the light-insensitive area of the sensor, and hence 
the subpixel edge positions are not as accurate as they could be 
when using a camera with a high fill factor. Unfortunately, in this 
example, the object's edge positions are such that their location 
is highly correlated with the blind spots. Hence, this effect is not 
unexpected. When cameras with high fill factors are used the ac- 
curacy when using the least-squares adjustment is significantly 
better than when using the extrapolation. 
To test the accuracy of the extracted angles, the IC was rotated 
50 times for a total of 5.83°. Again, 10 images were taken in 
every orientation. The residual errors from a straight line fit, dis- 
played in Figure 4(b), show that the angle accuracy is better than 
1/12? (5^) for the extrapolation method, better than 1/40? (1.37) 
for the least-squares adjustment using one iteration, and better 
than 1/100? (0.6") for the least-squares adjustment using three it- 
erations (ignoring the systematic error for very small angles, for 
which all three methods return the same result; this is probably an 
error in the adjustment of the turntable that was made when the 
images were acquired). Since in this case the IC is rotated, the 
errors in the subpixel positions of the edges caused by the low 
fill factor average out in the least-squares adjustment, and hence 
a significantly better accuracy for the angles is obtained using the 
least-squares adjustment. 
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