The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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5. DISCUSSION 
Sequence images are acquired in the gaze tracking procedure at 
15 frames/sec. Selected images from the sequence of images 
are shown in this section as input data and results. Geometrical 
accuracy is calculated using images captured from the various 
directions. Figures 15, 16, and 17 show the geometrical 
accuracy via 3-D models overlaid on the images captured from 
these directions. The variance of pixel error values in images is 
shown as the 2-D error2, and the variance of relative distance 
error values between the reference 3-D model and the measured 
results is shown as 3-D error2, in Table 1, 2, and 3. 
5.1 Approach 1: The gaze tracking procedure with known 
3-D model (CAD model) 
Direction 1 Direction 2 
Figure 15. Results for Approach 1 
Table 1. Results for Approach 1 
Distance 50~60cm 
Direction 
2D error2 
[pix2] 
3D error2 
[mm2] 
1 
4.86467 
4.83595 
2 
5.33922 
5.07165 
3 
2.08338 
5.18490 
4 
3.50135 
4.46132 
Average 
3.94716 
4.88846 
5.2 Approach 2: The gaze tracking procedure with known 
3-D model (stereo matching procedure) 
Table 2. Results for Approach 2 
Modell Apartment 
Distance 50-60cm 
I 
2D error2 
3D error2 
Direction 
[pix2] 
[mm2] 
1 
3.57346 
2.33406 
2 
4.20294 
3.03302 
3 
5.75622 
4.64325 
4 
4.02823 
3.30154 
Average 
4.39021 
3.32797 
Model3 
Restaurant 
Distance 50-60cm 
2D error2 
3D error2 
Direction 
[pix2] 
[mm2] 
1 
4.73232 
3.50161 
2 
4.11710 
2.29355 
3 
4.45813 
2.73230 
4 
5.56429 
3.46175 
Average 
4.71796 
2.99730 
Model2 Simple building 
Distance 50~60cm 
Direction 
2D error2 
[pix2] 
3D error2 
[mm2] 
1 
5.57506 
4.39045 
2 
5.32057 
4.10617 
3 
2.70112 
3.11947 
4 
2.63687 
2.16738 
Average 
4.05841 
3.44587 
Model4 Retail stores 
Distance 50-60cm 
Direction 
2D error2 
[pix2] 
3D errori 
[mm2] 
1 
6.08988 
2.59569 
2 
2.93348 
3.31654 
3 
5.28145 
3.66510 
4 
4.05963 
2.75304 
Average 
4.59111 
3.08259 
5.3 Approach 3: The gaze tracking procedure without 
known 3-D model 
Model 1 
Model 2 
Model 3 
Model 4 
91 
Figure 17. Results for Approach 3 
Table 3. Results for Approach 3 
Distance 50-60cm 
2D error2 
3D error2 
Model 
[pix2] 
[mm2] 
1 Apartment 
3.19023 
3.38763 
2:Simple building 
1.49326 
2.40126 
3:Restaurant 
1.39170 
3.89351 
4:Retail stores 
0.82100 
0.93149 
Average 
1.72405 
2.65347 
5.4 Overview 
Model 1 
Model 2 
; s 
Model 3 
Model 4 
Figure 16. Results for Approach 2 
5.4.1 Geometrical accuracy 
Tables 1, 2, and 3 show the variances of relative distance error 
values between the reference 3-D models and the measured 
results. 
The average 3-D error2 in Table 1 is 4.88846. That is, the 3-D 
error in Approach 1 is 2.21 [mm]. The 3-D error2 values in 
Table 2 are between 2.99730 and 3.44367. Therefore, 3-D 
errors in Approach 2 are between 1.73[mm] and 1.86[mm], The 
average 3-D error2 in Table 3 is 2.65347. Therefore, the 3-D 
error in Approach 3 is 1.63[mm], 
The accuracy of stereo matching measurement is approximately 
1 mm in these experiments. Therefore, the geometrical 
accuracy of object recognition, from these results, is sufficient 
for the gaze tracking procedure in these experiments. 
The 3-D errors in Approaches 1, 2, and 3 include not only