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Figure 3. Flow of Outlier Detection in Tracking Process 
These processes are performed to all video frames repeatedly. 
Finally, corresponding points on each video frames are obtained. 
2.4 Robust Bundle Adjustment Process 
From the results of tracking process, exterior orientation 
parameters for each video frames and 3-D coordinates of 
natural feature points are calculated simultaneously by using 
bundle adjustment. However, bundle adjustment is usually 
impossible because the result of tracking includes some error 
corresponding points. In previous study, in order to resolve this 
problem, the authors have been developing relative orientation 
by using LMedS method. In addition, for the more robustness 
of bundle adjustment and for solution of the limitation for 
camera motion because of the limit of relative orientation, 
authors use LMedS in the backward intersection procedure in 
this study. Figure 4 shows the flow of bundle adjustment of this 
study and details are as follows. 
Figure 4. Flow of Bundle Adjustment 
2.4.1 Initial Value of 3D Coordinate for First Frame : The 
initial value of 3D coordinate for natural feature points in first 
frame is calculated from relative orientation procedure using 
LMedS method with random sampling algorithm. At the first, 
stereo pair frame is selected by checking the arrangement of 
corresponding points on video frames automatically. As the 
next, random sampling for corresponding points in stereo pair 
frame is performed and estimation of LMedS for residual of y- 
parallax is calculated. These procedures are performed repeat 
edly, and relative orientation parameter to minimize LMedS of 
residual y-parallax is selected. Finally, initial value of 3D coor 
dinates of natural feature points are calculated with forward in 
tersection using stereo pair frames. 
2.4.2 Initial Value of Exterior Orientation Parameter: 
The initial value of exterior orientation parameters for each 
video frames are calculated from backward inter section using 
LMedS method. Figure 5 shows the flow of backward intersec 
tion in this study and details are as follows; 
a) At the first, random sampling of corresponding points 
which have initial value of 3D coordinate is performed. 
b) The exterior orientation parameters are calculated 
with backward intersection from selected corresponding 
points. 
c) Moreover, estimation of LMedS for residual of image 
coordinate is performed. 
d) These procedures are performed repeatedly, and 
exterior orientation parameter to minimize LMedS is 
selected. 
e) Finally, detection of outlier in corresponding points is 
performed by thresholding for residual of image coordinate 
for corresponding points. 
Detection of Outlier 
Figure 5. Backward Intersection using LMedS 
2.4.3 Bundle Adjustment: The bundle adjustment for each 
video frames is performed using initial value of exterior orienta 
tion parameter and 3D coordinate of natural feature points 
which obtained previously. As the result of bundle adjustment, 
exterior orientation parameter and 3D coordinate of natural fea 
ture points is adjusted. 
2.4.4 3D Coordinate for Natural Feature points: The ini 
tial value of 3D coordinates for new added natural feature 
points are calculated from forward intersection using all video 
frames which include corresponding point for same natural fea 
ture point. Forward intersection is calculated with weighted 
least-squares method and the weight of each video frame is cal 
culated from the RMSE of residual of image coordinate for 
each video frames. 
These processes are performed to all video frames repeatedly. 
Finally, exterior orientation parameters for all video frames and 
3D coordinate of each natural feature points are obtained.