s to write the 
derived from 
(7) 
om system of 
Ww; (8) 
W, 
(9) 
X», Yo, Zo and 
as a test field, 
m x 1.8 m. The 
ets density in 
1 with original 
ide robust and 
n in the image 
er. 
; points allows 
rior parameters 
the procedure is 
ra in required 
The image of the test field with recognized coded targets is 
shown in Figure 3. 
  
Figure 3. Calibration test field 
Original calibration procedure (Stepanyants D., 2000) for low 
precision test field is used. For calibration procedure 16 images 
of test field are captured (8 images for each camera). The test 
field is located in front of camera approximately at average 
distance between camera and test field about 8 m thus providing 
image capture at infinity adjustment. Images are captured for 
angle positions of cameras of a=0,+45°, wx0,+45°, k=0, 180°. 
Some of the images at different angle positions acquired 
for calibration are shown in Figure 4. 
  
Figure 4. A samples of test field images for calibration 
Image coordinates of reference points marked by coded targets 
are determined automatically with sub-pixel accuracy by ellipse 
operator. The additional parameters describing CCD camera 
model in co-linearity conditions are taken in form: 
Ax - Ax, Xr Ky e Xr Ke Xr9Ks (2 2x7)  2xyP, m 
Ay =Ay, + yr Ky 5r* Ky + rOKy + 258 + (2 + 2y2)P, 
EM AX, iy ==-m (y—¥, )ir= |x’ + 5° 
where x, y, — the coordinates of principal point, 
m,, m, — scales in x and y directions, 
K,K,K; — the coefficients of radial symmetric 
distortion 
P,P, — the coefficients of decentering distortion. 
These parameters of interior orientation are to be estimated. 
The available means for producing test fields do not allow to 
provide desired accuracy of independent determination of 
reference point coordinates. Only the relative distances between 
reference point could be measured with required precision of 
2.0 mm. Therefore plane test field is used for calibration. 
Table 5 presents distances between given reference points used 
for calibration and residual errors in reference distances after 
bundle adjustment procedure. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
# Reference Distance, Residuals, 
point # mm mm 
0 1-36 1644 -0.1257 
1 6-30 1040.5 -0.0017 
2 1-6 1000.5 0.0003 
3 6-36 1300.5 0.0020 
4 1-30 1447.5 -0.0000 
5 30-36 260 -0.0015 
6 8-29 986.5 -0.1159 
7 11-26 986.5 0.0096 
8 8-11 603 -0.0058 
9 11-29 781 -0.0079 
10 8-26 781 -0.0072 
11 26-29 602.5 -0.0056 
12 1-29 1315.5 0.1256 
13 8-36 1315.5 0.1252 
14 11-30 806 0.0002 
15 6-26 1315 -0.0004 
  
  
  
  
  
Table 5. Reference distances used for calibration and residual 
errors in reference distances after bundle adjustment 
The estimated parameters vector includes: 
e exterior orientation parameters of all the images 
e interior orientation parameters of both cameras 
* coordinates X, Y of all the object reference points 
excluding two points determining object space 
coordinate system. With the plane test field 
assumption Z coordinates of all points is taken to be 
Zero. 
The first stage of calibration procedure (image set acquisition) 
is not automated now and the test field is installed at given 
position manually. After that calibration procedure is executed 
automatically performing the following steps: 
e reference points recognition and their image 
coordinate determination in all acquired images; 
* initial values for exterior orientation parameters 
definition; 
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