zetedAccuracy 
sm —— 
  
  
  
15 
Warp [mm] 
| accuracy 
by the warp of 
varp up to 5mm 
ficient value for 
rposes. 
alibration on the 
iccuracy as well 
on the flat sheet 
or to that on the 
ng 5 pictures up 
ites. 
ed Work-Time 
y photographing 
it 10 minutes 
out 2 hours 
€ 
N 
nd AF functions, 
nd accuracy. To 
alibration system 
yarameters at the 
1 interpolating all 
the least squares 
ne. 
process their data 
t to calculate the 
we calculate each 
d values as the 
we can make 3D 
  
  
Calibration by Flat Sheet at Several Focal Positions 
E NH Preparation 
Interpolating each coefficient of correction models 
of each focal position by an approximate curb 
  
  
  
  
Measuring and photographing on site 
  
Calculating focal length of the Picture taken 
by Self Calibrating Bundle Adjustment 
Calculating each of the correcting coefficient 
of model equation by the focal length 
  
  
With each calculated coefficient as the Interior Orientation 
Parameter of Camera we can make 3D measurement 
  
  
  
Figure9. On-Site Calibration 
3.2 Test 
We tested our system to see if it really works. 
We placed 6 focal positions between 7.2mm and 50.8mm of 
dimage7 at 7.2mm, 8.7mm, 11mm, 25mm, 39mm, 50.8mm and 
on each position we made calibration 5 times on a flat sheet. 
Thus we tested the reproducibility and accuracy as well as 
applicability of approximate curb line. 
As to the model equation we used the correction model equation 
with the Parameters K;~K, of Radial lens Distortion. 
Ax=-%, + (Ki + KP + Ea + Ki X( 2-%,) (1) 
Ay 7 -yy * (Kar! * Kor* t Kar? Kar!)( y - y, ) 
where X,y = image coordinates 
X», yp 7 coordinates of principal point 
As to the equation (1), K3 and K, did not practically affect the 
accuracy in our test. Therefore, we deleted K4 and K, as 0 and 
made the equation much more simple as below (2). This means 
that we can ignore the parameters in Tangential Distortion even 
in the correction model which uses the Tangential distortion pa- 
rameters. 
Ax-7-x t(Ku*Ka'(x-x,) ©) 
Ay 7 -y t (Ki * Kay - y, ) 
In the Figures 10-13, we have the graphs illustrating the 
reproducibility and applicability of an approximate curb 
regarding the calibrations made 5 times at each of the 6 focal 
positions. 
-57-— 
  
3 4 
— eo 5 ® Simulation 
Kl — A pproximateCurve 
  
  
  
5.00E-03 
4.00E-03 
3.00E-03 
2.00E-03 
1.00E-03 
0.00E+00 
  
-1.00E-03 
Figure10. K, and focal length 
K2 
1.00E-05 
0.00E+00 
-1.00E-05 
-2.00E-05 
-3.00E-05 
-4.00E-05 
-5.00E-05 
-6.00E-05 
-7.00E-05 
  
Figurell. K; and focal length 
XP 450 
4.57 
4.55 
4.53 
4.51 
4.49 
4.47 
4.45 
443 
441 
4.39 
  
7.2 8.7 11.6. 248 390 522 
Figurel2. x, and focal length 
Yp 
3.48 
3.46 
3.44 
3.42 
34 
3.38 
3.36 
3.34 
  
7.2 8.7 11.6 24.8 39.0 52.2 
Figurel3. y, and focal length