Ilkka Niini 
mm Te 
  
  
  
  
  
  
  
  
  
gen ow [To] B [oN eR Lm UN 
lata cases, the Projective 1 0.999775 | -4.220081-10 ? | 597.817 | 538.963 | 1408.079 | 589.448 | 540.172 | 4017.083 
Projective 2 0.999414 | -8.12970-10 7 | 602.658 | 532.943 | 1407311 | 593.685 | 537.734 3990.033 
Physical 1 0.999441 | -4.019406-107° | 601.903 | 531.888 | 1408.079 | 593.191 | 537.052 4004.177 
Bundle 1 0.999441 | -4.019406-107° | 601.903 | 531.888 | 1408.079 | 593.191 | 537.052 4004.177 
Common data cases | 0.999415 | 2.17050-107* | 603.000 | 538.612 | 1406.692 | 593.808 | 547.306 3987.526 
  
  
  
  
  
  
  
  
  
  
Table 5: Adjusted interior orientation parameters. Note: common o, f. Images 1-4: 7° 
= 
rT Ee Et OS 
/ Jl + 5011 J 
»Yp » Cp. Images 5-8: x; , yy » c. 
  
  
  
  
  
  
  
Projective 1 4.23910 | 5426-10 71453410 | -6316-10 ; 1 -1.0769:10° 
Projective 2 -1,234-107*-[15, 318-1011 | 4627-10-17 -7 955-107" /°-1,050-10>7 
Physical 1 1.22410" |:5258-10- 17 |3,852-10-21./1-8.461-10>- | 1.165100 
of equations Bundle 1 1.224.107: [523510 17 13862-1021 [3461-10 7 | -1.168 107 
Common data cases | -1.240-10^* | 5.423.104 | 4.533.107! | -5.936-10-7 | -9.135-10=7 
). The RMSE 
? the same y 
also the same, 
Common dati 
ghtly different 
|| results were 
rder, etc.) in 
rwise. It also 
sented in this 
re the same. 
hown in Table 
dle results, is 
ilt was 0.9527 
"W constraints 
3 times wors 
value (0.9527 
object modd 
d 7. They ar 
principal point 
ot the zoomed 
ar, despite the 
  
  
  
  
  
  
  
  
Table 6: Adjusted non-linear distortion parameters of images 1-4. Radial distortion coefficients: ki, k5, ks. Tangential 
distortion coefficients: pi, p5. 
  
  
  
  
  
  
  
[ Case | ET k7 i7 p! | m | 
Projective 1 3.62310 [2 27 10 CP [201-10 = -5.099-10-5 | 1.517-10-7 
Projective 2 3423-1075 [1017-10-17 | 122116 7! -9.046-10^? | 5.984-10-* 
Physical 1 3.459-10-* | 9784-10-75 | 1.07510 71 | 4097-109 | 6941-1075 
Bundle 1 3.459-10-5 | 9.784-10- 5 | 1.075-10-7! -4.097-10-° | 6.941-10-5 
Common data cases | 3.623-10 ? | 5.127-10- 75 | 3.601-1077 | 4.981107 | 7.779.108 
  
  
  
  
  
  
  
  
Table 7: Adjusted non-linear distortion parameters of images 5-8. Radial distortion coefficients: k', KY, ki. Tangential 
distortion coefficients: p!', p5. 
6 CONCLUSIONS 
In this article, the two stages of the projective block adjustment methods based on singular correlation were compared to 
the free-network bundle adjustment method. The bundle method requires the 3-D object unknowns and their approximate 
values in the adjustment. The new method does not contain 3-D object unknowns, nor requires approximate values for 
the exterior orientations. The 3-D model can be intersected from the adjusted orientation parameters. 
The projective version of the new adjustment method cannot necessarily use all available data because the block param- 
eters are the singular correlation parameters between certain, optimal image pairs only. To make the projective system 
stronger, two new constraints were used. The first one constraints the determination of the interior orientation parameters, 
and the second one allows us to use some of the possibly missed data. Finally, the physical version of the method enhances 
the results from the projective stage by re-adjusting all data. 
The projective and physical version of the method were compared to the free-network bundle method. Examples with real 
images show that the final results from the physical version are well comparable with the results of a corresponding bundle 
adjustment. This can make a further adjustment with the bundle method unnecessary. Of course, the bundle method can 
be used already after the projective stage. 
The results from the projective stage are quite good, too, in this example. Even if all possible image observations could 
not be used, the RMSE values of the obtained 3-D model were not worse than 1.1 times the bundle results. It was also 
demonstrated that if exactly the same data could be used in the three adjustments, the results were exactly the same. 
In the new block adjustment method, the outliers in the data can be a problem because the computation of singular 
correlation matrices is fragile in the presence of outliers. Additionally, hidden outliers can pass the first, projective stage 
of the adjustment, and cause problems in the physical stage. In future, a proper method to clean any real data from the 
outliers in advance or on-line has to be developed. For example, the random sampling consensus could be used. See (Torr 
and Zisserman, 1998). 
REFERENCES 
Fraser, C. (1982). Optimization of Precision in Close-Range Photogrammetry. The Photogrammetric Engineering and 
Remote Sensing, 48(4):561—570. 
Heikkilä, J. (1992). Systemaattisten kuvavirheiden kompensointi sädekimppublokkitasoituksessa (Compensating sys- 
tematic image errors in the bundle block adjustment, in Finnish). Master’s thesis, Helsinki University of Technology, 
Finland. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 649