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
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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