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Edward M. Mikhail
Table 5 shows the results of object reconstruction using both real data sets; i.e., Fort Hood and Purdue EE. With Fort
Hood, cases are shown with ground point intersections using only the two near vertical frames versus using all three
frames simultaneously. There are 19 control points and 18 check points. With the Purdue EE data set, results from
intersection of frames 42 and 43 are compared to three frame simultaneous intersection. For this close range data set,
there are 8 control points and 8 check points. Note for the Fort Hood data set that the nonlinear refinement offers
significant improvement over the linear solution, especially for the three-frame case.
Fort Hood Data Set Purdue EE Data Set
Model # | 2 Frame Intersection 3 Frame Intersection | 2 Frame Intersection | 3 Frame Intersection
Method RMS (meters) RMS (meters) RMS (meters) RMS (meters)
X Y Z X Y Z X Y Z X Y Z
Linear 1 0:07 | 0.09 | 0.17 | 025 0.80 1.24 033 | 3,79 | 651 | 023 | 2.63 | 0.35
2-4 006 | 009 | 0.14 | 0.12 0.49 | 0.72 | 0.16 | 0.34 | 0.06 | 0.15 | 0.34 | 0.08
Non- 1 0.07 | 0.09 | 0.17 | 0.23 0.260 | 0.53 | 0.33 | 379 | 080 | 022 / 262 | 035
linear 2-4 0.06 | 0.07 | 0.14 | 0.04 0.04 | 0.09 | 0.16 | 0.34 | 0.06 | 0.16 | 0.34 | 0.08
Table 5. Object Reconstruction with Real Data Sets
4 CONCLUSIONS
Invariance techniques are relatively fast and efficient, and are especially useful for application to imagery obtained from
uncalibrated cameras and with unusual geometry. By recognizing photogrammetric implications and applying the
necessary constraints, improvements in robustness and accuracy for invariance techniques can be obtained. Although
these refined techniques are attractive, the simpler linear techniques can not be abandoned since they provide reasonable
initial approximations for the more robust nonlinear techniques. More specifically, it was reinforced that to establish
the relationship between image coordinates of a triplet of images, there should be three independent equations per point
and 18 independent parameters. Finally, for a rigorous solution to either the image transfer or object reconstruction
problem, linearization with respect to the observations is required.
ACKNOWLEDGMENTS
The research presented is sponsored by the U.S. Army Research Office under Grant No. DAAHO04-96-1-0444. The
views expressed in this paper do not necessarily reflect the views of the U.S. Government or the U.S. Army Research
Office.
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 591
