Jeffrey Shan
3.2 Orientation parameters
Exterior orientation parameters are determined by bundle adjustment with robust estimation. Different thresholds are
tested to eliminate blunders remained from the previous automatic feature extraction and image matching step. As is
shown in Tab.2, different thresholds have only minor affection on the final orientation parameters, however, the
orientation angles show small instability relative to various thresholds.
Tab.2 Exterior orientation elements
Blunder Orientation (in deg.) Position (in m)
threshold s = = X: 7 Z
1.860 | -1.29535 | -0.10104 | -88.39527 46.482 605.524 |4202.176
1.9600 | -1.29975 | -0.09158 | -88.39479 46.787 604.746 | 4202.268
2.000 | -1.29859 | -0.08755 | -88.39251 46.691 604.342 |4202.119
Tab.3 gives the estimated standard deviation for orientation parameters obtained from the covariance matrix in bundle
adjustment. Comparing to the image scale of 1:27,000, the planimetric precision of the camera center is within 10 um or
1/3 pixel, while the precision of Zc is approximately 0.002% flying height (4100m). Multiplying the standard deviations
for ¢ and ® with flying height indicates that they are compatible with the precision of camera positions. Such a high
precision is only made possible by the high redundancy in space resection and its good geometry of wide-angle
photography. The standard deviation s, for image coordinates reflects the precision of feature extraction, image
matching and other errors caused by image scanning, camera calibration and DTM interpolation etc. This value varies
slightly with different blunder thresholds in bundle adjustment.
Tab.3 Precision of orientation parameters estimated by covariance matrix
s,=31.9um © © K Xe Ye Zc
s(deg.,m) | 0.00325 | 0.00253 | 0.00110 | 0.264 0.230 | 0.091
3.3 Ground points
Ground coordinates for 25 check points, which are chosen by the test organizer, are obtained with the mono-image
intersection method described in last section. The test organizer will use them as an external check.
4 EVALUATION
In order to evaluate the accuracy of the proposed approach, 97 evenly distributed conjugate points are manually
measured on the aerial image and orthoimage. The image coordinates on the orthoimage are scaled and translated to get
the planimetric coordinates on the ground. Elevations for those ground points are then obtained through DTM
interpolation. The derived 3-D ground coordinates will be used as either control points or check points to evaluate the
proposed approach.
The evaluation is first done on the designated 25 image points, whose coordinates on the aerial image are provided by
the test organizer. In this case, the manual measurements are used as control points to estimate exterior orientation
parameters. Mono-image intersection described in Section 2 is thereafter conducted to calculate the ground coordinates
of those chosen points. Comparing thus obtained ground coordinates with the ones obtained from automatic image
matching does the evaluation. Tab.4 shows their root mean square errors (RMSE), which reflect the influence of
different exterior orientation parameters on ground coordinates.
A first analysis on Tab.4 reveals that the proposed automatic approach virtually obtains the same elevation as the
manual measurements do. This shows that the elevation accuracy for ground point is mainly dependent on DTM
interpolation rather than space resection. The difference on planimetric coordinates is at the order of 1 pixel, even when
large percentage of matched points is screened out in space resection. Since the manual measurement is performed on
the screen in mono mode, space resection done with those measurements will be no better than the one from automatic
matching. Thus, as a conservative estimation, when the two resection methods have the same affection on the RMSE in
Tab.4, the variance of planimetric coordinates of ground points in automatic matching is 0.57m (0.7 pixel).
834 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
