Edward M. Mikhail
2.4 Experiments
Three data sets are used in the experiments: simulated data with different levels of perturbations; real data over Fort
Hood, Texas including 2 near vertical and 1 10w oblique aerial frame photographs; and real close range photographs of
the EE building on the campus of Purdue University taken with a 75 mm hand-held camera. For each of the data sets,
the image transfer process is performed and tested on a triplet of images using each of the methods. First, image
coordinate measurements of "control points" on all three photographs are used to solve for the parameters associated
with the current method. Then, using those parameters and the measured image coordinates on the first two images of
"Check points", the conjugate image coordinates on the third image are computed. Finally, the computed and measured
image coordinates of the check points on the third image are differenced and collectively expressed as root mean Square
(RMS).
2.4.1 Simulated Data. Simulated ground points are situated in the range of 0 to 400 meters in X and Y, and between 0
and 125 meters in Z. The ground points are intersected in the image planes of 3 simulated convergent frame
photographs with nominal camera station heights of 460 meters and focal lengths of 150 mm. Two photographs are
tilted at nominal angles (¢) of 33 degrees, while one photograph is near-vertical. The image coordinates on the three
photographs are perturbed with noise of magnitudes 10, 15, and 25 micrometers. The results for all of the discussed
image transfer methods are shown in Table 1: note that points are transferred to the near vertical photograph.
A Irem ee E
| 10 um perturbation 15 um perturbation | 25 um perturbation |
ELLE A
Model x RMS (mm) | y RMS (mm) | x RMS (mm) | y RMS (mm) | x RMS (mm) RMS (mm)
| voz. | 904 0.038 0.055 0.038 0.075 |
| 0044 | 0074 |
|
Model 2
|
|
|
2 0.049 0.042 |
Model 3 0.046 | 0.042 | 0044 | 0.074
Model 4 10046 | 0042 0.044 0.074
3F: | 0.049 0.056 0.041 Ip 0051 | 0073
2F's 0.083: 410.139 0.054 0.041 0.206 0.194 |
Table 1. Image Transfer Experiments with Simulated Data, 8 control points and 7 check points
2.4.2 Fort Hood Data. The Fort Hood data set consists of two near vertical aerial frame photographs taken at 1650
meters above mean terrain, and one low-oblique aerial frame photographs taken at a flying height of 2340 meters with a
25 degree (from the vertical) side-looking angle; see Figure 4. The pixel size for all three photographs is 30 by 30
micrometers. Table 2 shows the results of image transfer to the oblique photograph.
Model x RMS .
| (pixels) | (pixels) |
| Modell* | 064 | 059 |
| Model 2** [m
[Model 3 | 047 | 061 |
[Model 4 ES Loo $c >)
(as OH odin]
[Fs 050 | 062 |
Table 2. Image Transfer Experiments with Fort Hood Data,
19 control points, 18 check points
* After scaling image coordinates to range from
-1to+1.
Figure 3. Fort Hood: Footprints of 2 ril
'** After rotating image coordinates by 90 degrees.
Vertical Aerial Frames Overlaid on 1
Oblique Frame
As noted by the asterisks below Table 2, the raw image coordinate data must be augmented for Models 1-3 in order to
obtain those results. Since Model 1 does not rigorously linearize with respect to the observations, the image coordinates
must be scaled in order to prevent the solution from becoming unstable. A degenerate case occurs for Models 2 and 3
for this particular case of aerial photography where the air base direction between the two near vertical photographs is
parallel to the image x coordinate direction and the first three algebraicly independent equations, i.e. Equations (7), are
selected.
588 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
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