The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008
figuration, which represents the case of aerial photography, wer
e generated for the experimentation. The six photos are captured
in two strip lines (each strip consists of three photos).
The exterior orientation parameters of the six camera stations ar
e listed in Table 2. The base distance to flying height ratio was 0
.8. The image coordinates (x, y) for each object point were com
puted from the camera parameters and the ground coordinates o
f this point using the collinearity condition equations (Equations
2, 3). Then, the perturbed data set was generated with LiDAR p
lanimetric standard deviation (in the X, Y directions) of 0.300 m
eters and the vertical (in Z direction) standard deviation of 0.10
0 meters. On the other hand, the image standard deviation was c
hosen as 6 microns, which resulted in expected accuracy in the
object coordinate system of 0.300 meters in the X, Y directions a
nd 0.530 meters in the Z direction.
Format Size
(mm)
100 x
100
x 0 (mm)
0.018
f (mm)
50
y 0 (mm)
-0.015
Table 1: Specifications of the simulated camera
Parameter
Norl
Nor2
Nor3
Nor4
Nor5
Nor6
¿y(deg)
0.5
-0.5
1.5
2.0
-1.0
0.5
0(deg)
0.5
0.5
-0.5
1.0
0.5
0.5
x-(deg)
1.5
1.0
-1.0
1.0
1.5
1.5
Xc( m)
1500
3500
5500
1500
3500
5500
Yr(m)
1850
1850
1850
5600
5600
5600
Z c (m)
2600
2600
2600
2600
2600
2600
Table 2: Exterior orientation parameters of simulated photos
In all experiments, the used approaches were as follows:
- Control Lines:
(1) Model 1: Coplanarity Constraint for Lines.
(2) Model 2: Variance-Covariance Expansion in Image
Space.
(3) Model 3: Variance-Covariance Expansion in Object
Space.
(4) Model 4: Weight Restriction in Image Space.
(5) Model 5: Weight Restriction in Object Space.
- Control Patches:
(6) Model 6: Coplanarity Constraint for Planar Patches.
(7) Model 7: Variance-Covariance Expansion in Object
Space.
(8) Model 8: Weight Restriction in Object Space.
Experiments were conducted to simulate the case of single photo
resection using linear features as well as bundle adjustment using
both linear and areal features extracted from LiDAR data
applying these eight models as illustrated in the following sub
sections.
4.1 Experiments for Single Photo Resection
In this sub-section, experiments were conducted to simulate the
case of single photo resection using control lines applying the
models for linear features (Model 1 to Model 5). The single photo
resection process was performed to solve for the EOP of the
photo. The IOP of the photo were considered as known
parameters, which simulates the case of calibrated frame camera.
Single photo resection was conducted twice on two photos to
evaluate the solution by performing an intersection process for a
set of check points lying on the overlapping area between these
two photos. In other words, the single photo resection
experiments were conducted on photo Norl using 11 control lines.
Then, the experiments were conducted on photo Nor2 using 11
control lines. After solving for the EOP for each of the two used
photos separately, the ground coordinates of a set of 15 check
points were computed. Then, the solution was evaluated through
root mean square error (RMSE) analysis of these 15 check points.
Results are summarized in Table 3 where we can find all used
five models resulted in reliable and comparable results.
Model No.
Mo dell
Model2
Model3
Model4
Model5
RMSEy (m)
0.276
0.292
0.358
0.305
0.358
RMSEy (m)
0.344
0.312
0.346
0.322
0.346
RMSE Z (m)
0.408
0.372
0.456
0.404
0.456
RMSEtou,, (m)
0.600
0.566
0.675
0.600
0.675
Table 3: RMSE analysis for single photo resection using linear
features for the 15 check points
4.2 Experiments for Bundle Adjustment
Experiments here were conducted to simulate the case of bundle
adjustment using both linear and areal features extracted from
LiDAR data. The number of control lines was 16 lines. The
number of control patches was 32 patches. In all experiments
using both linear and areal features, the number of tie points was
35 points. To evaluate the solution, a root mean square error
analysis was performed considering the 35 tie points as check
points. Results are illustrated in Table 4.
Mode! No.
Modetl
Model2
Model.t
Model4
Models
Modeló
Model?
Models
RMSEy (m)
0.350
0.350
0.383
0.350
0.388
0.349
0.365
0.365
RMSEy (m)
0.440
0.440
0.514
0.440
0.517
0.416
0.414
0.417
RMSEz (m)
0.529
0.522
0.628
0.522
0.637
0.487
0.494
0.486
RMSEy,,,ui (m)
0.772
0.767
0.897
0.767
0.908
0.729
0.740
0.737
Table 4: RMSE analysis for bundle adjustment using both linear
and areal features for the 35 check points
Table 4 shows a comparison between the values of RMSE X ,
RMSEy, RMSE Z and RMSE To tai for the bundle adjustment using
control lines and tie points, and bundle adjustment using control
patches and tie points. The table shows that all used
mathematical models resulted in comparable results. In addition,
Model 3 (expanding the error ellipse in the line direction in the
object space) and Model 5 (restricting the weight matrix in the
line direction in the object space) produced relatively higher
values of root mean square error compared to the other models
for lines (Model 1 to Model 5). The reason behind this is that
we used different identification codes for the image points along
the linear features for each image to compensate for the non
correspondence of line end points in image space, and therefore
the images were not tied well. However, the results provided by
all used models were still acceptable and comparable.
5. CONCLUSIONS AND RECOMMENDATIONS
This paper presented different approaches for incorporating bot
h linear and areal features from LiDAR data in establishing goo
d photogrammetric georeferencing. The performance of the pro
posed approaches was evaluated using simulated datasets. Exper
iments were conducted to simulate the case of both single resect
ion and bundle adjustment. The experimental results of both of t
he two cases showed that using control linear features and areal
features extracted from LiDAR for photogrammetric georeferen
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