1055
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
5.3 Geometric accuracy performance from independent
check point analyses
As already pointed out, the overall absolute geometric accuracy
can only be estimated from independent reference points. Thus
the three different blocks were independently processed and the
reference points differences statistically analysed. At the time
of paper writing not all georeferencing variants have been
available thus only parts of the processing results are presented
and discussed in the following. So far, two different strategies
have been investigated. The results from direct georeferencing
(DG), based on the above boresight calibration are compared to
the classical bundle adjustment (AT) based on control points
only. All signalised points have been measured manually in all
images, additional automatic tie points were matched using
MATCH-AT (Version 5.1) from INPHO GmbH, Stuttgart,
Germany.
The theoretical accuracy (precision) of object point
determination for each block configuration is reflected in the
theoretically estimated values from error propagation, i.e.
inversion of normal equation matrix. The precision is only
dependent on the individual block geometry and reflects the
influence of random errors only, i.e. no influence of systematic
errors. The corresponding values for the three block
configurations (GSD 7cm, GSD 14cm, GSD 20cm) are listed in
Table 4. These values are obtained from all non-control points,
including the check points and automatically matched tie points.
Quite interesting is the difference in precision for the x- and y-
(horizontal) coordinate, which obviously is due to the specific
block geometries. The difference in precision in north
component is up to three times worse compared to the east
component. The block configurations analysed here consist of
three parallel flight lines (east-west, west-east) each, with fairly
high side-laps. The side looking, oblique dual head camera
configuration also causes a special image ray geometry which
also influences this effect. Still it is not fully clear why this
effect is present and further investigations have to be done to
explain it in detail. Considering the precision in the vertical
component, the values are close to one pixel (GSD) or slightly
below. The precision of object coordinates gives a first
estimation on the maximum accuracy that can be expected from
the independent analyses at check points. Thus the later
presented results from absolute accuracy always have to be
compared to the precision values here.
Block
GCP
#
ChP
#
Std.Dev. fm]
AEast
ANort
h
AUp
GSD 7cm
32
33
0.011
0.030
0.068
GSD 14cm
51
93
0.017
0.045
0.104
GSD 20cm
77
149
0.028
0.068
0.171
Table 4: Precision (Std.Dev.) of object point coordinates
(estimated from error propagation).
The accuracy from check point analysis is given in the
following tables for all three different GSD blocks. Table 5
shows the results for the GSD 7cm flight, Table 6 for the flight
with 14cm GSD and Table 7 for the 20cm GSD block, finally.
Note that for the 7cm block only the three flight lines without
cross strips have been used.
As one can see, the ground control point based aerial
triangulation was done in three different variants. In the first
case no additional parameters have been introduced during
processing (AT no). Then the additional parameter set as
proposed by Grim (1978) using up to 44 polynomial
coefficients is added (AT 44). In the final third case only 3
additional parameters modelling changes in camera principal
point and focal length are used (AT io). In all cases two
individual sets of additional parameters are estimated, one for
each of the two camera heads separately. In order to get the best
additional parameter values for each of the blocks their values
have been determined in a previous step, where all available
control points have been used. For the GSD 7cm block the
images from the three cross strips were also involved for the
estimation of self-calibration terms. The non significant values
have been eliminated. For the final runs, the additional
parameters were used as fixed values only, i.e. they have been
used with very high weights. Therefore these values basically
remained unchanged from their values from the previous run.
Vers.
GCP
#
ChP
#
ctO
[pml
RMS |m|
AEast
ANorth
AUp
DG
0
65
4.08
0.045
0.075
0.130
AT no
32
33
1.50
0.033
0.070
0.134
AT 44
32
33
1.41
0.022
0.037
0.088
AT io
32
33
1.47
0.022
0.039
0.096
Table 5: Absolute accuracy from check point analysis for GSD
7cm block.
Vers.
GCP
ChP
ctO
RMS [ml
#
#
[pm]
AEast
ANorth
AUp
DG
0
144
5.17
0.075
0.156
0.376
AT no
51
93
1.36
0.039
0.108
0.231
AT 44
51
93
1.27
0.022
0.067
0.161
AT io
51
93
1.33
0.025
0.067
0.173
Table 6: Absolute accuracy from check point analysis for GSD
14cm block.
Vers.
GCP
#
ChP
#
ctO
Iflm]
RMS [ml
AEast
ANorth
AUp
DG
0
226
3.28
0.066
0.149
0.333
AT no
77
149
1.98
0.062
0.124
0.250
AT 44
77
149
1.41
0.035
0.070
0.156
AT io
77
149
1.45
0.038
0.071
0.174
GPS-
AT no
4
222
1.45
0.098
0.155
0.244
Table 7: Absolute accuracy from check point analysis for GSD
20cm block.
Looking into the results in some more detail one can see that
the direct georeferencing already delivers nice results. In all
three cases the accuracy (RMS) of the east coordinate is within
half of a pixel (GSD), at least. For north component the quality
is slightly worse and reaches up to one pixel (GSD). There
obviously is a certain difference in performance of both
horizontal coordinates, which has to be due to the block
geometry, as already shown and discussed from the analyses of
object point precision (see Table 4). If one compares the DG
cases with the AT without any self-calibration the similar
behaviour can be seen in the RMS values of horizontal
coordinates.
It is also astonishing to see how well the horizontal
performance of DG already agrees with the standard AT case
without additional self-calibration. For the GSD 20cm and 7cm
