iat the shift
.e impact on
an Testfield
NSFORMATION
raluating the
n, the flat
stfield was a
round point
however, it
spect, namely
.ransformation
ng an insight
1otogrammetric
id second- and
'ansformations
round control
coordinates
£f the three
'ercise was to
the image
provide an
e order to be
ynomials.
at full-110 km
carried out,
second stage
formations in
each of
length. The
ground point
ormations are
ble it can be
: localised
ler residuals
(field, except
area (Set 4)
porer control
owing points
Table 1 are
xt of this
3Mdistinction
the 4.5m HR
lution (LR)
tributable to
ontrol point
er quality of
a notable
second-order
ared to the
i more modest
ding from ^a
-order model,
r areas (Sets
re is that a
second- or
t appropriate
erpolation of
meters in the
-order models
ground „point
1 {0.7 pixels
the i full +110
, 1996
Table 1: RMS values of residuals from 2-D transformations between image coordinates
and ground control point planimetric coordinates for both the entire testfield and
four 25 km x 40 km sections, each containing about 20 points. Results are given for
each channel, for first-, second- and third-order models. Units are metres.
CHANNEL FULL, TESTFIELD SET 1
SET 2 SET 3 SET 4
Ist! 2nd 3rd|1st 2nd 3rd
5, nadir {12.9 9.700 419.37 8.3 G.1
6, forward (41.4 8.7 8.71 9.028.661
7) backward {12.4 9.1.68.7 110.3 9.1: 6.9
ist 2nd 3rd) 1st 2nd 3rd] 1st (2nd 3rd
p
Sv
4 6.7 258144141 5.8 4.9110.1 9.5. 9.4
6160 5:0 110.0: 6.0. ..5.0111.9.11.2310.8
1.8.2 .648:120.6-7.5-6.6111.,8:11.0::9.,8
km length of the testfield, and at the
5-7m level (0.4-0. pixels) in three
of the four 1000 km’ areas. While these
values are impressive in their own
right, what is more important is the
inference that the bundle adjustment
should yield a similar or better
planimetric triangulation accuracy.
5. TRIANGULATION RESULTS
5.1 Overview
In -the ‘evaluation of the MOMS-02/D2
triangulation " accuracy, attention was
focussed on the impact upon the bundle
adjustment results of three variables:
the number of control points and their
distribution, the number of OIs, and the
order of the Lagrange interpolation
functions. Of the many triangulation
adjustments conducted only a sample are
considered here. The results presented
have been obtained with the two
independently observed sets of image
coordinate data referred to earlier,
namely a three-channel set from The
University of Melbourne and a two-channel
set from ETH Zurich. The former comprised
a total of 62 points, the latter 48.
Tables 2 and 3 provide a summary of the
accuracies obtained for the two data sets
under conditions of differing numbers of
control points and OIs, and changing
orders for the interpolation functions
for exterior orientation parameters.
Listed in the tables are the RMS values
of XxyYz object coordinate discrepancies
for the triangulated checkpoints for each
bundle adjustment. In the cases of the 12
and 20 control points, the RMS
discrepancy values listed are each
effectively the means of the checkpoint
residuals from two separate control point
configurations (see Figure 1}.
In comparing the results in Tables 2 and
3, the most striking feature is the fact
that contrary to expectations (at least
in ’planimetry)” the” 2-ray triangulation
yields significantly superior accuracy to
that of the 3-fold stereo imagery. This
is thought to be partly a consequence of
Inte
211
rnational Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
the superior quality of the image
coordinates from ETH Zurich, which were
measured with the aid of a more refined
image enhancement process involving
Wallis filtering and interactive quality
evaluation. As has already been
mentioned, there was a difference of 0.7
pixel (RMS) between the image coordinates
of the two sets. This would account for a
component of the discrepancy between the
values listed in the two tables, which is
generally at the level of 2-4m or up to
0.3 pixel for the LR channels.
Kornus et al (1995) refer to the
appearance of unforeseen and unknown
Systematic effects in the MOMS-02/D2
image data which they attribute to
calibration errors due possibly. to. in-
flight changes in camera geometry. The
presence of such systematic error in
interior orientation is further indicated
by the fact that the bundle adjustments
of the three-fold stereo imagery yield
poorer .planimetric. accuracy than the
individual 2-D transformations for each
channel. Inispite of. this, : RMS- point
positioning accuracies at the 0.5 to 0.8
pixel | level (with respect to the IR
channels) are obtained.
A further quality measure of the ground
point determination results is provided
by a comparison of the internal precision
(standard errors) and external accuracy
(checkpoint discrepancies). Over the
range of bundle adjustments of the 2-ray
imagery represented in Table 2, the mean
standard errors obtained from each of the
covariance matrices C, varied by only a
modest amount and averaged Oxy = 4m and
0, = 7m. For the 3-ray triangulations of
Table 3 the corresponding values were Oy,
= Am and oz LOM The difference in
heighting precision arises primarily as a
consequence of the higher level of
triangulation misclosure in the case of
three-fold stereo coverage. Here, the RMS
value of image coordinate residuals was
close to 0.3 pixel, as compared to 0.2
pixel for the 2-ray triangulations. This
influence of the difference in image
coordinate residuals is balanced for
planimetric precision by the stronger 3-
ray intersection geometry.
Tr
