International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
The points matched in 3 combinations yield, as expected, the
best results with RMS height differences of about 4 m in the
moderate terrain of the TS #2 and #5 and of about 5 m in the
mountainous terrain of TS #4. There also exist some blunders
with differences up to nearly 90 m. 3-ray-points matched in 2
combinations lead to acceptable 4-5 m height differences in
moderate terrain. In mountainous terrain, however, the RMS
differences increase to nearly 12 m and the blunders to more
than 160 m. For 2-ray-points this situation is even worse. In
figure 7 the histogram of the height differences for TS #5 is
depicted as an example separately for the 3 point groups.
e 15 ] 3 rays
= | | | (3 comb.)
> 10 4
e | | | —— 7 (0YS
9 5 | | | (2 comb.)
8 | E |
uL | | | | 2 rays
0 : iy
-30 20 10 0 10 20 30
Height difference [m]
Figure 7: Histogram of height differences dh [m] for TS #5
Table 8 shows the respective statistics on height differences
obtained from a pure HRS data set without considering the
HRG data. This implies new matching runs without transfer
points (see section 3.3) and also no estimation of correction
polynomial coefficients (see section 3.4.3.2); i.e. the matched
image points are directly transferred into object space using
the supplied auxiliary data and the local adjustment described
in section 3.5.1. The standard deviation are approximately
20% worse compared to the results achieved with bundle
adjustment and matching in 3 combinations (see table 7).
Additionally a systematic height error of approximately 9 m
occurs, which still is subject to further investigation since the
results of the bundle adjustment did not show a comparable
systematic effect (see tables 5 and 6)
image columns and rows and by increments of 250 m in
object height (from —250 m to 2250 m). From these points
the best coefficients of the rational functions are determined
by least squares adjustment. For forward and backward
looking directions rational functions of degree 3 in numerator
and denominator are used. In case of the nadir looking
direction a 3™ order polynomial is adjusted, since it has not
been possible to adjust any polynomial denominator without
zeros in the domain of the image footprint.
3.6.1 Matching in image space (region growing)
In a first step the rational functions are used, as an alternative
to the strict model, to transform the image points, matched in
3 combinations using the region growing algorithm (see
above) into object space. The statistics on the height
differences between the resulting object coordinates and the
coordinates computed with the strict model are listed in
table 9. The difference turned out to be not significant and
confirms the findings of an earlier analysis using MOMS-02
images, where it was concluded that stereoplotting with
rational functions is as accurate as using a rigorous model
(Alamüs et al, 2000). Therefore, no new DSM are produced,
i.e. it is assumed, that this rational function approach is also
represented by the strict model DSMs.
TS N Min Mean Max RMS G
#2 601041 -93 -0.6 15.7 0.6 0.2
#4 ' 485449 -16.6 -0.3 18.1 0.5 0.3
45 678164 -8.5 -0.4 14.8 0.5 0.2
TS N Min Mean Max RMS o
#2 997949 -63.4 8.6 121.2 9.8 4.7
#4 _ 940159 -155.1 9.1 288.3 14.0 10.7
#5 2956022 -100.5 9.6 75.9 10.6 4.6
HG 5375775 1317 * 18.6 154.1 21.1 9.9
Table 8: Statistics on height differences dh [m] between the
3D object points derived from HRS data only and
the reference DTM
It was stated above, that the nadir looking view of the HRG
channel does not contribute very much to the height
accuracy. This is true from the geometric point of view in the
case of well identifiable check points. Here, in the case of the
automated mass point generation process by image matching
we can see, that the third view considerably improves the
results in terms of accuracy and reliability, especially in
mountainous regions.
3.6 DSM by rational functions
As a second method of DSM generation rational functions
are employed. Two sets of 1331 equally distributed points
per image are transformed into object space; one for the
HRS/HRG data using the 9 estimated correction parameters
(see 3.4.3.1), the other using pure HRS data without applying
correction polynomials (see 3.4.3.2). The points are equally
distributed in a cube, defined by increments of 1200 pixels in
Table 9: Statistics on height differences [m] between the
points, matched in 3 combinations, derived from
rational functions and from the strict model
3.6.2 Matching in object space (ISAE)
In a further step the commercial software ISAE (Krzystek,
1991) is used, which applies feature based matching in object
space. Two DSMs are generated from HRS1 and HRS2
images using two different sets of rational functions. The
first one is deduced from the data cube sets derived from
HRS/HRG using the 9 estimated correction parameters and
the second one from pure HRS data without applying
correction polynomials. A grid step of 45 m and an a priory
accuracy of 2.5 m is selected. In both DSMs more than 17
millions of matching points with more than 5 points per mesh
are found. An internal height accuracy of 0.9 m is obtained
for the first DSM and 1.3 m for the second, which proved to
be too optimistic compared to the empiric quality measures
presented in the next section.
4. ASSESSMENT OF GENERATED DSM
Table 10 lists the statistics on the height differences dh'
between the DSM raster point heights (10 m grid) and the
reference DTM. In addition to the pure point errors dh listed
in table 7, these dh' values also include the DSM
interpolation error. Without considering the HRG data the
standard deviations for the TS 42 and #5 located in moderate
terrain deteriorate only about 1096 compared to the results
achieved with HRG and bundle adjustment in addition to the
already mentioned systematic height error of 9 m. In the
mountainous terrain of test area #4 the results deteriorate
about 60%, which again underlines the importance of the
third view in mountainous terrain, at least for this DSM
generation method applying region growing image matching.
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