art B3. Istanbul 2004
| on the total twenty-
>d on the available
performing a PTP
| Z-component of the
] that omitting such a
ved height values.
VleanztStd;,m
0.944 + 0.853
0.023 + 0.194
ation values of the
ce points with and
(PTP) correction
ffine parameters are
sets of results were
? correction using the
le); and with PTP
; (Equations 8). The
estimated roll angles
ect points, 16 points
used as GCP in the
ints, shown as green
1t scene
PTP-
TP PIP, estimated
true y
V
S 2.63 2.58
0 5.00 6.09
3-5 | 1.35e-5 | 1.35e-5
>-7 | 4.88e-7 | 4.88e-7
e-6|-5.58e-6| -5.58e-6
e-4|-3.26e-4| -3.26e-4
:-9 | 4.81e-9 | 4.87e-9
3-5 | 1.35e-5 | 1.35e-5
>-6 | 1.17e-6 | 1.17e-6
e-5|-1.13e-5| -6.06c-6
| parameters and roll
je estimated variance
ig the estimated roll
hand, omitting PTP
variance component.
indicated in Equation
erence is attributed to
1 flat terrain. On the
estimated roll angles
e smallest variance
/ of the estimated 2-D
| performed based on
ates of the points in
arlier. The estimated
1e true values and the
6.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV , Part B3. Istanbul 2004
Mean yStdyy,m MeanztStd;,m
No PTP 0.000 + 1.675 0.000 + 0.858
PTP true y 0.000 + 1.699 0.000 + 0.070
PTP estimated | 0.000 + 1.685 0.000 + 0.015
e No PTP 0.674 + 1.666 0.472 + 0.486
RN PIP quu. | 068141720 0.030 + 0.039
Bots PTP eximaled | 0.55241 600 | 002: 0.001
Table 6. Mean error and standard deviation of the indirectly
estimated object space GCP and check points
As shown in Table 6, no bias can be seen in the estimation of
object coordinates of the GCP. Again, a smaller Std, is achieved
by using the indirectly estimated roll angle, compared to those
using the true roll angles. The same conclusions can be drawn
for the check points (see Table 6) except for the existence of
bias values. A comparison of Tables 6 and 4 reveals the
suitability of indirect methods (that is, using GCP) compared to
the direct methods (that is, using navigation data).
6. CONCLUSIONS AND RECOMMENDATIONS
In this paper, parallel projection is chosen to model space
scenes such as IKONOS. The rationale behind selecting this
model is that many space scenes have narrow AFOV and
acquired in very short time. Because the original scenes comply
with the rigorous perspective geometry, scene coordinates have
to be altered in PTP transformation so that they comply with
parallel projection. The parallel projection model is discussed
together with its linear and non-linear forms and the
transformation between them. The former is preferred when
GCP are available while the latter is preferred when navigation
data are available. The derivation of the parallel projection
parameters from the navigation data is also presented. Finally,
focussing on PTP transformation, a mathematical model is
developed to estimate the scanner roll angles together with the
scene parameters using GCP. The developed transformation and
mathematical models are verified using synthetic data. Although
the estimated roll angles differ from the true ones, the errors in
the object space using the estimated angles are smaller. In
addition, indirect parameters estimation using GCP gives
smaller error values in the object space, compared to those
derived using the navigation data.
Future work will include experiments using real data such as
IKONOS and SPOT scenes. Inclusion of higher order primitives
(such as linear and areal features) and object space constraints
to the parallel projection model will be analyzed. Finally,
normalized scenes, DEM and ortho-photos will be generated
based on the parallel projection.
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