superimposition, based on coordinates which are equivalent to
those of the perspective model. The perspective sensor model
maintains one model coordinate system, which on the one
hand defines the movement directions of the instrument
encoders (hand-wheels etc.) and which, on the other hand,
holds the model coordinates which applications receive and
use to control instrument movements. Applications normally
would derive ground coordinates from model coordinates
using a transformation matrix which is also provided by the
RTP.
Since the real-time movements of the spot sensor model are
performed in a different coordinate system (see chapter
"Mathematical Aspects of the Real-Time System"), additional
RTP internal computations had to be implemented to compute
model coordinates which can be used in the same way as
described above. In fact, these model coordinates are ground
coordinates; consequently, the transformation matrix for
deriving ground coordinates is a unit matrix.
The definition of the ground coordinates (TM, UTM and
Lambert) can be given by the user during the orientation. The
desired output system, TM, UTM or Lambert. is also specified
during orientation so that the RTP considers this system of
ground coordinates and delivers the appropriate information to
applications.
- the mono and stereo superimposition system had to be
supported; this has been no concern at all, because the
integration of the superimposition into the RTP is such that
any sensor model is supported without any necessary changes
for the superimposition.
4.1 Mathematical Aspects of the Real-Time System
A real-time analysis of SPOT has been done by KRATKY (1987). For
clarity, the ‘model’ system refers to the co-ordinate system in which the
orientation is calculated, in this case the inertial geocentric system. xy’
refer to the left image co-ordinates, and x” and y” refer to the right
image co-ordinates. Real-time model panning on a photogrammetric
plotter requires that the plate position be updated at a high frequency;
25 Hz is known to be adequate.
The orientation parameters of a dynamic system change with time and
is different for every scan-line (x-image co-ordinate). A RTP for SPOT,
if driven by encoder-input in ground units, would require an iterative
computation as the x-image co-ordinates are required (and not known)
to calculate the orientation parameters. In six iterations, this could
result in more than 500 floating point (FP) multiplications per image
which is about 20 times the required number in a perspective RTP
system. This would be difficult to achieve on typical CPUs of the day
like an INTEL 486/66 MHz.
An SD operator expects the same feel as a model based on the
perspective geometry. Thus, encoder-input devices must respond in
similar fashion and the floating mark should move in the same
consistent direction when the encoder input-devices eg. handwheels are
operated. RTPs for conventional photogrammetric models are driven by
model co-ordinates with axis almost aligned to the photo-co-ordinate
system.
To achieve the same effect, image co-ordinates (x’y’) would be the
logical choice of encoder input for a linear array RTP system. There
may be a misalignment of X- and Y-axis from the expected movement
of the floating mark due to the placement of the image in the SD.
This problem is solved in an analytical plotter by using the kappa
rotation from the inner orientation matrix of the left image to transform
the basic encoder input. After model set-up, the right image could be
rotated in kappa (as necessary) to ensure correspondence with with
‘DOVE’ prisms in an analytical system but in a digital
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
photogrammetric system this is compounded by the need for image
resampling image resampling (and re-display).
Accordingly, the operator expects the floating mark to move at right-
angle to the plate when the foot disk is displaced as is the situation in
conventional photography. This requires that the height (h) be the
choice of input for the third encoder. This height should refer to the
local geodetic system and would. therefore, compound the
implementation because orientation is done in the geocentric system.
A compromise is to have encoder input in x'y'H. The height allows for
scale to be solved in the collinearity model and thus the transformation
to the model system is accomplished in one step without iterations.
Then the calculation of x"y" proceeds iteratively. Less than 300 FP
calculations per cycle are achievable here, but this may still not be fast
enough.
Figure 4: Optimisation drill for the RTP of SPOT
step 1:
iteraive iteraive
This requires many iterations and, therefore, takes too long.
step 2:
This is faster but the Z-floating mark may not move
vertically to the image planc.
Step 3:
[I sete an aprox. Z(geoc). for each X y' grid pt. on the left-image
[2- compute XY7. (ECH). then transform to ECEF. and then to ENR 5]
E (EN h)
Zu = Zi+h-h;
until huh
Then fit to Kratkys polynomial coefficients
Z = F(x, y,h); after collection of terms
This should work well but can still be further optimised
Step 4:
similar polynomials could be calculated linking the following:
X'y'h to x^y"(notimplemented in the Leica system)
x'y'h ^to HN
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