(x cxt)
(x -x! 2j
io
(y -y* )
1.50]
coordi-
groun-
cients,
, pitch
ulation
y affect
values
ice the
the di-
- in the
derive
which
ssump-
e been
nearity
Xf the
f high
| coor-
y radar
ich in-
point
**3/yi
33*4/yi
For single strips these equations at least have to be
reduced for the unknown parameter for the
terrainheight zi. For flat terrain the terms depending
on the terrain height zi are zero. The principle idea of
this method for the formulation of algorithms goes
back to Baker ( 1975 ), who applied it on line
scanner imagery, which has been modified for SLAR
and SAR image geometry. These equations can al-
ready be used without the knowledge of the content
of the parameters AO to A4, respectively BO to B13,
which are stated as follows:
AGS -kx 7 x'oO/h -:k»i£$90
Ais kx-k@/h
A2- kx?-x'o1/h?
AS- kxs445 - x'o2/h4*35
A4= kx/h
BO--ky-y'oO/h-*r'o-z'oO/h-ky-QO-r'o-dz/h*r'a-dky-dro'
Bis-ky-z'oce/h?*-r'o-O0 /h*ky/n?-dz*(-ky/hr1/h) -dky
B2= -kx-ky-y'oiíi/h* "kx -6'GO-2'01/h3
B3m —kx?-ky-y'o2/hs*S9kx?-ro-z'o2/h«s«3
B4- -kx-ky-z'oi/h**3
BS= -ky-Q@/h?
B6- -kx?-ky-y'o2/h**4
B7= 2-kx**3-ky-z'o2-z'ol/h**4
BB- kx**4-ky-z'o2?/h**5
B9- -ky-2'o0/h
BiO0- -kx-ky-z'ol/h*?
Bii -kx?*-ky-2'o02/h**3
B12-ky/h
BiS3cky-(2i-2z'O0-kx-2'O01-xi/h-kx?-2'O1-xi?/h22)/th-y1)
This approach can be extended by variation of the
sensor behaviour, in particular by calculating for the
"real flight path", as gained from housekeeping GPS
and by additional parameters , including the
introduction of the Doppler information of the Radar-
image, to fit smoother to the ground control point
field. As compared to heuristic approaches, which
are still in use even for very advanced image
processing devices, arbitrariness is subdued and the
3rd dimension can be calculated.
For recent radar campaigns the polynomial approach
as derived from equivalent collinearity equations,
showed an accuracy of approximately + 10m.
To use the advantages of existing bundle block ad-
justment software for conventional photography, an
approximate transformation of the radar geometry
into the conventional image geometry and vice versa
also successfully has been carried out. The modified
BINGO- program of the Institute for Photogrammetry
of the University of Hannover according to Kruck et
al. ( 1986 ), for 47 ground control points allowed to
obtain an accuracy of about 22.5 pixels for a SIR -B
image of the testsite Freiburg, as carried out by
WIGGENHAGEN.
2.3 Combined Approaches
The following method gives an example for a
combined approach between parametric and non-
parametric solutions: Radar image coordinates (xi',
709
yi) for ground coordinates of particular points with
known object coordinates (xi, yi, zi), including output
pixels (e.g., anchor points), can be calculated from
known ground control points (xp, yp, zp). Supposing,
roll-, pitch- and yaw-values are neglectable and under
the condition, the object coordinate system and the
radar image coordinate system are in parallel, the
following approach approximately is valid:
x1'=xp'+kx((xi-xp)/h)
yi—yp-ky((yi-DELTA Yi-yo'i)/(z-zo'i)
-(yp-DELTAYp-yo'p)/(z-zo'p))
with DELTAYi-h (zi-z) / (yi-yoj).
For the calculation of DELTAYp the index "i" has to
be replaced by "p". The results improve by applying
this approach onto surrounding control points. The
deviations of the resulting image coordinate pairs for
xi and yi' can be eliminated by the weighted mean
approach. To apply this method, a great amount of
ground control points is needed, which can be de-
termined by radar block adjustment etc..
3. RADAR MAPS AND RADAR ORTHO-
PHOTOS
3.1 Quicklook results
The proposed SAR image standard product is
ground range imagery, because it is accepted by the
user community. This output result for areas with flat
terrain might even be considered as a final product, in
particular for ocean regions and for coastal sites.
3.2 Radar orthophoto
For tasks, which require map accuracy(usually +1...3
pixels, see DOYLE (1975) and KONECNY et
al.(1984b)), like
- GIS-input
- mosaicing,
- multisensor imagery and
- change detection etc.,
for hilly and mountainous terrain, a digital geometric
pixel by pixel image restitution, including terrain
height effects is needed, preferable applying the indi-
rect rectification method. To handle larger output
blocks and to calculate for regional or even particular
pixel wise terrain heights, according to suggestions of
Egels and Massou d'Autume of the IGN (France) and
Konecny (1985) the following method for digital im-
age rectification has been established:
Step 1 and 2: anchor point determination:
1. For minimum and for maximum terrain height