International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
models to process almost all the high resolution optical imagery
(Eros-A, QuickBird, IKONOS, Cartosat-l, GeoEye-l,
WorldView-1 and 2), was updated to manage also and SAR
imagery, acquired by COSMO-SkyMed and TerraSAR-X;
moreover a new original matching methodology, both suited for
optical and SAR imagery and now patent pending, was
implemented.
Here the application and the results of the overall procedure for
radargrammetric DSMs generation was applied to TerraSAR-X
imagery, acquired in Spotlight mode over Trento (Northern
Italy). Two different tiles with extensions of 2-3 Km? were
selected, considering different morphological situations and
some difficult cases for automatic image matching. Paragraphs
2, 3 and 4 present the fundamentals of the DSMs generation
procedure, mainly focusing on the orientation models (rigorous
and RPFs), the pre-processing denoising strategy and the
matching methodology; paragraph 5 discusses the results
related to the processed images and finally the conclusions are
drawn in paragraph 6.
2. RADARGRAMMETRIC ORIENTATION MODEL
2.1 Geometric reconstruction to
radargrammetry
according
The radargrammetry technique performs a 3D reconstruction
based on the determination of the sensor-object stereo model, in
which the position of each point on the object is computed by
the intersection of two radar rays with two different look
angles.
In the first step, the relationship between the image and ground
coordinates is established through the orientation model, that
reconstructs the SAR geometry during the image acquisition.
The model is based on two fundamental equations.
The first equation of (1) represents the general case of zero-
Doppler projection: in zero-Doppler geometry the target is
acquired on a heading that is perpendicular to the flying
direction of satellite; the second equation of (1) is the slant
range constrain (Capaldo et al., 2011).
NS uA. x rY Y«(Z m4. 0.0570
Vr (Xp = Xs) + vy (Yp—Ys )+ vs, (Zp -Z5)=0
where Xp, Yp, Zp are the coordinates of the generic ground
point P (time independent)
Xs Ys Zs are the coordinates of the satellite sensor
(time dependent)
Vsx Vsx Vsx are the cartesian components of the
satellite sensor velocity (time dependent)
Ds is the so-called “near range"
CS is the slant range resolution or column spacing
Iis the column position of point P on the image
The relationship between image coordinate J and the time /, can
be expressed by a linear relation,
; 1
= start _ time + J
RF
(2)
in which the start time of the acquisition (start time) and the
Pulse Repetition Frequency (PRF), the sampling frequency in
azimuth direction, are involved.
36
A refinement of the orbital model, that has to be taken into
account to comply with and to exploit the potentialities of the
novel high resolution (both in azimuth and in range), is based
on the Lagrange polynomial orbital model.
The orientation is performed without Ground Control Points
(GCPs), using only the metadata supplied with imagery. For
TerraSAR-X imagery, previous orientation test showed that the
accuracy of the geolocation is around 2-3 m in horizontal and in
vertical direction.
2.2 RPCS generation
The RPFs model is a well-known method to orientate optical
satellite imagery. This model relates the ground coordinates
(latitude o, longitude 4 and height 4) to the image coordinates
(I, J) in the form of ratios of polynomial expressions whose
coefficients (RPCs) are often supplied together with imagery. In
fact, some satellite imagery vendors have considered the use of
RPFs models as a standard to supply a re-parametrized form of
the rigorous sensor model in terms of RPCs, secretly generated
from their own physical sensor models.
Moreover, since residual biases may affect the supplied RPCs,
the orientation can be refined on the basis of some GCPs even if
RPFs models are used; usually a 2D shift (2 parameters) or a
2D affine (6 parameters) transformations are estimated, so quite
few GCPs are necessary to obtain a refined RPFs orientation,
which can reach the accuracy level of an orientation based on a
rigorous model (Hanley and Fraser, 2004).
The RPCs can be generated according to a so-called terrain
independent scenario, starting from a rigorous orientation
model.
A tool based on this approach is implemented in SISAR and is
now able to manage both optical and SAR high resolution
imagery. A 2D image grid covering the full extent of the image
is established and its corresponding 3D object grid with several
layers slicing the entire elevation range is generated. The
horizontal coordinates (X, Y) of a point of the 3D object grid are
calculated from a point (/, J) of the image grid using the already
established and mentioned rigorous orientation model with an a
priori selected elevation Z. Then the RPCs are estimated in a
least squares solution using as input the 3D object grid points
and the image grid points (Crespi et al. 2009).
To avoid instability due to high RPCs correlations, in our
approach the Singular Value Decomposition (SVD) and QR
decomposition are employed to evaluate the actual rank of the
design matrix and to select the actual estimable RPCs.
Moreover, the statistical significance of each estimable RPC is
checked by a Student T-test, so to avoid overparametrization; in
case of not statistically significant RPCs, they are removed and
the estimation process is repeated until all the estimated RPCs
are significant,according to the “parsimony principle” (Crespi et
al. 2009).
It has to be underlined that, as regards the RPCs generated by
SISAR, the shift/affine RPCs refinement is not necessary in
order to achieve the best accuracy, since the RPCs are a re-
parametrized form of the geometric radargrammetric model,
already well calibrated on the accurate metadata information.
Overall, the use of the RPFs of model is common in several
commercial software, at least for three important reasons: the
implementation of the RPFs model is standard, unique for all
the sensors and much more simple that the one of a rigorous
model, which have to be customized for each sensor; the
performances of the RPFs model can be at the level of the ones
from rigorous models; the usage requires zero or, at maximum,
