International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
polynomial models, Direct Linear Transformations (DLT) and
affine projections.
The rigorous models try to describe the physical properties of
the sensors acquisition and are based on collinearity equations,
which are extended in order to describe the specific geometry of
pushbroom sensors. Some rigorous models are designed for
specific sensors, while some others are more general and can be
used for different sensors. Few models are designed for both
spaceborne and airborne linear scanners.
In case of spaceborne sensors, different approaches have been
followed. V. Kratky (Kratky, 1989) developed a software,
called: = SPOTCHECK +,“ “thes “principle “of “* rigorous
photogrammetric bundle formulation is combined with the
sensor external orientation modelling. The satellite position is
derived from known nominal orbit relations, while the attitude
variations are modelled by a simple polynomial model (linear or
quadratic). For self calibration two additional parameters are
added: the focal length (camera constant) and the principle
point correction. The exterior orientation and the additional
parameters of the sensor model are determined in a general
formulation of the least squares adjustment (Gauss-Helmert
model). The use of additional information, e.g. from
supplemented data files is not mandatory, but if this information
is available it can be used to approximate or pre-set some of the
unknown parameters. This model has been used for the
orientation of SPOT-2 (Baltsavias et al., 1992), MOMS-02/D2
(Baltsavias et al., 1996), MOMS-02/Priroda (Poli et al., 2000),
Landsat TM and JERS-1 (Fritsch et al., 2000) scenes. An
advantage of this software is that it can easily integrate new
pushbroom instruments, if the corresponding orbit and sensors
parameters are known. The model was also investigated and
extended in (Fritsch et al., 2000).
The principle of i orientation images? was used at DLR for the
geometric in-flight calibration and orientation of MOMS-2P
imagery (Kornus et al., 1999a, Kornus et al., 1999b). This
method is based on extended collinearity equations (Ebner et
al., 1992). The exterior orientation parameters are determined in
the so-called orientation images and between the orientation
images the parameters of an arbitrary scan line are interpolated
using Lagrange polynomials. For the modelling of the interior
orientation for each CCD array five parameters are introduced.
All unknown parameters are estimated in a bundle block
adjustment using threefold stereo imagery. For the
determination of the unknown parameters a large number of tie
points which are automatically measured is required.
In the group of Prof. Ebner at TU Munich a mathematical
model of photogrammetric point determination for airborne and
spaceborne three-line scanners has been developed and tested
on MOMS-02/D2 and P2 (Ebner et al., 1992), MEOSS (Ohlhof,
1995), HRSC and WAOSS (Ohlhof et al., 1994) sensors. The
model is based on a polynomial approach in case of airborne
imagery, whereas orbital constraints are utilised in case of
spaceborne imagery. In the airborne case the exterior orientation
parameters are estimated only for some so-called orientation
points, which are introduced at certain time intervals, e.g. every
100th readout cycle. In between, the external orientation
parameters are expressed as polynomial functions (e.g.
Lagrange polynomials) of the parameters at the neighboring
orientation points. For preprocessed position and attitude data,
e.g. acquired by differential GPS and INS, observation
equations are formulated. Systematic errors of the position and
attitude observations are modelled through additional strip- or
block-invariant parameters. By limitation to constant and time-
dependent linear terms, which describe the main effects, 12
additional parameters, namely a bias and a drift parameter for
each exterior orientation parameter, are introduced. For the
satellite case, the spacecraftis epoch state vector is estimated
with the assumption that all scanner positions lie along an orbit
trajectory. Due to the lack of a dynamic model describing the
cameraís attitude behaviour during an imaging sequence, for the
spacecraftís attitude the concept of orientation points is
maintained.
The University College London (UCL) suggested a dynamic
orbital parameter model (Gugan et al, 1988). The satellite
movement along the path is described by two orbital parameters
(true anomaly and the right ascension of the ascending node),
that are modelled with linear angular changes with time and
included in the collinearity equations. The attitude variations
are modelled by drift rates. This model was successfully applied
for SPOT level 1A and 1B (OíNeill et al, 1991), MOMS-02
and IRS-1C (Valadan Zoej et al., 1999) imagery. In (Dowman
et al., 2003) this approach was investigated and extended for the
development of a general sensor model for along-track
pushbroom sensors.
The [IPI Institute in Hannover the program system
BLUH/BLASPO is used for the adjustment of satellite line
scanner images (Jacobsen, 1994). Just the general information
about the satellite orbit together with the view directions in-
track and across-track are required. Systematic effects caused by
low frequency motions are handled by self-calibration with
additional parameters. In this model the unknown parameters
for each image are 14, that is, 6 exterior orientation parameters
for the uniform motion and 8 additional parameters for the
difference between the approximate uniform movement and the
reality. This program seems very flexible, because it has been
successfully used for the orientation of MOMS-02 (B, y, ksalih
et al, 2000) SPOT, KFA1000, KVR1000 and IRS-IC
(Jacobsen et aL, 1998), DPA, IKONOS and Quickbird
(Jacobsen et al., 2003) and SPOT-S/HRS (Jacobsen et al.,
2003).
In (Westin, 1990) the orbital model used is simpler than in the
previous models. A circular orbit instead of an elliptical one is
used with sufficient accuracy. Using data from SPOT ephemeris
data seven unknown parameters need to be computed for each
SPOT image.
Among specific models developed for one sensor, the procedure
used at JPL, Pasadena, for the orientation of MISR sensors
reproduces the image acquisition using a large number of
reference systems and specific MISR parameters measured
during laboratory calibration. The external orientation
parameters are calculated from precise ephemeris (Jovanovic et
al, 1998).
An alternative image orientation approach widely used is the
Rational Function Model (RFM), or Rational Polynomial
Coefficients (RPC), which provide a means of extracting 2D
(3D) information from single (stereo) satellite imagery without
explicit reference to either a camera model or satellite
ephemeris information. The RFMs describe the relationship
between image (line, sample) and object space (typically
latitude, longitude and height) coordinates and viceversa
through quotients of polynomials, usually of 3 order (Fraser et
al., 2001). In (Grodecki et al., 2003) a block adjustment with
Rational Polynomial Coefficients (RPC) is proposed and
applied for the orientation of high-resolution satellite images,
such as IKONOS. The same model has been implemented at
IGP, ETH Zurich, for the orientation of SPOT-5/HRS and
SPOT-5/HRG stereo images (Poli et al., 2004).
Other approaches for satellite imagery acquired by CCD linear
array scanners are based on affine transformations.
Prof. Okamoto (Okamoto, 1981) proposed the affine
transformation to overcome problems due to the very narrow
