International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
field of the sensor view. The imaging geometry is converted
from the original perspective imagery into an affine projection.
Later the method was applied to SPOT stereo scenes of level |
and 2 (Okamoto et al., 1998). The theories and procedures of
affine-based orientation for satellite line-scanner imagery have
been integrated and used for the orientation of SPOT, MOMS-
2/P (Hattori et al., 2000) and IKONOS (Fraser et al., 2001)
scenes. Under this approach an initial transformation of the
image from a perspective to an affine projection is first
performed, then a linear transformation from image to object
space follows, according to the particular affine model adopted.
The assumption is that the satellite travels in a straight path at
uniform velocity within the model space. The model utilises the
Gauss-Krueger projection plane and ellipsoidal heights as a
reference system, therefore height errors due to Earth curvature
must be compensated. The results demonstrated that 2D and 3D
geopositioning to sub-pixel accuracy can be achieved (Fraser et
al., 2001).
(Gupta et al, 1997) proposed a simple non-iterative model
based on the concept of fundamental matrix for the description
of the relative orientation between two stereo scenes. The model
was applied on SPOT across-track stereo scenes. The unknown
parameters for each pair are: the sensor position and attitude of
one scene at time 0, the velocity of the camera, the focal length
and the parallax in across-track direction.
The Direct Linear Transformation (DLT) approach has also
been investigated. The solution is based only on ground control
points and does not require parameters of the interior
orientation and ephemeris information. The DLT approach was
suggested for the geometric modelling of SPOT imagery (El
Manadili et al., 1996) and applied to IRS-1C images (Savopol
et al, 1998). In (Wang, 1999) it was improved by adding
corrections for self calibration.
In general, the approaches based on 2D and 3D empirical
models, as those presented, are advantageous if the rigorous
sensor model or the parameters of the acquisition system are not
available.
In case of pushbroom sensors carried on airplane or helicopter
GPS and INS observations are indispensable, because the
airborne trajectories are not predictable. Anyway, the original
position and attitude measurements are not enough accurate for
high-precision positioning and require a correcion.
The IGP at ETH Zurich (Gruen et al., 2002a) investigated three
different approaches for the external orientation modelling of
the Three-Line Scanner (TLS) developed by Starlabo
Corporation: the Direct Georeferencing, in which the translation
displacement vector between the GPS and camera systems is
estimated for the correction of GPS observations, the Lagrange
Polynomials, as used in (Ebner et al., 1992) for spaceborne
sensors and the Piecewise Polynomials, where the sensor
attitude and position functions are divided in sections and
modelled with 1* and 2" order respectively, with constraints on
their continuity. The sensor self-calibration has also been
integrated in the processing chain. Further investigations on the
models performances are in progress.
In the LH-Systems photogrammetric software for the ADS40
processing, a triangulation is applied for the compensation of
systematic effects in the GPS/IMU observations (Tempelmann
et al., 2000). These effects include the misalignment between
IMU and the camera axes and the datum differences between
GPS/IMU and the ground coordinates system. For the
orientation of each sensor line the concept of orientation fixes is
used. The external orientation values between two orientation
fixes are determined by interpolation using the IMU/GPS
observations.
From the analysis of the above literature we can see that
nowadays both approaches based on rigorous and non rigorous
models are widely used. In case of rigorous models the main
research interests are the sensor external and internal orientation
modelling. The external orientation parameters are often
estimated for suitable so-called iorientation linesi and
interpolated for any other lines. A self- calibration process is
recommended, as least to model focal length variation and first
order lens distortions. In order to avoid over-parameterisation
the correlation between the parameters must be investigated and
tests on the parametersí significance and determinability are
required. Moreover it is recommended to take advantage of
additional information for the external orientation estimation
(orbital elements and ephemeris for spaceborne sensors, GPS
and INS measurements for spaceborne and airborne sensors).
Few models can be applied for both airborne and spaceborne
sensors.
The orientation methods based on rational polynomials
functions, affine projections and DLT transformations are
mostly used for high-resolution satellite imagery. They can be a
possible alternative to rigorous model when the calibration data
(calibrated focal length, principal point coordinates, lens
distortions) are not released by the images providers or when
the sensor position and attitude are not available with sufficient
precision (Vozikis et al., 2003).
3. SENSOR MODEL DESCRIPTION
A rigorous sensor model for the georeferencing of a wide class
of linear CCD array sensors has been developed at IGP and
already applied to different linear scanners carried on satellite
and aircraft (Poli, 2003). The photogrammetric collinearity
equations describe the perspective geometry in each image line.
The sensor position and attitude are modelled with piecewise
2" order polynomial functions depending on time. The platform
trajectory is divided into segments according to the number and
distribution of available Ground Control Points (GCPs) and Tie
Points (TPs) and for each segment the sensor position and
attitude are modelled by 2™ order polynomials. At the points of
conjunction between adjacent segments constraints on the zero,
first and second order continuity are imposed on the trajectory
functions. Additional pseudo-observations can tix some or all
parameters to suitable values. For example, if the 2" order
parameters are fixed to zero, the polynomial degree is reduced
to 1 (linear functions). This option allows the modelling of the
sensor position and attitude in each segment with 2" or 1%
order polynomials, according to the characteristics of the
trajectory of the current case study. In case of sensors carried on
aircraft, additional GPS and INS observations can be included
in the model (Poli, 2002).
The sensor model includes also a self-calibration, which is
required for the correction of the systematic errors due to
principal point displacement (d,, d,), focal length variation (d..),
radial symmetric (k,, Æ) and decentering lens distortion (p;, p>),
scale variation in CCD line direction (s,) and the CCD line
rotation in the focal plane (0). The model can be applied to
single lens sensors with synchronoous (i.e. TLS, ADS40,
WAOSS) and asynchronous (EROS-A1) along-track stereo
capability and to multi-lens sensors (i.e. SPOT-5/HRS, ASTER,
MOMS-02, MISR).
The functions modelling the external and the internal
orientation are integrated into the collinearity equations,
resulting in an indirect georeferencing model. Due to their non-
linearity, the complete equations are linearized according to the
Interne
first-or
parame
adjustr
modell
parame
Statisti
In cas:
sensor
genera
the se
require
numbe
availak
referen
centerc
In case
include
polyno
GPS a
the ler
errors (
For the
are mai
e deter
best
self
exter
GCP
e exter
funct
traje
e self-c
confi
The cl
include
correla
orienta
Statisti
the GC
assessr
The m
airborn
and mt
acquisi
concer
etal...
02/P, ^
in (Pol
carried
the lat:
summa
4.1 SI
Within
was ge
Resolu
satellit
in ord
coordi
positio
