SCANNER RESECTION USING TRAJECTORY DATA
Fergal Shevlin
Dept. of Computer Science,
Trinity College Dublin, Ireland.
KEY WORDS: Satellite, Scanner, Precision, Calibration, Orientation, Vision, Geometry, SPOT.
ABSTRACT
A new solution to the problem of determining the parameters of satellite scanner exterior orientation is presented.
The scanner problem is simplified to that of the frame camera by making use translational and rotational
trajectory data recorded during the scanninging period. An accurate solution to the frame camera is then
presented which works even with poorly-distributed ground control points.
1 Introduction
Current scanner resection solutions are divided into
two main classes — those that ignore translational and
rotational variation over the imaging period, and those
which use polynomial approximations of motion vari-
ation [Shevlin, 1996]. The latter are significantly more
accurate than the former but owing to the amount of
approximation required they do not achieve optimal
estimates of the unknowns. As far as this author can
determine, no currently-published resection solution
uses actual trajectory data in finding the unknown pa-
rameters of exterior orientation. This paper explains
how the use of trajectory data can facilitate the near
optimal determination of the parameters of exterior
orientation.
With the advent of space-qualified GPs attitude and
orbit determination receivers the problem of satellite
scanner resection will not be as important in the near
future as it is today. At the current time, however,
resection is still required for remote sensing platforms
such as SPOT whose interior and exterior image ge-
ometry needs to be known precisely for photogram-
metric applications. Trajectory data supplied with
imagery typically consists of samples of angular ve-
locity recorded by the attitude and orbit control sys-
tem throughout the imaging period and estimates of
orbital position determined from Doppler analysis of
telemetry signals in conjunction with orbital models.
It has been shown by the author that a using suitable
parameterisations of rotation, angular velocity sam-
ples can be splined and integrated to yield a rota-
tional trajectory (specified as a set of discrete rota-
tions R;,i = 1,... ,n for n scanlines) relative to the
unknown orientation Ro at the start of the imaging
period [Shevlin, 1994; Shevlin, 1995]. Since the esti-
mates of position are approximated using orbital mod-
els they cannot be considered correct in terms of abso-
lute coordinates but they can be used to give an accu-
rate approximation of relative translation (specified as
a set of discrete translations t;) over the imaging pe-
riod. Hence rotational and translational trajectories
over the imaging period (which can be considered as
the parameters of interior orientation in scanned im-
agery) are known, the unknowns are the parameters
of exterior orientation - position po and orientation
R at the start of the imaging period.
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
2 Problem statement
Many different frame camera resection solutions have
been proposed. À dissertation from 1958 documents
over 80 different approaches (referenced in [Haralick
et al, 1989]). Considering that this was before the
advent of computer vision and digital photogramme-
try it gives some idea of how many solutions exist in
the literature (see [Tsai, 1987; Tsai, 1989] for compre-
hensive classification and review).
The vast majority of solutions rely on the same con-
straints relating the imaging and scene coordinate
systems — collinearity, coplanarity, and coangular-
ity. Different equations specifying these constraints in
terms of the unknowns are formulated and a wide va-
riety of techniques applied to solve them. Currently
published scanner resection solutions all seem to be
based on the collinearity constraint specified through
the equations of perspective projection. Primarily due
to the way in which motion is modelled these solutions
are not as accurate as they could be [Shevlin, 1995].
The aim of the work presented here is to use an accu-
rate model of scanner motion to achieve resection of
higher accuracy than that of current techniques.
In approaching this problem the author did not
want to duplicate or modify existing techniques since
most are already minor modifications of a few well-
established ones. A new perspective of the problem
was sought. This was eventually achieved with the
observation that scene point projections on the focal
plane and the focal point (as well as other interior
orientation parameters) are sufficient to form a bun-
dle of lines in the imaging coordinate system. These
lines specify the paths travelled by image-forming light
rays reflected off scene objects. This is shown for
the frame camera and scanner geometries in figure 1.
The collinearity condition for resection could then be
considered as fitting the bundle of lines to the scene
points, or more formally—
Given the relative positions and orientations of a set
of image-forming rays in an imaging coordinate sys-
tem and a corresponding set of observed control points
in a scene coordinate system, determine the exterior
orientation of the former system with respect to the
latter such that the perpendicular distances between
the rays and the corresponding control points are min-
imised.
