Currently role of various types of scanner imaging systems in photogrammetric applications is
steadily growing. Photogrammetric processing of scanner images sufficiently differs from the case
of central projection photographs due to dynamic nature of image acquisition. This paper is
devoted to describe practical experience in the development of computational procedures for
digital photogrammetric system PHOTOMOD (RACURS company, Russia).

The most common type of scanner satellite imaging systems is a pushbroom sensor
(SPOT - HRV, HRVIR, HRG; IRS - PAN; Terra - ASTER; EROS - NA-30; Ikonos), that's why such systems
are mainly in question in this paper. But even among digital imagery products acquired by
pushbroom sensors there is a wide variety in the content of ancillary data set, which the images
are supplied with. Depending on the data sets two main approaches may be applied: physical
(also known as "geometrical") and mathematical (sometimes called "algebraic").

Physical approach consists in detailed image acquisition process modeling including motion of
spacecraft center of mass, satellite rotation about it and, that is most important, in using
precise geometric camera model.

Since a single image is acquired on rather short part of the trajectory, it can be modeled
either by orbital motion equations or by polynomial approximation. In either case it's almost
always necessary to know relation between image line number and its acquisition time. Although
they are supposed to be linearly dependent for pushbroom imaging system, usually
ephemeris/attitude data are given with respect to time (sometimes indirectly - due to using
inertial reference frame), but photogrammetric processing requires knowledge of sensor position
in relation to image line number.

Attitude is usually modeled by a polynomial (of low degree - linear or quadratic) depending
on image line number or its acquisition time. Often image is supplied with angular velocities of
the sensor rotation, but when processing imagery of not very high-resolution (about 10 m) using
ground control points for sensor orientation refinement, according to gained experience, this
data may be ignored without significant accuracy loss.

The most important condition for the possibility to realize physical approach to
photogrammetric processing is availability of the geometric camera model that gives vector of
sight (related to the reference frame fixed with respect to sensor) as a function of pixel number
on the image line. The function may be defined by a table with values specified on a lattice
with some step along image line (or only for the extreme pixels of an image line), and linear
interpolation should be used to calculate the vector between the nodes of the lattice. Besides
that, some geometric model may be used, for example, planar analogue of central projection.
In any way, the model should be as accurate as possible because its refinement during bundle
adjustment makes this procedure unstable and less accurate. If, nevertheless, the refinement is
really necessary, planar central projection model already mentioned is suitable because it
contains only two parameters to be estimated ("efficient focal length" (expressed in pixels)
and number of the "principal pixel") and their initial values can be easily obtained.

Using these three models one can calculate vector of sight and sensor position as a function
of pixel coordinates of an image point: first, camera geometric model gives sight vector
direction in the sensor reference frame, then attitude model lets to transform the vector into,
generally speaking, geodetic reference frame, and motion model provides us with sensor position.

When all the models listed above are elaborated and initial values of their parameters are
estimated, bundle adjustment procedure should be performed. In PHOTOMOD system currently the
procedure is carried out for each image separately and is based on assumption that ray, whose
direction (vector of sight) and vertex (sensor position) are calculated using ground control
point coordinates on the image should pass through the point on the earth. This procedure is
performed iteratively by least squares method and requires from tens to thousands iterations
depending on models which were applied.

Since the satellite position and sight vector are known as functions of image point
coordinates, it's possible to solve two main photogrammetric problems:

- to calculate image coordinates from ground coordinates (what is necessary for forming
orthoimagery) through iterative process using a single image
- to obtain ground coordinates of a point from its image coordinates on a stereopair, what
is necessary for digital elevation model computation (Picture 1 gives an example of digital
elevation model derived from panchromatic SPOT stereopair). This operation is called
triangulation; it should be taken into account that the calculated rays will not intersect
in fact, therefore some additional considerations should be used to get the ground point.
In the simplest case we can suppose that both rays are obtained with the same precision and
the point in question is the middle of their common perpendicular.

As opposed to the physical modeling, mathematical approach can be applied, when only
imagery but no ancillary data are available. This method consists in using direct expressions
for pixel coordinates of an image point as a function of its ground coordinates. Structures of
the expressions are determined by some assumptions (usually the assumptions are very general,
for example, that some value changes linearly or very slowly, and therefore they impose rather
strong limitations) about imaging system. The expressions contain a set of numerical parameters
that are to be estimated using ground control points by adjustment procedure based on
least-squares method. Then the first of two main photogrammetric problems, listed above, can be
solved directly using these expressions, and the second problem is equal to set of four equations
with three unknowns. Often the equations can be transformed to linear ones, and then the
generalized solution of the equations set is easily obtained using least squares method.

Comparison of these two approaches shows, that mathematical one is simpler (and therefore
faster), requires no ancillary data and consequently this approach yields more universal
algorithms. The last assertion means that such algorithm can be applied without modification to
a rather wide class of imaging systems, in contrast with the physical approach, which should take
into account many specific features of each system. For imaging systems with ground resolution
about 10 m accuracy obtained may be almost the same, but, of course, since physical approach is
stricter, usually it gives better results. Another advantage of physical approach is that it
requires significantly fewer amounts of ground control points (see Table 1; it should be noted,
that ground points coordinates was gathered using maps of scale 1:25000 in the case of IRS imagery
and 1:50000 in the case of SPOT; so final accuracy was sufficiently affected by the errors in the
ground control points coordinates).

Picture 1: An example of digital elevation model derived from SPOT stereopair by digital
photogrammetric system PHOTOMOD.

Table 1: The difference between physical (geometric) and mathematical (algebraic) approaches to
photogrammetric processing of satellite scanner imagery
Nevertheless it seems obvious, that due to one meter and sub-meter resolution imaging systems
the situation will radically change. Simple algebraic formulas, such as expressions of projective
transformation, which are often used now in the scope of mathematical approach, raise doubt to
be able to provide results with accuracy adequate to image resolution. Really, many of simple
structured formulas used in this approach may be obtained by physical modeling of image
registering process with very rigid conditions - for example, in assumption of uniform and
straightforward motion of a satellite with no rotation about its center of mass during image
acquisition. The errors, caused by such rough model, was negligible in many cases due to smooth
motion and precise stabilization of the satellite, but in case of high resolution imagery it will
not have a place. Therefore those expressions, which cannot take into account nonlinear nature of
some processes, will become inconsistent.

Since volume of sales of high-resolution imagery depends on availability of photogrammetric
systems, which support its processing, remote sensing data provider should supply imagery with
all the necessary ancillary data, described above.

There is another question closely related to the product data content. It's the problem of
provided data format. Current situation is that every data provider uses own format with specific
content of ancillary data. In fact both data users (including software developers) and data
providers are interested in some universal, but extendable, data format, which has common
(mandatory) part and additional part. The first should contain standard data that allow performing
processing using physical approach, while the second may include some unique advanced or special
information. Such approach will guarantee that any data, which are stored in this format, are
suitable for rigorous photogrammetric processing, and, on the other hand, data supplier may
believe that any standard software will be able to fulfill this processing.

* Published in: *Geospatial Today, September-October 2002, vol. 1, issue 3, pp.27-30*