Digital photogrammetric system PHOTOMOD and its usage for pushbroom imagery processing
Summary. The paper is intended to present digital photogrammetric system PHOTOMOD,
to outline basic methods of pushbroom imagery processing and to describe in brief their
implementation in PHOTOMOD.
The main features of PHOTOMOD system are summarized (concerning airborne central projection
blocks as well as pushbroom imagery). Basic principles of currently used approaches (rigorous,
parametric, replacement) to photogrammetric processing of pushbroom imagery are explained.
Spaceborne optical sensors supported by PHOTOMOD listed and supplied with short remarks regarding
methods applied. Offtheshelf orthoimagery costefficiency analyzed as opposed to performing
orthorectification on one's own.
1. PHOTOMOD system overview
PHOTOMOD is the wellknown digital photogrammetric system developed by company RACURS, Russia.
The software package allows flexible workflow organization; it supplies user with the capabilities
to perform the complete cycle of photogrammetric processing without engaging any thirdparty
tools, and, on the other hand, it's suitable for integration with wide variety of software due to
enhanced import/export procedures (supporting the vast set of exchange formats) and special
interface utilities. Due to modular organization PHOTOMOD allows flexible deployment to provide
user with the most suitable and costeffective solution.
PHOTOMOD is uptodate system supporting film and digital airborne cameras as well as film,
pushbroom CCD and radar spaceborne sensors. The output data are digital elevation models,
orthoimages, 3D vectors, digital maps; they may be used as final products or to be transmitted to
GIS or mapping applications for further processing. Rigorous algorithms applied and numerous
control procedures available on every processing step ensure quality of the PHOTOMOD output data.
The system is highly automated to reduce laborious manheld operations. It also allows to speedup
the timeconsuming procedures due to its general productivity and network organization; the latter
also helps to optimize usage of data storage and other hardware resources as well as to organize
distributed parallel work with large imagery blocks.
PHOTOMOD complies with modern requirements concerning compatibility with specific
photogrammetric hardware like complicated manipulators (multibuttons mice), stereoscopic glasses
and various display stereomodes (anaglyph, interlace, pageflipping).
The last but not the least advantage of PHOTOMOD software is very affordable prices and
modulebased offering policy.
2. Photogrammetric processing of satellite pushbroom imagery:
basic concepts.
Modern spaceborne pushbroom sensors are capable of acquiring imagery of quality and spatial
resolution enough for topographic mapping. Due to dynamic linebyline acquisition process,
pushbroom imagery requires implementation of specific photogrammetric processing methods, because
the basic principles of classical photogrammetry, assuming that the image is the central
projection of the object space, do not hold for pushbroom images [Adrov, Titarov, 2002].
In fact, each line of pushbroom imagery has its own elements of external orientation.
Pic. 1: Pushbroom image acquisition.
Photogrammetric processing implies solution of two main problems. One of them is often called
"space intersection" and is solved to create digital elevation model. The problem consists in
determination of objectspace coordinates X, Y, Z of a point starting from
its pixel coordinates x_{1}, y_{1}, x_{2},
y_{2} on the stereopair images. Another problem called "space resection" is
solved for orthoimage generating and 3D vectorization; it consists in calculation of the point
pixel coordinates x, y from its objectspace coordinates X, Y, Z.
There are main three approaches to the photogrammetric processing of pushbroom imagery,
based on rigorous, parametric and replacement models.
Rigorous approach consists in physical modeling of the image acquisition process,
including geometrical sensor model (internal orientation elements for the image line),
sensor position model (coordinates of the sensor, they are linear elements of external
orientation) and sensor attitude (angular elements of external orientation). The sensor
internal geometry can be provided, for example, as a set of lineofsight vectors for
detectors of specified numbers in the sensor detector line, or as some approximating model
like 2Dcentral projection sensor, or something else. The sensor position can be modeled
by orbital relations or polynomials for each of three sensor coordinates; the sensor attitude
is commonly presented as the sum of onboard measured attitude angles and polynomial refinements
determined by the adjustment procedure. If parameters of all the aforementioned models (sensor
internal geometry, position and attitude) are known (provided by the image supplier or
determined by adjustment), it's possible to reconstruct the ray (i.e. its vertex radiusvector
S given by sensor position and sight vector r calculated on the basis
of internal sensor geometry and attitude) observed by specified pixel of the image (see Pic. 2).
Pic. 2: Reconstructed rays and space intersection problem solution.
In terms of rigorous approach, the space intersection problem solution consists in intersecting
of rays relating to corresponding points on the stereopair images, while the space resection
problem is commonly solved by iterative search of image point observing the ray passing through
the given point in the object space.
The methods following rigorous approach are potentially the most accurate, require moderate
ground control points number, but, on the other hand, their implementation is the most
problematic. Some of the difficulties can be overcome (such as adjustment process computational
instability), but the others make this approach inadaptable, for example, the lack of information
concerning sensor internal geometry.
The next approach still has not commonly adopted name; we will call it "parametric". In
the sense of genesis it may be treated as "coarse rigorous" approach: it consists in physical
modeling involving some approximate assumptions which make the final objectspace to imagespace
relations to be very simple and include a small set of parameters. The parameters values are
determined by adjustment procedure; but, contrary to rigorous approach, on the stages of
adjustment and subsequent using of the adjusted models, the parameters values are not interpreted
in any physical way.
For example, assuming uniform straightforward and completely angular stabilized motion of
sensor of 2Dcentral projection internal geometry, following expressions for objectspace to
image mapping can be derived [Titarov, 2002]:

(1) 
The most widely known parametric model is Direct Linear Transformation (DLT) based on the
relations [Kaczynski, 2002]:

(2) 
The last approach to discuss is based on socalled replacement models [Tao, Hu, 2000].
The models are built in two steps. The first step consists in approximating the objectspace
to image relations, derived from rigorous model, by some generalform algebraic expressions.
The second step is refining the models by adjustment procedure using ground control points
(of cause, the second step is necessary only if the ground control points were not involved into
the derivation of the initial rigorous model). So the algebraic model replaces rigorous model.
The model (especially its part derived during the first step) can hardly be physically
interpretable, but, nevertheless, it can yield almost the same accuracy as rigorous model while
requiring significantly less amount of ground control (for refinement) and being more
computational stable.
The example of replacement model is Rational Polynomial Coefficients (RPC; sometimes the model
is also called Rapid Positioning Capability, but the abbreviation RPC holds in any case).
Recent years RPC are in great use because the model is adopted for almost all highresolution
satellite systems, namely IKONOS, QuickBird and OrbView. The expressions in use to approximate
rigorous model are [Grodecki, Dial, 2003]:

(3) 
where

(4) 
The subscript "N" means that the appropriate value is normalized so that its module
does not exceed 1.
The recommended refinements are following [Grodecki, Dial, 2003]:

(5) 
The image coordinates in the right parts of the equations (5) are the denormalized values
calculated following expressions (3), (4).
In any case when the straightforward expressions x = F_{1}(X,Y,Z) and
y = F_{2}(X,Y,Z) are used (see (1), (2), (5)), the space resection problem is
solved by immediate calculation. The space intersection problem is mathematically equivalent
to the system of four equations (two equations per image of stereopair) containing three
unknowns X, Y, Z. Sometimes the system can be transformed to a linear form
(e.g., (1), (2)), but in some cases it's impossible (particularly, for RPC, see (4)), so the
initial approximation is required to perform the adjustment procedure of determining the
generalized solution of the equations system. The initial solution can be found by means of
some supplementary approximate model, which allows linear representation, for example, DLT.
The DLT parameters values should be obtained by approximating refined RPC model but not by
reducing it (that is assuming coefficients at nonlinear terms of the RPC polynomials to be zero).
3. Photogrammetric processing of satellite pushbroom imagery:
PHOTOMOD implementation
PHOTOMOD system implements pushbroom imagery processing methods following all of the three
approaches mentioned above. The choice of method to apply is based on the contents of metadata
accompanying the image (see Table 1). The rigorous method is used to process SPOT 15, ASTER
and EROS imagery; the accuracy (in terms of root mean square error) of output products achieves
the value of spatial resolution of the image. RPCbased processing is performed in the case of
IKONOS, QuickBird and OrbView3 imagery; sometimes the single ground control point is enough to
obtain the orthoimage of accuracy equal to source image resolution. If the metadata contains
neither sensor geometric model nor RPC, socalled universal algorithm is used implementing some
modification of DLT method. It usually gives less accurate results; although sometimes for rather
flat terrain the results are the same as with rigorous model or RPC, but it's more realistic to
expect the accuracy will be twice or three times worse. Universal algorithm is applied for IRS,
MSUE and even Landsat (it is not pushbroom sensor; it acquires imagery pixelbypixel; but some
of PHOTOMOD users has good experience with it) imagery processing; one can also try to use it
for any pushbroom imagery in the case when the metadata is insufficient for any other method.
Table 1. Pushbroom imagery supported by PHOTOMOD
Currently PHOTOMOD supports three types of pushbroom imagery processing workflow:
 single image processing: source data are imagery, ground control points and digital
elevation model (DEM); the main target product is orthoimage (of cause, one can also perform
2D vectorization and create digital maps);
 stereopair processing: input data are images of the stereopair and ground control points,
and output data are DEM, contour lines, 3D vectors, orthoimage;
 mosaic workflow can be performed in two ways. Currently implemented "independent projects
mosaic" allows creating color and brightnessadjusted orthomosaic from any count of any type
PHOTOMOD projects. So one can mosaic aerial block and satellite pushbroom images as well as,
for example, ASTER and IKONOS images (Pic. 3). The drawback of the approach is that the
adjustment procedure is performed quite separately for each component project without using
tie points. Another approach is to use the single adjustment procedure for all the images to be
included into mosaic. It's rather difficult to implement such procedure for a quite
heterogeneous data set; so the upcoming (currently in testing) version PHOTOMOD 3.7 will be
capable of adjusting only blocks of images supplied with RPC. The preliminary test results
shows that the involving tie points into adjustment procedure helps to achieve better joining
of the correspondent details on the images of mosaic. (Pic. 4) Further development will be
aimed at adjustment of blocks consisting of arbitrary heterogeneous pushbroom imagery.
Pic. 3: ASTER and IKONOS images mosaic
Pic. 4: Mosaics built without (left) and with (right) tie points.
4. Photogrammetric processing of satellite pushbroom imagery: some economical
considerations.
One of the main products commonly derived from satellite pushbroom imagery are orthoimages,
so it's rather reasonable to discuss economical aspects as concerned to this matter. Remote
sensing data providers usually offers ready offtheshelf orthoimagery, in addition to images
of lower processing levels, so the following question came up: what's better, to buy the
orthocorrected imagery from the data provider or to order imagery of lower preprocessing level
and to perform the orthorectification on one's own? The answer is obvious after analyzing
Tables 2, 3. The tables are based on IKONOS imagery prices but the situation does not differ
significantly for other systems.
Table 2 shows that if the appropriate photogrammetric software capable of performing
orthorectification of pushbroom imagery is available, the offtheshelf orthoimage appears
to be more then twice as expensive then generated on one's own. Table 3 below illustrates
in turn, that even if the software is not still available, it will pay off on processing area
as small as 200 km^{2}. It should be noted that the minimum order of IKONOS imagery is
100 km^{2}, while 200 km^{2} is rather typical area for a single IKONOS image.
Table 2. Cost comparison of generated on one's own and offtheshelf orthoimage for
IKONOS (assuming that the appropriate photogrammetric software is available).
Table 3. Cost comparison of generated on one's own and offtheshelf orthoimage for IKONOS
(assuming the appropriate photogrammetric software is not available).
5. Conclusion
Uptodate satellite pushbroom sensors acquire imagery of very high (up to submetre) spatial
resolution; appropriate photogrammetric processing methods are capable of yielding the same
accuracy (in terms of rootmean square errors) of the output products. While remote sensing data
providers offer offtheshelf final photogrammetric products, it is more costefficient to
perform the processing on one's own. Digital photogrammetric system PHOTOMOD can be recommended
as a powerful, completecycle tool supporting processing of various satellite pushbroom imagery.
References
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