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Digital photogrammetric system PHOTOMOD and its usage for pushbroom imagery processing

V.Adrov, P.Titarov (Racurs)

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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. Off-the-shelf orthoimagery cost-efficiency analyzed as opposed to performing orthorectification on one's own.

1. PHOTOMOD system overview

PHOTOMOD is the well-known 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 third-party 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 cost-effective solution.

PHOTOMOD is up-to-date 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 man-held operations. It also allows to speed-up the time-consuming 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 (multi-buttons mice), stereoscopic glasses and various display stereo-modes (anaglyph, interlace, page-flipping).

The last but not the least advantage of PHOTOMOD software is very affordable prices and module-based 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 line-by-line 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 object-space coordinates X, Y, Z of a point starting from its pixel coordinates x1, y1, x2, y2 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 object-space 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 line-of-sight vectors for detectors of specified numbers in the sensor detector line, or as some approximating model like 2D-central 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 on-board 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 radius-vector 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 object-space to image-space 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 2D-central projection internal geometry, following expressions for object-space 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 so-called replacement models [Tao, Hu, 2000]. The models are built in two steps. The first step consists in approximating the object-space to image relations, derived from rigorous model, by some general-form 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 high-resolution 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 = F1(X,Y,Z) and y = F2(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 non-linear 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 1-5, 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. RPC-based processing is performed in the case of IKONOS, QuickBird and OrbView-3 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, so-called 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, MSU-E and even Landsat (it is not pushbroom sensor; it acquires imagery pixel-by-pixel; 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 brightness-adjusted 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 off-the-shelf 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 off-the-shelf 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 km2. It should be noted that the minimum order of IKONOS imagery is 100 km2, while 200 km2 is rather typical area for a single IKONOS image.

Table 2. Cost comparison of generated on one's own and off-the-shelf orthoimage for IKONOS (assuming that the appropriate photogrammetric software is available).

Table 3. Cost comparison of generated on one's own and off-the-shelf orthoimage for IKONOS (assuming the appropriate photogrammetric software is not available).

5. Conclusion

Up-to-date 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 root-mean square errors) of the output products. While remote sensing data providers offer off-the-shelf final photogrammetric products, it is more cost-efficient to perform the processing on one's own. Digital photogrammetric system PHOTOMOD can be recommended as a powerful, complete-cycle tool supporting processing of various satellite pushbroom imagery.

References

Adrov V., Titarov P. - 2002, "Photogrammetric processing of satellite scanner imagery." - Geospatial Today, September-October 2002, vol. 1, issue 3, pp. 27-30.

Grodecki J., Dial G. - 2003, "Block adjustment of high-resolution satellite images described by rational polynomials." - Photogrammetric Engineering and Remote Sensing, Vol. 69, No. 1, January 2003, pp. 59-68.

Kaczynski R. - 2002, "Dokladnosc opracowania ortofotomapy cyfrowej z danych CARTERRA GEO Pan i QuickBird Pan." - Archiwum Fotogrammetrii, Kartografii i Teledetekcji Vol. 12a, Warszawa 2002, pp. 172-177.

Tao C., Hu Y. - 2000, "A comprehensive study on the rational function model for photogrammetric processing", Paper submitted to the Photogrammetric Engineering and Remote Sensing, 2000.

Titarov P. - 2002, "The method of approximate photogrammetric processing of pushbroom imagery in the case of unknown sensor parameters." - Geodesy and Cartography, No. 6, Moscow 2002, pp. 30-34. (in Russian).

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