**Wieslaw Wolnieiwcz**

Warsaw University of Technology

[email protected]

**Introduction**

Very often and user taking advantage of the final product in form of orthophotomap, aerial photographs and VHRS can see no difference whatsoever between them. Hence the question arises whether geometrical relations obtained from classical aerial photogrammetry correspond with the contemporary VHRS systems and how much are they different.

We tend to transfer the very well known geometry of aerial photogrammetric cameras to geometry of satellite camera. However, we should be aware of the fact that there are substantial differences between them, so we should have completely different approach to geometry of satellite images, especially the ones of very high resolution. The differences consist in the following:

- Satellite scanners, including in particular the VHR ones, can be characterized with a very small angle of view. First of all it results from a very long focal of the optical system (for instance, in Ikonos system, the telescope has a focal 10.2 meters long, and its angle of view is 0.950
- Internal geometry is very well defined (camera is calibrated) and the parameters of calibration are fixed in time (stable conditions in space).
- Elements of external orientation of images are constantly measured with great accuracy and frequency. Positions with single meters accuracy is measured with a use of GPS, and the elements of angle orientation with precision to single angle seconds by inertial system (INS). Systematic error of inertial system (drift) is adjusted by star tracker.
- Imaging is produced in a progressive way by way of dynamic recording.

In result of the above mentioned we hale his option to localize (georeference) the image objects solely on the basis of on-board data (i.e. without the points of ground control) with accuracy to a dozen of meters. Such opportunity revolutionized the new approach in satellite photogrammetry and created the new equations for mathematical relations between image and ground – RFM (Rational Function Models).

**Characteristics of IKONOS system **

Geometry of orbit of the system is show on figure 1 while figure 2 shows the spectrum range of IKONOS system.

**Figure 1. Orbital Geometry of IKONOS. Figure 2. Spectral range for each bend.**

The satellite moves some 7 km/s, what means that the ground pixel 1 m for a single element CCD is exposed within the time of 0.14 ms. This time is too short; for creation of sufficient charge on CCD elements, one needs at least min. 0.7 ms, what corresponds to the distance of 5 m. In order to solve this problem, one uses so called TDI – Time Delay Integration. Every panchromatic line of CCD contains a dozen or more physical lines, thus forming a rectangular table CCD of shape enhanced orthogonally to the direction of flight. The charge is produced on every element of the line CCD and it is – pursuant to the lock tact – with a pace of moving image – moved to element in the next line, what provides for “accumulation” of charges forming a given pixel of image from a number of dozen or so physical elements of CCD. It is said that in the background surface of system VHRS there is a line CCD producing panchromatic images, and 4 lines producing images in the narrow ranges of spectrum. It is a considerable simplification. Actual positioning of lines is far more complicated. The figure does not include the lines of length exceeding dozens of thousands of pixels and for this very reason the physical panchromatic line is composed of several separate segments (for instance: of 3 in system Ikonos). These segments slightly overlap along the line and they are orthogonally slightly separated (in the direction of satellite run). In result of preliminary processing, from images produced of several segments, one generates a single virtual line of image. Similarly, the spectral lines are composed of segments, separated due to physical dimensions from panchromatic segments. This means that in effect the spectral images are produced a moment later, after a panchromatic image.

IKONOS has the digital system design pushes the state-of-the art in with focal plane array consists of multiple. panchromatic and multispectral line arrays (figure 3).

**Figure 3. IKONOS Focal Plane Unit (Space Imaging 2001).**

- Unit size: 10in. x 9in. x 9in. (25cm x 23cm x 23cm)
- Panchromatic sensor: 12 micron pixel pitch, 13,800 pixels
- Multispectral sensor: 48 micron pixel pitch, 3375 pixels

IKONOS is equipped with the Kodak Space Remote Sensing Camera, producing 13 800 pixels with imaging width 11.3 km in nadir point enabling to obtain a size of ground pixel of 82 cm. Of course, this parameter depends on inclination angle of optical system.

The following table illustrates the influence of the deflection angle of optical system upon the size of ground pixel and upon the width of the imaging area, respectively in the systems IKONOS. Figure 4 illustrates the ground size of pixel in relation to the angle of deflection of the optical system.

Table 1 Influence of the deflection angle of optical system upon the size of ground pixel and upon the width of the imaging area

Angle of view of the camera optical system is fixed. Also, the angles of view of individual pixels of CCD line are fixed. Deflection of the optical system from nadir position results in a change of trace of these angles on the ground area, so they change the dimensions of the ground pixels as well as the width of the imaging area. It has been illustrated on Figure 4.

**Figure 4. Influence of the angle of optical system deflection upon the land size of pixel of image and on the width of the imaged strip.**

From simple geometrical relations, pursuant to figure 1, one can define the relations between the ground size of pixel in nadir location of camera axle, and its size in the event the camera is deflected.

……………..(1)

……………..(2)

where:

PX – size of the ground pixel in direction of X (i.e. crosswise trajectory track),

PY – size of the ground pixel in direction of Y (i.e. along trajectory track),

PXo, PYo- sizes of the ground pixel in the nadir location of optical system, respectively in direction of X and Y,

γX – deflection of the optical system towards X,

γY – deflection of the optical system towards Y.

Respectively, the width of the imaged area will be:

……………..(3)

where:

LX – width of the imaged area with the optical system deflected crosswise by angle ?X,

LXo – width of the imaged area with the nadir location of optical system.

**Principles of adjustment models**

The basis for geometrical correction is definition of mathematical connection between land coordinates of the points (X, Y, Z) and the coordinates of their images (x, y). One applies here several substantially different approaches that result in different „geometrical models”. In typical commercial software ( PCI ) we have two fundamentals corrections models: RFM and Parametrical model

**1. PFM.** The purpose of a replacement camera model is to provide a simple, generic set of equations to accurately represent the ground to image relationship of the physical camera. We might write that relationship as (x,y) = F(P,L,H ) where F( . ) is the replacement camera model function, (x, y) is an image coordinate, and *X,Y,Z* is a ground coordinate. The IKONOS satellite image vendors, computes the rational polynomial coefficients (RPC) for each image and distributes it with raster data. In other words, with a use of the polynomial coefficients one can determine the relations between the coordinate system of an image and the position of the field object shown in equation no. 4.

File given by vendors contains the coefficients for Rapid Positioning Capability , also called Rational Polinomial Coefficient ( RPC ). This is mathematical mapping from object spacedinate to image space coordinates.

Where the polynomial Pi ( i = 1, 2, 3, and 4) has the following general form:

P (X,Y,Z) = a1 + a2X + a3Y + a4Z + a5XY + a6XZ + a7YZ + a8X2 + a9Y2 + a10Z2 + a11XYZ + a12X3+

+ a13XY2 + a14XZ2 + a15X2Y + a16Y3 + a17YZ2 + a18X2Z + a19Z + a20Z3…………………………(5)

And where (x,y) are the column and row of each image point and (X,Y, Z) ground point. For each image, 80 rational polinomial coefficients ( aijk ,bjk, cijk ,dijk ) , m1, m2, m3, n1, n2, n3 are 0-3, where i+j+ k ≤ 3.

For RPCs, when we talk about the adjustment of the first level, we take into consideration an influence of distortion due to optical projection, while for the second level we take into consideration an influence of the Earth curvature, refraction of an atmosphere and distortion of an optical system. Other and more advanced aspects affecting the imaging distortion are eliminated on the third level when we use RFM.The standard approach is to use RFC method without GCP. Using exact data in form of GCP we talk about enhancing the ground accuracy

**2. Parametrical model** describes in strictly geometrical terms the relations between the terrain and its image. Such model has to take into consideration the above-mentioned multi-source distorting factors. In the event of classical photogrammetric image, such strict model is based on the assumption of co-linearity, which is fundamental for photogrammetry

Because parametrical model describes the real geometrical relations, individual terms of the model have their specific geometrical interpretation. Parametrical models should produce better results than non-parametrical models, they should be more resistant to distribution of photopoints, and possible errors in data, and they should also require less photopoints necessary for determination of unknown parameters. The leading manufacturers of photogrammetric software supplement their products with the options enabling for elaboration of satellite images obtained from the basic systems, including recently the elaboration of the very high resolution satellite images. Usually, they offer optional selection between the strict model and quotient multinomial one. One should especially notice the recent version of packet Geomatica OrtoEngine offered by the Canadian company PCI, which includes a „firmware” in form of the strict models of the most important satellite systems elaborated by T. Toutin – a researcher from the Canada Centre for Remote Sensing – CCRS. This model enables for correction of satellite images with a little number of photopoints available (less than 10). System administrator – Space Imaging – has not published however the strict model of Ikonos, but T. Toutin reconstructed this model on the basis of theoretical assumptions as well as on the basis of meta-data that constitute a standard attachment to distributed images.

**Geometrical capability of IKONOS images**

The goal of experiment conducted was to determine the procedures and technologies for generation of orthophotomaps taking into consideration the influence of the following geometrical models: multinomial and strict, offered in the commercial packets PCI. Ortho-adjustment process were conducted using commercially availeble softwere : PCI Geomatica 9 including a module Ortho-Engine. Thise sottware enable the use of severial methods geometrical adjastmen. In the framework of tests two methods were used : RFM and Parametrical model

The tests of IKONOS images geometry were conducted in the following ranges:

- evaluation of influence of adjustment method (parametrical and multinomial RPC methods, with a use of parameters of models delivered with the image in form of metadata or without such data), evaluation of influence of a number and distribution of the ground control points used upon the results of geometrical adjustment.
- evaluation of influence of NMT quality upon the results of geometrical adjustment,
- evaluation of influence of optical system inclination upon accuracy of orthoadjustment process.
- evaluation of accuracy of DSM generation with a use of commercial software.

. Preliminary analyses proved that the very main factor determining accuracy of orthoadjustment is a number, distribution and quality of photopoints used for leveling in adjustment process (so-called GCP – Ground Control Points). The goal of this experiment was to obtain an answer to this question: how a number of GCP and application of a given adjustment method affects the accuracy of orthoadjustment process? Evaluation was done on ICP points.

**Figure 5. Accuracy of IKONOS for Parametric and RFM approach.**

Tabele 2 Comparison of RMS and maximum errors over 35 ICPs of parametric and RFM models computation with 10 GCPs

II. Besides the ground control points, the quality of NMT is a decisive factor for accuracy of images orthoadjustment achievable in practice. Practical influence of NMT was investigated by way of orthoadjustment of Ikonos image with the application of NMT of various altitude accuracy. The following tables and figures show the results of correction of Ikonos images obtained in environment of PCI Geomatica. The tables present the average and maximum errors of adjustment with the application of various NMT and various correction methods. These errors were evaluated at the control points. For the needs of correction, one used three types of NMT on the areas of minor ground leveling: DTEDo, SRTM and DTED 2. The first one is NMT of grid 1000×1000 m. with an average error 10 RMSz, the second one, 100×100 m. with its terror 5 m and the third one 25×25 m with error 3.5 m.

Tabele 3 Comparison of RMS and maximum errors over 30 ICPs of parametric and RFM approach computation with 9 GCPs

**Figure 7. Accuracy of IKONOS for RFM a) and parametric b) approach.**

III. In the framework of experiment investigating influence of inclination of optical system for accuracy of the image orthoadjustment process of the very high resolution, one used two IKONOS scenes. One of them could be characterized with inclination from nadir point by 10.5o and the second one by 43o. In order to generate orthophotomap in PCI environment .

Table 4 Comparasion of RMS and maximum errors over 15 ICPs of parametric and RFM approach computation with 10 GCPs, with 43 and 10.5 deg. off nadir.

**Figure 8. Accuracy of IKONOS for RFM a) and parametric b) approach.**

IV The selected areas are around 23.3 km long by 12.4 km with covering an area about 121 sq. km in the north – west part of Krakow. Normal collection azimuth and normal elevation angle of satellite was used for calculating convergent angle (see Table 1). Overlapping was 97.3%. In order to realize the process of 3D geopositioning , were processed of 31 GCP with an accuracy of about 10 cm planimetric and 20 cm vertical. The height of the ground points range from 244 to 429 m During the survey, the terrain point were documented with photographs, on which the terrain situation and survey position were visible. The process of determining coordinates future points to be used for correlation and for controlling 3D geopositioning accuracy. In each case we tried to ensure that the accuracy of GCP identification on the imagery was definitely below one pixel.

Figure 9 present a specification of acquired accuracy of generated DSM on a number of GCP points. Achieved accuracy was checked on control points (ICP), with did not taken part in the process of DSM generation.

Table 5 Comparison of RMS over up to 30 ICP of RFM Model

**Figure 9. Accuracy of IKONOS Stereo Imagery.**

**Figure 10. IKONOS, pan sharpen dropped over DSM.**

**Conclusion**

Satellites IKONOS can be characterized by their considerable mobility and flexibility of imaging in the framework of a single run in range of the receipt station ROC. Thanks to considerable capacity for inclinations of optical system, one can achieve image for the needs of stereoscopy, optimization of programming the imaging of large areas and where one expects considerable inclination. From altitude of 680 km it is possible to focus optical telescope on the selected area of ground with accuracy of the dozens of meters. The data achieved in RPC format enable for geometrical adjustment of IKONOS images for application on a level of 1: 10 000. The very basic conclusions from experiments conducted may be formulated in the following way:

- The very basic factor influencing the value of residual geometrical deviations in orthophotomap generated from IKONOS images is the selection and accuracy of ground control points used (GCP). The GCP used should be selected very thoroughly, and in the process of orthoadjustment they should be very carefully measured and interpreted.
- For flay areas, with a use of NMT of altitude accuracy 2-4 m (type DTED Level 2) and with a use of one GCP from DGPS survey (of planimetric accuracy some 20-40 cm) by orthoadjustment of IKONOS image with an application o polynomial method (RFM) one achieved an average error in range 1-1.5 m. It was also noted that with the use of one GCP only one achieved a considerable improvement of orthophotomap accuracy.
- At the same time, with the application of parametrical model, for adjustment of this imaging on the same GCP, one found out that its is necessary to use even 9 GCP In order to achieve the same accuracy as it is achieved with the use of multinomial model.
- Good results were also obtained with a use of GCP from topographic maps scaled 1:10 000. The main advantage of such approach is a considerably lower cost of achievement of GCP from maps as compared with the measurement executed with a use of GPS technology.
- Numerical Terrain Model coming from SRTM is sufficient for orthoadjustment of the VHRS. Even for strongly corrugated areas, Numerical Terrain Model DTED Level 2 and SRTM produce similar results for both types of image and methods correction.
- Despite a considerable increase of pixel dimensions in the case of imaging with considerable inclination (30º-45º) it is relatively easy to obtain orthophotomap of an average error some 2 m, both with a use of multinomial and parametrical models.

Orthoadjustment of imaging of large inclination requires a use of greater number of GCP (for both adjustment models).

- Stereoscope images IKONOS may be an excellent source for DSM generation. In case where there is no option to be supported by GCP, one can obtain RMSz of accuracy 7-6 m. When supported by several GCP one can achieve considerable improvement using RFM and taking advantage of multinomial coefficients obtained from RPC.

**Acknowledgments**

The author thanks to Mr Sebastaian Rozycki for corection IKONOS stereo images and help with owerly IKONOS ower DSM.