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Geometric Potential of IKONOS Images
 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:
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