# Comparison of Different Algorithms to Orthorectify WorldView-2 Satellite Imagery  
[PERSON] and [PERSON]  
1 Department of Sciences and Technologies, University of Naples \"Parthenope\", Centro Direzionale Isola C4, Naples 80143, Italy; [EMAIL_ADDRESS]  
1  
Footnote 1: email: roberto.berto. To correct imagery geometric distortions, models and mathematical functions are necessary: either 2D/3D empirical models (such as 2D/3D polynomial or 3D rational polynomial functions, RPFs) or rigorous 2D/3D physical and deterministic models [2]. A physical model should model the platform (attitude, velocity, and altitude), sensor (field of view, panoramic effect), world (ellipsoid and 3D relief), and cartographic projection distortions [14]. Such 2D/3D empirical models can be used when the parameters of the acquisition systems or a rigorous 3D physical model are not available. In addition, they are based on different mathematical functions (2D or 3D polynomial functions, 3D rational functions) [15]. Physical models (also called rigorous models) are based on a standard photogrammetric approach, where the collinearity equations link the image and the ground coordinates, and the parameters involved have a physical meaning. In addition, knowledge regarding the sensor on the specific satellite and orbit characteristics is required [16]. These 2D/3D empirical models do not reflect the real physical condition of imaging, but they define it approximately. Three different sensor replacement models are defined in ISO 19130 \"Geographic Information--Imagery Sensor Models for Geopositioning\": (1) simple polynomial fitting; (2) rational function model--RFM; and (3) universal sensor model--USM [14]. Simple polynomial fitting is useful only for low- and medium-resolution satellite images [17] and can be adopted for VHRSIs in small area mapping. In fact, we can also assume that the sensor moves linearly in space and that the attitude is almost unchanged [18]. The relationship between the position of a point on the image and the corresponding point on the object is represented by polynomial functions. The coefficients of each polynomial are computed using an appropriate number of ground control points (GCPs) with known locations (X, Y) on the map and easy detections (X', Y') in the image [19]. An RFM matches the image and object spaces through a ratio of two polynomial functions to compute the image row, and a similar ratio to compute the image column [20]. Also, in this case an appropriate number of GCPs is necessary to calculate the coefficients of each polynomial, named RPCs (rational polynomial coefficients). RPCs are widely adopted by image vendors and government agencies, who do not want to provide any satellite/sensor information with the image, and by commercial workstation suppliers; consequently, the various image vendors around the world provide third-order RF parameters [21]. RFMs have been used to approximate physical sensor models for many years due to their capability to maintain the full accuracy of different physical sensor models, their unique characteristic of sensor independence, and real-time calculation [22]. With USMs, an image scene is divided into multiple subdivisions or sections and RFM is applied to each section; the modified polynomials are of a variable order (up to the fifth power of the two horizontal coordinates and up to the third power for elevation); the denominator polynomials are usually omitted; image positional correction tables can be incorporated; and the ground coordinates can be expressed in any ground coordinate system [23]. Several applications about the use of 2D/3D empirical models as well as 2D/3D physical and deterministic models to orthorectify VHRSIs are available in literature. [PERSON] et al. [24] compared rigorous approach and RFM to achieve the best geometric accuracy in orthorectified imagery products obtained from IKONOS (Geo Ortho-kit), QuickBird (Standard OrthoReady), and EROS 1A level data.