A theoretical review of different mathematical models of geometric corrections applied to remote sensing images

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Abstract
One of the objectives of remote sensing is to go beyond simple visual interpretation in order to provide the user with quantitative information for producing documents that conform to cartographic standards and for deriving digital data files compatible with geographical information systems (GIS). In this framework, rigorous geometrical correction is essential. Error sources which introduce geometrical image distortions are related to the platform vector (attitude, altitude, speed), the sensor (distortions, oblique viewing), and to the earth (rotation, earth curvature, ellipsoid, relief). Many methods can be applied for correcting each error separately or for globally correcting the image from all geometrical distortions. This theoretical review has two complementary parts. The first section deals with errors causing deformations on satellite images and related to the platform vector, the sensor and the earth, as well as the mathematical formulation for each error. In the second section, we discuss three different mathematical models which permit overall geometric correction for the entire image from all types of errors of geometric origin. The first is based on the equations of collinearity, the second is based on the equations of collinearity related to celestial mechanics, and the last is based on polynomial equations. Because it takes into consideration parameters related to the viewing geometry of the earth and elements of the orbit, the mathematical model based on the condition of collinearity related to celestial mechanics is the best for topological mapping which requires high precision geometric corrections, while if the image geometry is stable, the earth is flat enough and if the geodetic grid is of good quality, the polynomial methods also provide good results for thematic mapping.

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