Transformation between Rational Function Model and Rigorous Sensor Model for High Resolution Satellite Imagery

The rigorous sensor model based on the collinear equation describes the imaging geometric relationship between the image points and homologous ground points, with parameters which have understandable physical meanings. However, it lacks generality because of its complexity and varying with different sensor types. Especially, the physical parameters are often made unavailable intentionally or unintentionally. Rational Function Model (RFM) has been applied in remote sensing and photogrammetry to represent the transformation between the image space and object space. It attracts more attention for its generality and ability of providing almost the same accuracy as the rigorous sensor model. At the same time, there also exist some disadvantages for RFM, such as difficulty in interpreting the parameters and possibility of correlation between the RF coefficients. In order to utilize the advantages of both, this paper studied the transformation between the two models. Firstly in the experiments, RF coefficients are computed using the virtual control points generated from the rigorous sensor model. The derived RFM gives almost the same accuracy as the original model, with only 1mm decline in stereo positioning accuracy. On the other hand, as for linear array sensor images, the interior orientation (IO) parameters x0 and f are correlated, x0 need to be fixed as a static value in order to define a camera coordinate system for the purpose of retrieving the physical parameters. If x0 is given, the parameters of rigorous sensor model can be retrieved with high accuracy. There is ±0.001mm error in internal orientation parameters, ±5cm error in perspective center coordinates and ±0.002” error in rotation angles. If x0 is unknown and fixed as an assumed value of 0, it results in the modification of the rotation angle parameters, which compensates the departure of x0. The perspective center coordinates are little affected by this assumption. Further more, the retrieved rigorous sensor models of the stereo image pair are employed for geopositioning, the accuracy decline is less than 1mm, which indicates that the proposed method for rigorous sensor model recovery is applicable.