Multiobjective Genetic Optimization of Terrain-Independent RFMs for VHSR Satellite Images

Rational polynomial coefficients (RPCs) biases and over-fitting phenomenon are two major issues in terrain-independent rational function models. These problems degrade the accuracy of extracted spatial information from very high spatial resolution (VHSR) satellite images. This study particularly focused on overcoming the over-fitting problem through an optimal term selection approach. To this end, multiobjective genetic algorithm was used in order to optimize three effective objective functions: the RMSE of ground control points (GCPs), the number, and the distribution of both RPCs and GCPs. Finally, the technique for order of preference by similarity to ideal solution, as an efficient multicriteria decision-making method, was applied to select the best solution, i.e., the optimum terms of RPCs, through the ranking of solutions in the optimum set. The performance of the proposed method was evaluated by using three VHSR images acquired by GeoEye-1, Worldview-3, and Pleiades satellite sensors. Experimental results show that subpixel accuracy can be nearly achieved in all data sets, when over-fitting problem is addressed. The optimal selected terms leaded to a significant improvement compared to the original RPCs. Indeed, our method, which is independent of GCPs distribution, not only requires a small number of GCPs, but also leads to a 30% to 75% improvement when compared to the original RPCs. This improvement in VHSR images, usually makes no more need to remove the RPCs biases.