Optimization of RFM's Structure Using a New Reformulation of PSO in Case of Limited GCPs

Metaheuristic algorithms have been widely used in determining the optimum rational polynomial coefficients (RPCs). By eliminating a number of unnecessary RPCs, these algorithms increase the accuracy of geometric correction of high-resolution satellite images. To this end, these algorithms use ordinary least squares and a number of ground control points (GCPs) to determine RPCs' values. Due to the cost of GCPs collection, using limited GCPs has become an attractive topic in various researches. In this study, a new reformulation of particle swarm optimization (PSO) algorithm, namely, Discrete-Binary PSO for Rational Function Model (DBPSORFM), is presented to find the optimal number and combination of RPCs in the case of limited GCPs. Based on the fact that the maximum number of RPCs, the values of which are obtained through least squares, is twice the number of GCPs, the particle of the proposed algorithm is composed of two binary and discrete parts. The discrete part contains the number of rational coefficients that can vary from 1 to 78. In the binary section, which contains 0 and 1 values, the absence or presence of the corresponding coefficient in the discrete section is investigated. This method is not only compatible with the nature of the metaheuristic algorithms but also significantly reduces the search space. The proposed method has been tested on various types of high-resolution data. The results of the experiments indicate the superiority of the proposed method in comparison with the conventional approach in metaheuristic algorithms.