Effective Determination of Optimal Regularization Parameter in Rational Polynomial Coefficients Derivation

Recently, massive archives of ground information imagery from new sensors have become available. To establish a functional relationship between the image and the ground space, sensor models are required. The rational functional model (RFM), which is used as an alternative to the rigorous sensor model, is an attractive option owing to its generality and simplicity. To determine the rational polynomial coefficients (RPC) in RFM, however, we encounter the problem of obtaining a stable solution. The design matrix for solutions is usually ill-conditioned in the experiments. To solve this unstable solution problem, regularization techniques are generally used. In this paper, we describe the effective determination of the optimal regularization parameter in the regularization technique during RPC derivation. A brief mathematical background of RFM is presented, followed by numerical approaches for effective determination of the optimal regularization parameter using the Euler Method. Experiments are performed assuming that a tilted aerial image is taken with a known rigorous sensor. To show the effectiveness, calculation time and RMSE between L-curve method and proposed method is compared.