RPC Estimation via $\ell_1$-Norm-Regularized Least Squares (L1LS)

Abstract

A rational function model (RFM), which consists of 80 rational polynomial coefficients (RPCs), has been widely used to take the place of rigorous sensor models in photogrammetry and remote sensing. However, it is difficult to solve the RPCs because of the requirement for numerous observation data [ground control points (GCPs)] in a terrain-dependent case and the strong correlation between the coefficients (ill-poseness). Regularization methods are usually applied to cope with the correlations between the coefficients, but only l 2 -norm regularization is used by the existing approaches (e.g., ridge estimation and Levenberg-Marquardt method). The l 2 -norm regularization can make an ill-posed problem well-posed but does not reduce the requirement for observation data. This paper presents a novel approach to estimate RPCs using l 1 -norm-regularized least squares (L1LS) , which provides stable results not only in a terrain-dependent case but also in a terrain-independent case. On one hand, by means of L1LS, the terrain-dependent RFM becomes practical as reliable RPCs can be obtained by using much less than 40 or 39 (if the first denominators are equal to 1) GCPs, without knowing the orientation parameters of the sensor. On the other hand, the proposed method can be applied to directly refine the terrain-independent RPCs with additional GCPs: when a single or several GCPs are used, direct refinement performs similarly to bias compensation in image space; when more GCPs are available, the direct refinement can achieve comparable accuracy of the rigorous sensor model (better than conventional bias compensation in image space) .