A Novel Family of Mathematical Self-calibration Additional Parameters for Airborne Camera Systems

Self-calibration additional parameters (APs) have identified their significant role in photogrammetric calibration and orientation since 1970s. However, the traditional APs might not be adequate for the digital airborne camera calibration. A novel family of mathematical self-calibration APs is presented in this paper. We point out that photogrammetric self-calibration can, to a very large extent, be considered as a function approximation or, more precisely, a curve fitting problem in mathematics. Based on the rigorous approximation theory, the whole family of Legendre APs, which is derived from well-defined orthogonal Legendre Polynomials, is developed. Legendre APs are in general efficient to calibrate all the frame airborne cameras. They can also be considered as the superior generalization of the conventional APs developed by Ebner and Grün. A solution strategy by using Legendre APs is also suggested for in-situ camera system calibration. Extensive tests on various cameras including DMC, UltracamX, UltracamXp and DigiCAM illustrate the good performance of Legendre APs. The optimal theoretical accuracy can be achieved by applying Legendre APs, if a dense pattern of ground control points (GCPs) is available. The comparisons with the traditional APs show the theoretical and practical advantages of Legendre APs. * Corresponding author.