New Mathematical Self-calibration Models in Aerial Photogram- metry

A new family of self-calibration additional parameters (APs) is presented for calibrating airborne camera systems. We point out that photogrammetric self-calibration can to a very large extent be considered as a function approximation problem in mathematics. Based on the mathematical approximation theory, a novel family of so-called Legendre APs is developed based on the orthogonal Legendre polynomials. It is permitted in theory that Legendre APs can fully calibrate the image distortion of all digital frame-format airborne cameras, as long as the proper degree of APs has been chosen. It is also shown, that Legendre APs can be considered as the superior generalization of the conventional polynomials APs proposed by Ebner and Grün in the 1970s. The good performance of Legendre APs is demonstrated by using the data from the recent DGPF project and from other field tests. Despite the promising results, however, we finally reveal an essential deficiency of all polynomials APs, caused by the high correlations. Algebraic polynomials may be not the optimal mathematical choice and further work is desired for more rigorous self-calibration.