New rigorous and flexible Fourier self-calibration models for airborne camera calibration

This paper presents a new family of rigorous and flexible mathematical self-calibration additional parameters (APs) for airborne camera calibration. Photogrammetric self-calibration can – to a very large extent – be considered as a function approximation problem in mathematics. It is shown, that algebraic polynomials are less desirable for designing self-calibration APs due to the highly correlated terms. Based on the mathematical approximation theory, we suggest that Fourier series be the optimal mathematical basis functions for self-calibration purpose. A whole family of so-called Fourier self-calibration APs is developed, whose solid theoretical foundations are the Laplace’s Equation and the Fourier Theorem. Fourier APs are orthogonal, rigorous, flexible, generic and efficient for calibrating the image distortion of frame-format airborne cameras. The high performance of Fourier APs is demonstrated in many practical tests on different camera systems, including the DMC, DMCII, UltracamX, UltracamXp and DigiCAM cameras. We illustrate the theoretical and practical advantages of the Fourier APs over the physical APs and the popular polynomial APs. The joint applications with physical models are promoted for specific applications as well. On account of the theoretical justifications and high practical performance, Fourier APs should be preferred for in situ airborne camera calibration.