Analytical camera pose estimation and inverse modelling of high order radial lens distortion polynomials for close range photogrammetry - Ikokou, Guy Blanchard (School of Architecture, Planning and Geomatics, 2025)
Camera calibration aims at estimating intrinsic and extrinsic camera parameters that accurately describe the projection of points from the 3D scene to the 2D image sensor. The absence of numerical estimates of parameters describing the camera internal and external geometry can prevent absolute readjustment of bundles of rays that project 3D points from the scene onto the image plane. When information derived from photographs is used for metric purposes, small imaging errors can significantly affect the accuracy of derived information. Current analytic a l method for camera pose calibration failed to exploit the intrinsic geometric properties associated with each camera parameter within the structures of individual coefficients of the projective transformation matrix. This resulted in these methods being prone to parameter coupling, sign ambiguity, and multiple roots associated with some of the parameters. In the same way, recursive reversions methods proposed to compute inverses of radial distortion coefficients in order to correct radial distortions were found not suitable for high-degree radial distortion polynomials and failed to model the inverse profiles of severe barrel, pincushio n, and moustache distortions inherent to consumer-grade cameras used in close range photogrammetry. This PhD research successfully developed two analytical calibration systems. The first calibration system decomposed the coefficients of the projective transformation matrix into nineteen robust equations that independently estimate individual parameters describing the internal geometry of the camera as well as its location and orientation in a 3D scene. The second calibration system, based on the concept of forced differential equation, successfully modelled inverse coefficients of high-order quintic, sextic, and octic radial distortion polynomials and reduced the effects of severe barrel, pincushion, and moustache radial distortions on distorted points. The experimental results demonstrate that both developed calibration strategies achieved root mean square reprojection errors of 0.0843 and 0.057 pixels, respectively. These values are substantially lower than those reported by several current state- of-the-art methods, which exhibit average errors around 3.63 pixels. Such a signific a nt reduction in error by nearly two orders of magnitude not only confirms the high accuracy of the proposed approaches but also underscores their suitability for close-range photogramme tr y applications where sub-pixel precision is essential. In practical terms, this level of accuracy enables more reliable 3D reconstructions and measurements in scenarios where even small deviations can lead to substantial errors. These results affirm the reliability and effective ness of the proposed calibration strategies, making them well-suited for high-precision 3D reconstruction, industrial metrology, cultural heritage documentation, and other close-range imaging tasks where geometric accuracy is paramount.