High-Precision Camera Distortion Correction: A Decoupled Approach With Rational Functions

This paper presents a robust, decoupled approach to camera distortion correction using a rational function model (RFM), designed to address challenges in accuracy and flexibility within precision-critical applications. Camera distortion is a pervasive issue in fields such as medical imaging, robotics, and 3D reconstruction, where high fidelity and geometric accuracy are crucial. Traditional distortion correction methods rely on radial-symmetry-based models, which have limited precision under tangential distortion and require nonlinear optimization. In contrast, general models do not rely on radial symmetry geometry and are theoretically generalizable to various sources of distortion. There exists a gap between the theoretical precision advantage of the Rational Function Model (RFM) and its practical applicability in real-world scenarios. This gap arises from uncertainties regarding the model's robustness to noise, the impact of sparse sample distributions, and its generalizability out of the training sample range. In this paper, we provide a mathematical interpretation of how RFM is suitable for the distortion correction problem through sensitivity analysis. The precision and robustness of RFM are evaluated through synthetic and real-world experiments, considering distortion level, noise level, and sample distribution. Moreover, a practical and accurate decoupled distortion correction method is proposed using just a single captured image of a chessboard pattern. The correction performance is compared with the current state-of-the-art using camera calibration, and experimental results indicate that more precise distortion correction can enhance the overall accuracy of camera calibration. In summary, this decoupled RFM-based distortion correction approach provides a flexible, high-precision solution for applications requiring minimal calibration steps and reliable geometric accuracy, establishing a foundation for distortion-free imaging and simplified camera models in precision-driven computer vision tasks.