Sample balancing of curves for lens distortion modeling and decoupled camera calibration

State-of-the-art camera calibration methods usually estimate the pinhole model and lens distortion together by strict point correspondence. However, in many applications, only part of the full calibration result is required. Simpler calibration patterns like straight lines are studied in many works to calibrate only the lens distortion but lack precision compared with conventional methods. In this paper, we study the geometric invariants of line straightness and proposed a method to accurately estimate the normal vector of the original line from the distorted curve. We discovered that unbalanced samples have a significant influence on estimation accuracy. We proposed a sample balancing method and linear COD determination methods based on normal geometry. The proposed method requires little positioning restrictions of the camera or the calibration pattern, and lines are very easily found or established patterns. The proposed method is demonstrated with both synthetic data and real images. We show by experiment that camera calibration can be decoupled, and more flexible calibration patterns can be used for each stage.