The projected circle centres and polar line for camera self-calibration

Epipolar geometry is an important concept in projective geometry, and it has been applied to camera calibration only gradually. In this study, using three non-concentric circles as a calibration pattern to ascertain the coordinates of the projected circle centres, the vanishing line could be computed by taking advantage of the linear relationship between the pole and the polar line to determine the camera's intrinsic parameters. In the image plane, the line passing through the two projected circle centres is a degenerate conic section, so it can be written in the form of a linear combination of two projected circles. In addition, the projected circle centre can be obtained by solving a linear equation. Because the relationship between the centre of a circle and the vanishing line is similar to the relationship between the pole and the polar line, the vanishing line can be determined by solving a linear equation. The results of our experiments show that this approach is effective and has high precision.