Eccentricity error compensation for geometric camera calibration based on circular features

Circular features are very common in geometric camera calibration. The projection of a circular feature is generally a deformed ellipse, not a true ellipse, due to the presence of lens distortion. The center of the deformed ellipse, obtained by fitting the boundary points with an ellipse, does not necessarily coincide with the distorted point corresponding to the center of the undistorted projection of the circular feature. An eccentricity error will be introduced if the two points are considered to be coincident. In this study three main factors that affect the amount of the eccentricity error are discussed, including the form and amount of lens distortion, the size of the circular feature and the tilt of the supporting plane. Then, an effective geometric camera calibration method is proposed where the eccentricity error is compensated by establishing the correspondence between the estimated model position and the real position of the fitted center of the deformed ellipse. Both simulation and measurement data verify the existence of the eccentricity error and the effectiveness of the proposed method.