Does the calibration from circular pattern do any kind of correction to the centers of the circles?
According to the pinhole camera model, a circle in the 3D world will appear as an ellipse in the 2D image, it is well known that the center of the circle does not project to the center of the ellipse in the image, or, in other words
The center of the requisite ellipse does not correspond with the center of the circle being projected, but it displaced away from the vanishing point and toward the observer.
I think that the goal of findCirclesGrid is just to extract the centroids of the circles without any kind of corrections and it seems to me that calibrateCamera ignores the kind of used pattern: does calibrateCamera do any kind of corrections?
Some references:
HEIKKILA, Janne. Geometric camera calibration using circular control points.Pattern Analysis and Machine Intelligence, IEEE Transactions on, 2000, 22.10: 1066-1077.
ZHANG, Guangjun; WEI, Zhenzhong. A position-distortion model of ellipse centre for perspective projection. Measurement Science and Technology, 2003, 14.8: 1420.
RUDAKOVA, Victoria; MONASSE, Pascal. Camera matrix calibration using circular control points and separate correction of the geometric distortion field. In: Computer and Robot Vision (CRV), 2014 Canadian Conference on. IEEE, 2014. p. 195-202.