A simple centroid-based method to find the principal point of an image plane for a pincushion distortion

A method to find the principal point of an image plane is proposed in this paper for the case of a pincushion distortion. The analytical foundation of the method is that a pincushion distortion causes a pair of distortion-free parallel lines to become a pair of curves, which are termed conjugate curves in this paper, and the shortest line segment connecting the pair of conjugate curves passes through the principal point. Thus, the principal point can be obtained by computing the intersection point of the shortest line segments of different pairs of conjugate curves. However, the case for a digital image is a bit different from the above. For the same pair of conjugate curves, there is a group of shortest line segments, which is called a shortest segment set. The coincidence region of the shortest segment sets of different pairs of conjugate curves is a polygon, the centroid of which is considered as the principal point. Therefore, the proposed method firstly needs to capture the pincushion-distorted images of some pairs of parallel lines, secondly to find the corresponding polygon and lastly, to calculate the centroid point. A synthetic image and a real image are tested using this method, and the results are satisfying.