As one of the classical theories of projective geometry, Pascal’s theorem is closely related to the conic, which is the image of a circle. A circle is the geometric element typically used as a template for camera calibration methods. In this work, we propose a calibration method based on Pascal’s theorem and its inference, in which a circle is used as the calibration template. The proposed calibration method can be applied to solve the image of the circular points via the Newton iteration method. The intrinsic parameters of the camera can then be determined based on the constraints of the images of the circular points and the image of the absolute conic. The results of simulations and experiments conducted verify the validity and feasibility of the proposed calibration method.

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A novel method for camera calibration is proposed based on an analysis of lens distortion in camera imaging. In the method, a line through the centre of concentric circles is used as a template in which orthogonal directions can be determined from an angle of circumference that corresponds to a diameter. By using three lines through the centre of concentric circles, based on the invariance of the cross-ratio, an image at the centre of the concentric circles can be used to obtain the vanishing point. The intrinsic parameters of the camera can be computed based on the constraints of the orthogonal vanishing points and the imaged absolute conic. The lens distortion causes points in the template to have a position offset. In the proposed method, we optimize the positions of the distortion points such that they gradually approach those of the ideal points. The simulated and real-world experiments demonstrate that the proposed method is efficient and feasible.

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