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A novel linear calibration method for a camera using two coplanar circles as the calibration template is proposed. Under projective transformation, the common pole-polar and common tangent of coplanar circles maintain invariance and homogeneity, respectively. The two tangent points on the common tangent, the four intersections, and the line passing through the centers of the two coplanar circles can form two groups of vertical parallel lines. Considering duality, a common polar passes through the centers of two coplanar dual circles in various positions with their corresponding poles located at infinity. The common tangent problem was solved iteratively by employing a search algorithm. Further, in the camera model, the vanishing points are obtained by using three images including the two coplanar circle template. The internal parameters can be solved based on the constraint relationship between the imaged circular points and the imaged absolute conic(IAC). In the simulation experiment, the solution of the common tangent and the noise experiment of the internal parameters. In the real experiment, the internal parameters by each method are verified and the projection error is analyzed. The results show that the algorithm is feasible and effective. [ABSTRACT FROM AUTHOR]

In the domain of computer vision, camera calibration is a key step in recovering the two-dimensional Euclidean structure. Circles are considered important image features similar to points, lines, and conics. In this paper, a novel linear calibration method is proposed using two separate same-radius (SSR) circles as the calibration pattern. We show that the distinct pair of dual circles encodes three lines, two of which are parallel to each other and perpendicular to the remaining line. When any two coplanar or parallel circles degenerate to SSR circles, a solution can be found to recover another pair of parallel lines based on the geometric properties of the SSR circles. Using the vanishing points obtained as the key helper for determining the imaged circular points and the orthogonal vanishing points, we deduce the constraints on the image of the absolute conic (IAC) and then employ it for complete camera calibration. Furthermore, a closed-form solution for the extrinsic parameters can be obtained based on the projective invariance of the conic dual to the circular points. Evaluations based on simulated and real data confirmed the effectiveness and feasibility of the proposed algorithms.

Two linear calibration methods based on space-line projection properties for a paracatadioptric camera are presented. Considering the central catadioptric system, a straight line is projected into a circle on the viewing spherical surface for the first projection. The tangent lines in a group at antipode point pairs with respect to the circle are parallel, with the infinity point being the intersection point; therefore, the infinity line can be obtained from two groups of antipode point pairs. Further, the direction of the polar line of an infinity point with respect to the circle is orthogonal to the direction of its infinity point. Hence, on the imaging plane, images of the circular points or orthogonal vanishing points are used to determine the intrinsic parameters. On the basis of the properties of the antipodal point pairs and a least-squares fitting, a corresponding optimization algorithm for line image fitting is proposed. Experimental results demonstrate the robustness of the two calibration methods, that is, for images of the circular points and orthogonal vanishing points. [ABSTRACT FROM AUTHOR]