Linear Determination of a Camera's Intrinsic Parameters Using Two Intersecting Circles

Abstract

An approach using two intersecting circles is proposed as a linear approach for determining a camera's intrinsic parameters. The two intersecting coplanar circles have four intersection points in the projective plane: two real points and two circular points. In the image plane, the diagonal triangle-on which the image of the four intersection points composes a complete quadrangle-is a self-polar triangle for the projection curves of the circles. The vertex of the self-polar triangle is the null space of the degenerate conic formed by the image of the four intersection points. By solving the three vertices of the self-polar triangle using the image coordinates of the two real intersection points, the degenerate conic can be obtained. The image of the two circular points is then computed from the intersection points of the degenerate conic. Using the image of the circular points from the three images of the same planar pattern with different directions, the intrinsic parameters can be linearly determined.

A Stereo Calibration Method of Multi-Camera Based on Circular Calibration Board

“…With the application of circular calibration pattern, Wang et al [17] proposed the Pascal theorem under the circular calibration template, solved the circular point image by Newton's iteration method, and then converted the absolute quadratic curve constraint into a Pascal line constraint to calibrate the camera internal reference, expanding the application scope of calibration. Xu et al [18] proposed to use two intersecting coplanar circles as calibration templates, using the theory of two intersecting circles at intersection points on the projection plane and a kernel line geometry to solve the dot image, and linearly determine the internal reference by linearly determining the dot images in three images in different directions of the same pattern.…”

“…In this paper, the 7 × 7 template for constructing Franklin moments is selected. The conventional algorithm of sub-pixel edge detection based on matrix only uses low-order moments, that is, the distance l is obtained by Equations ( 16) and ( 17), the step height k is determined by Equation (18), and the sub-pixel edge is judged according to l > l k and k > k t , where l t and k t are the threshold, and the average value of l and k matrix is obtained. Since the conventional algorithm does not consider the higher order moments, the edge lines detected are coarse, so the following edge determination conditions are used [19]:…”