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.
Highlights
Camera calibration is a basic requirement in providing three-dimensional (3D) geometry information from two-dimensional (2D) images
We describe the method for computing the image of the circular points from the two intersecting circles
Solving for the three vertices of the self-polar triangle vi from (11), with the coordinates of mA, mB, the images mI, mJ of circular points can be computed from the intersection points of the lines
Summary
Camera calibration is a basic requirement in providing three-dimensional (3D) geometry information from two-dimensional (2D) images. C. Han et al [13] discusses the positional relationship of any two coplanar circles on a plane and how they may be used to compute the intersections of conics in the image plane to obtain the image of the circular points. Han et al [13] discusses the positional relationship of any two coplanar circles on a plane and how they may be used to compute the intersections of conics in the image plane to obtain the image of the circular points This method of camera calibration using circles as calibration patterns has been widely researched, and it is suitable for calibrating cameras that monitor roundabout traffic scenes.
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