Camera calibration from a circle and a coplanar point at infinity with applications to sports scenes analyses

Circles, such as concentric circles, arbitrary coplanar or parallel circles, are often employed for camera calibration. An interesting observation in football or basketball scenes is that a circle called the center circle existing in the midfield. By taking into account the midfield line which passes through the center circle´ center, a novel camera calibration method using the images of the midfield is proposed in this paper. A point at infinity can be determined from the center circle and the midfield line using the pole-polar relationship. The image of a point at infinity is called a vanishing point. The image of a circle is called a circle image in this paper. From one circle image and one coplanar vanishing point, a cubic constraint on the IAC can be obtained. The degenerate cases are discussed, and some applications are given in this paper.