Circular control points detection is usually considered as the detection of ellipses. Due to the illumination, measuring angle and other reasons, the edges of control points may be incomplete. Furthermore, the noise edge of complex background or object will interfere with the extraction of control points. For those reasons, we propose a method of circular control point detection based on the circumscribed rectangle of an ellipse. Firstly, the center position of an ellipse is obtained by fitting director circle. Then the orientation and two semi-axis of an ellipse are determined by using the geometric properties of the external rectangle. The detected ellipses will be verified in order to reduce the detection errors. Finally, a clustering algorithm based method is proposed to extract the efficient control points. The simulation and real experimental results show that the proposed algorithm has high accuracy and excellent detection performance even for incomplete ellipses or cases in complex situation.