Abstract: Camera calibration from circles has proven to be useful in many fields.However,due to the large distortion,catadioptric camera calibration from circles remains a challenging and open problem.In this paper,we study the imaging theory of circles and its relationships with other geometric elements under a central catadioptric camera,which establishes the theoretical foundation for camera calibration methods based on circles.We prove that the catadioptric projection of a circle in the scene is a quartic curve.We find that this quartic curve can be reduced to the image of a point,line or sphere with respect to different sizes or locations of the circle.This observation conforms to previous conclusions,and provides a unified imaging theory for different geometric elements.Under this unified imaging theory,we discuss the catadioptric camera calibration based on different geometric elements.Our simulation experiments for the paracatadioptric camera validate the proposed approach.