This paper proposes a calibration method for catadioptric camera systems consisting of a mirror whose reflecting surface is the surface of revolution and a perspective camera as typified by HyperOmni Vision. The proposed method is based on conventional camera calibration and mirror posture estimation. Many methods for camera calibration have been proposed and during the last decade, methods for catadioptric camera calibration have also been proposed. The main problem with catadioptric camera calibration is that the degree of freedom of mirror posture is limited or the accuracy of the estimated parameters is inadequate due to nonlinear optimization. On the other hand, our method can estimate five degrees of freedom of mirror posture and is free from the volatility of nonlinear optimization. The mirror posture has five degrees of freedom, because the mirror surface has a surface of revolution. Our method uses the mirror boundary and can estimate up to four mirror postures. We apply an extrinsic parameter calibration method based on conic fitting for this estimation method. Because an estimate of the mirror posture is not unique, we also propose a selection method for finding the best one. By using the conic-based analytical method we can avoid the initial value problem arising from nonlinear optimization. We conducted experiments on synthesized images and real images to evaluate the performance of our method, and discuss its accuracy.