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Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. In this paper, we propose a novel method for the calibration of central catadioptric cameras using geometric invariants. Lines and spheres in space are all projected into conics in the catadioptric image plane. We prove that the projection of a line can provide three invariants whereas the projection of a sphere can only provide two. From these invariants, constraint equations for the intrinsic parameters of catadioptric camera are derived. Therefore, there are two kinds of variants of this novel method. The first one uses projections of lines and the second one uses projections of spheres. In general, the projections of two lines or three spheres are sufficient to achieve catadioptric camera calibration. One important conclusion in this paper is that the method based on projections of spheres is more robust and has higher accuracy than that based on projections of lines. The performances of our method are demonstrated by both the results of simulations and experiments with real images.