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 in space are projected into conics in the catadioptric image plane as well as spheres in space. We proved that the projection of a line can provide three invariants whereas the projection of a sphere can provide two. From these invariants, constraint equations for the intrinsic parameters of catadioptric camera are derived. Therefore, there are two variants of this novel method. The first one uses the projections of lines and the second one uses the projections of spheres. In general, the projections of two lines or three spheres are sufficient to achieve the catadioptric camera calibration. One important observation in this paper is that the method based on the projections of spheres is more robust and has higher accuracy than that using the projections of lines. The performances of our method are demonstrated by the results of simulations and experiments with real images.