In this paper we propose a new approach to compute the scale space of any omnidirectional image acquired with a central catadioptric system. When these cameras are central they are explained using the sphere camera model, which unifies in a single model, conventional, paracatadioptric and hypercatadioptric systems. Scale space is essential in the detection and matching of interest points, in particular scale invariant points based on Laplacian of Gaussians, like the well known SIFT. We combine the sphere camera model and the partial differential equations framework on manifolds, to compute the Laplace-Beltrami (LB) operator which is a second order differential operator required to perform the Gaussian smoothing on catadioptric images. We perform experiments with synthetic and real images to validate the generalization of our approach to any central catadioptric system.