Human visual system makes an extensive use of visual attention in order to select the most relevant information and speed-up the vision process. Inspired by visual attention, several computer models have been developped and many computer vision applications rely today on such models. However, the actual algorithms are not suitable to omnidirectional images, which contain a significant amount of geometrical distorsion. In this paper, we present a novel computational approach that performs in spherical geometry and thus is suitable for omnidirectional images. Following one of the actual models of visual attention, the spherical saliency map is obtained by fusing together intensity, chromatic, and orientation spherical cue conspicuity maps that are themselves obtained through multiscale analysis on the sphere. Finally, the consecutive maxima in the spherical saliency map represent the spots of attention on the sphere. In the experimental part, the proposed method is then compared to the standard one using a synthetic image. Also, we provide examples of spots detection in real omnidirectional scenes which show its advantages. Finally, an experiment illustrates the homogeneity of the detected visual attention in omnidirectional images.