Current computational models of visual salience accurately predict the distribution of fixations on isolated visual stimuli. It is not known, however, whether the global salience of a stimulus, that is its effectiveness in the competition for attention with other stimuli, is a function of the local salience or an independent measure. Further, do task and familiarity with the competing images influence eye movements? In this talk, I will present the analysis of a computational model of the global salience of natural images. We trained a machine learning algorithm to learn the direction of the first saccade of participants who freely observed pairs of images. The pairs balanced the combinations of new and already seen images, as well as task and task-free trials. The coefficients of the model provided a reliable measure of the likelihood of each image to attract the first fixation when seen next to another image, that is their global salience. For example, images of close-up faces and images containing humans were consistently looked first and were assigned higher global salience. Interestingly, we found that global salience cannot be explained by the feature-driven local salience of images, the influence of task and familiarity was rather small and we reproduced the previously reported left-sided bias. This computational model of global salience allows to analyse multiple other aspects of human visual perception of competing stimuli. In the talk, I will also present our latest results from analysing the saccadic reaction time as a function of the global salience of the pair of images.