This paper presents the results of two psychophysical experiments and an associated computational analysis designed to quantify the relationship between visual salience and visual importance. In the first experiment, importance maps were collected by asking human subjects to rate the relative visual importance of each object within a database of hand-segmented images. In the second experiment, experimental saliency maps were computed from visual gaze patterns measured for these same images by using an eye-tracker and task-free viewing. By comparing the importance maps with the saliency maps, we found that the maps are related, but perhaps less than one might expect. When coupled with the segmentation information, the saliency maps were shown to be effective at predicting the main subjects. However, the saliency maps were less effective at predicting the objects of secondary importance and the unimportant objects. We also found that the vast majority of early gaze position samples (0-2000 ms) were made on the main subjects, suggesting that a possible strategy of early visual coding might be to quickly locate the main subject(s) in the scene.