  In humans and in foveated animals visual acuity is highly concentrated at the
center of gaze, so that choosing where to look next is an important example of
online, rapid decision making. Computational neuroscientists have developed
biologically-inspired models of visual attention, termed saliency maps, which
successfully predict where people fixate on average. Using point process theory
for spatial statistics, we show that scanpaths contain, however, important
statistical structure, such as spatial clustering on top of distributions of
gaze positions. Here we develop a dynamical model of saccadic selection that
accurately predicts the distribution of gaze positions as well as spatial
clustering along individual scanpaths. Our model relies on, first, activation
dynamics via spatially- limited (foveated) access to saliency information, and,
second, a leaky memory process controlling the re-inspection of target regions.
This theoretical framework models a form of context-dependent decision-making,
linking neural dynamics of attention to behavioral gaze data.
