MODELLING EYE-MOVEMENT CONTROL VIA A CONSTRAINED SEARCH APPROACH G. Boccignone Universit´ a di Milano Dipartimento di Scienze dell’Informazione Via Comelico 39/41, Milano, 20135 Italy M. Ferraro Universit´ a di Torino Dipartimento di Fisica Sperimentale Via Giuria 1, Torino 10125, Italy ABSTRACT A model of visual search is presented where gaze shifts are driven by an hybrid deterministic/stochastic mechanism op- erating over a saliency field. Results of the simulations are compared with experimental data, and a notion of complexity is used to quantify the behaviour of the system in different conditions. Index Terms— Eye movements, random walk, active vi- sion, information encoding 1. INTRODUCTION Visual systems have a limited informational capacity [1], in the sense that only a small part of information present is regis- tered, at any given time, and reaches levels of processing that directly influence behavior; thus, an extensive, search over the whole visual field would be time-consuming and would prevent a fast response to the environmental stimuli. The problem for the organism is to select which part of the scene needs to be attended to, or, in other words, which fraction of information is useful for behavioral purposes and must be processed. Visual attention controls and ensures that selected information is relevant to behavioral priorities and objectives. Kustov and Robinson have suggested that the attentional pro- cess evolved as part of the motor system [2] and eye move- ments are directly related to the capability of the observer for exploring the environment. In particular, overt visual atten- tion, supported by movements of agent’s body, head and eyes ensures fast and fluent responses (e.g., detect a predator) to a changing environment. The visual system of primates achieves highest resolution in the fovea and the brain exploites saccades to actively repo- sition the center of gaze (fixation) on regions of interest so as to extract detailed information from the visual environment. The succession of gaze shifts is referred to as a scanpath. A scanpath of a subject scanning a natural scene is shown in Fig. 1: circles and lines joining circles, graphically repre- sent, respectively, fixations and gaze shifts between subse- quent fixations. Note that different observers (or even the same observer along different trials) could produce slightly different scanpaths, on the same figure, as regards the order in which different regions of interest of the image are vis- ited. The selection of a fixation point, which allows to set the Fig. 1. Scanpath eye-tracked from a human observer, graphi- cally overlapped on the original ”Horses” image observer’s focus of attention (FOA) on the foveated region, appears to be driven by two different mechanisms: “bottom up” process which produces rapid scans in a saliency-driven, task-independent manner and a slower “top down” process which is task-dependent and volition-controlled. The degree to which these two mechanisms play a role in determining at- tentional selection under natural viewing conditions has been for a long time under debate. In [3], a gaze-shift model (denoted Constrained Levy Ex- ploration, CLE) has been proposed and refined in [4, 5] for robotic applications. Such model is somehow akin to models of simple animal foraging, where the visual system hunts for areas that are rich in visual saliency. In other terms, eye move- ments and animal foraging address in some way the prob- lem of searching randomly distributed sites whose exact loca- tions are not known a priori. The exploration is guided by a Langevin equation, dr dt = −  ∇V (r)+ η, (1) where V can be modelled as a function of the saliency (land- scape) and η is a stochastic vector used to sample flight lengths from a Levy distribution. Levy distributions of flight lengths, as opposed, for instance, to Gaussian walk, may be essential for optimal search in foraging, where optimality is related to efficiency, that is the ratio of the number of sites visited to the total distance traversed by the forager [6]. The