On the reversibility of Markov scanning in free-viewing
The confusing relationship between the probability of fixating a feature and the scanning pattern can be clarified, at least conceptually, by considering scanning as a stochastic feedback system. On each fixation the brain makes a choice of the next fixation target. This choice will depend to some extent on non-visual influences (such as arousal or cognitive expectations), but to a large extent it will depend on the current retinal image. When the eye moves, the retinal image will change, so that the choice of where to move the eye on a fixation affects the choice on the next fixation. Thus, the choice mechanism has feedback because the retinal image, which is an input to the choice mechanism, depends on the current eye position which was the output of the previous choice of fixation (Figure 8.1). As with any feedback system, questions concerning closed loop dynamics cannot be answered by examining only open loop behaviour (such as saccade magnitude distributions). The question of whether the probability of fixating a feature is constantly changing as the scanning pattern evolves is a closed loop problem. It is equivalent to asking whether the system is stable.