Abstract
Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.
Highlights
Eye movements are crucial for visual perception
There is an inherent tradeoff in visual fixation as the platform for visual perception: Fixational eye movements constantly move the retinal image across the photoreceptors to refresh their inputs and thereby to prevent visual fading[9], while, at the same time, fixational eye movements maintain accurate fixation
All participants have in common that the displacement auto-correlation function (DACF) of the horizontal component reaches the first maximum at a larger time lag than that of the vertical one (100 ± 33 ms), see Fig. 3, indicating that the oscillatory behaviour of horizontal drift movements tends towards lower frequencies
Summary
Eye movements are crucial for visual perception. Saccades shift regions of interest of a scene to the centre of the visual field, where high acuity vision is possible. Recent neurophysiological studies reported a significant response of visual brain areas to MSs2,3,27, which indicates that MSs may play an important role in vision. Beyond these discussions of rather basic functions, recent studies suggest that FEM enhance vision of fine spatial detail[28,29,30,31,32]. Several studies suggest that the enhancement of fine spatial vision is achieved by a temporal encoding of visual information mediated by precisely controlled retinal image motion[31,32,34]. The MSD assumes the power-law form, i.e., MSD(τ) ∝ τα,
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