Modeling the Control of Fixational Eye Movements with Neurophysiological Delays

Abstract

We propose a model for the control of fixational eye movements using time-delayed random walks. Fixational eye movements produce random displacements of the retinal image to prevent perceptual fading. First, we demonstrate that a transition from persistent to antipersistent correlations occurs in data recorded from a visual fixation task. Second, we propose and investigate a delayed random-walk model and get, by comparison of the transition points, an estimate of the neurophysiological delay. Differences between horizontal and vertical components of eye movements are found which can be explained neurophysiologically. Finally, we compare our numerical results with analytic approximations.

Bayesian estimation of self-similarity exponent

“…The invariance of the Hurst exponent for different trials for 3 the same participant will be shown. I also validate the proposed method on simulated time series, mimicking the fixational eye movements based on a time-delayed model proposed in [95] and an integrated model introduced in [44]. I speculate that the integrated model describes data more closely, since the obtained results show qualitatively the same behavior.…”

“…The Hurst exponent, which parameterizes fBm, indicates its correlation behavior and allows the detection of the long-range dependencies inside the signal. Thus, FEM has been investigated so far using the approaches such as DFA and standard deviation analysis (SDA) [8] in work of Mergenthaler and Engbert [95], and a change of the scaling behavior from a persistent behavior on short time scales to anti-persistent behavior on long time scales was observed.…”

“…I underline here the fact that the DFA method (as well as its modificated versions [13,25,68,69,129]) is a widely used method for the Hurst exponent estimation. The DFA has been also used for the estimation of the Hurst exponent from fixational eye movements data [77,95], a research question which will be discussed in details in Chapter 6. The DFA algorithm can be summarized as follows:…”

“…95. Now, based on the work of Wagenmakers [125] I articulate several general problems associated with the frequentist approach:…”

“…On the other hand, the Hurst exponent which parameterizes the fractional Brownian motion, indicates the correlation behavior and allows the detection of the long-range dependencies inside fixational eye movements. This type of data has been investigated so far using the approaches such as detrended fluctuation and standard deviation analysis [31] in the work of Mergenthaler and Engbert [95], where a change of the scaling behavior from a persistent behavior on short time scales to an anti-persistent behavior on long time scales was observed. I investigate the estimation problem of the Hurst exponent for fixational eye movements data based on a sequence of increments of a discrete process over some scale in Chapter 6.…”