Ординатура / Офтальмология / Английские материалы / Progress in Brain Research Visual Perception, Part I Fundamentals of Vision Low and Mid-Level Processes in Perception_2006

from the microsaccades. Because the analysis is performed separately for horizontal and vertical components, the corresponding thresholds Zx and Zy define an ellipse in the velocity space (Fig. 3). As a necessary condition for a microsaccade, we require that all samples ~vk ¼ ðvk;x; vk;yÞ fulfill the criterion

Third, we apply a lower cutoff of 6 ms (or three data samples) for the microsaccade durations to reduce noise.

Fourth, microsaccades are traditionally defined as binocular eye movements (Lord, 1951; Ditchburn and Ginsborg, 1953; Krauskopf, 1960; see also Ciuffreda and Tannen, 1995). With modern video-based eye-tracking technology, binocular recording is easily available. Because (i) both eye traces can be analyzed independently and (ii) microsaccades are relatively rare events (roughly less than every 100th data sample belongs to a microsaccade), the amount of noise can be reduced dramatically, if we require binocularity. So far, we detected candidate microsaccades based on monocular data streams according to Eqs. (2)–(4). Operationally, we define binocular

microsaccade by a temporal overlap criterion. If we observe a microsaccade in the right eye with onset time r1 and endpoint at r2, we look through the set of microsaccade candidates in the left eye with corresponding onset time l1 and offset time l2. A temporal overlap of (at least) one data sample is equivalent to

It is straightforward to check the symmetry of the criterion by exchanging the roles of the left and right eyes. Figure 3 shows an example with three binocular microsaccades (numbered as 1–3). The two monocular microsaccades occurring in the left eye (labeled M and M0) are unlikely to represent outliers or noise, given the high peak velocity. Thus, we speculate that monocular microsaccades might also exist (Engbert and Kliegl, 2003b). We also identified differences in average orientations for monocular microsaccades (see Fig. 5). To implement a conservative detection algorithm, however, we generally use the temporal overlap criterion (Eq. (5)). More importantly, most researchers record the movements of one eye only, which precludes the use of the more-conservative binocularity criterion.

Additionally, we would like to remark that, if a temporal overlap is verified, the binocular

Left eye: Moved to origin

Left eye: Real locations

Right eye: Moved to origin

Horizontal component [°]

Right eye: Real locations

microsaccade is defined to start at time t1 ¼ min(r1,l1) and to end at time t2 ¼ max(r2,l2). As a consequence of this definition, microsaccades 1 and 3 in Fig. 3 in the right eye appear to start within the ellipse, i.e., with sub-threshold velocity. In the next section, we perform a quantitative analysis of the kinematics of microsaccades, which were detected by the algorithm discussed here.

Kinematic properties

Some of the kinematic properties of microsaccades can already be seen from visual inspection, if we plot all microsaccades generated by one participant

during 100 trials, each with a duration of 3 s, in a simple fixation task (Fig. 4). The top panels in the figure show all microsaccades generated by the participant with the starting point translated to the origin. The corresponding plots for the left and right eyes clearly indicate the preference for horizontal and vertical microsaccades, with oblique microsaccades only in rare exceptions.

The bottom panels in Fig. 4 show the same data with all microsaccades at their real locations. A glance at these plots verifies that microsaccades cover almost all parts of the central 21 of the visual field. Obviously, the majority of microsaccades is horizontally oriented. These descriptive results already demonstrate that microsaccades generate

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rich statistical patterns, which might reflect important requirements of the oculomotor and/or perceptual systems. Thus, patterns of microsaccades may be exploited to help to understand the oculomotor system and even aspects of visual perception and the dynamics of allocation of visual attention.

A polar plot of microsaccade orientations (Fig. 5) shows that the majority of binocular microsaccades is horizontally oriented. For those microsaccades that were detected monocularly, horizontal and vertical orientations are comparable in frequency (Fig. 5b). To understand these properties of microsaccades from the neural foundations, it is important to note that different nuclei in the brain stem circuitry for saccade generation are responsible for the control of horizontal and vertical saccades (Sparks, 2002). While neural mechanisms for the control of oblique movement vectors exist for voluntary saccades, we speculate that for microsaccades, which are generated involuntarily, such mechanisms are questionable. As a consequence, the distribution of angular orientations for microsaccades is dominated by the main contributions, i.e., purely horizontal or vertical orientations. Since binocular movements are related to the control of disparity, binocular microsaccades might contribute to changes of binocular disparity. Therefore, a preference of binocular microsaccades

for horizontal orientations seems compatible with oculomotor needs. From this perspective, the investigation of binocular coordination in microsaccades (Engbert and Kliegl, 2003b) might contribute to the general problem of monocular vs. binocular control of eye movements (Zhou and King, 1998).

A key property of microsaccades is that they share the fixed relation between peak velocity and movement amplitude with voluntary saccades (Zuber et al., 1965). This finding is a consequence of the ballistic nature of microsaccades. To underline the importance of the result, the fixed relation of peak velocity and amplitude is often referred to as the ‘‘main sequence’’ (Bahill et al., 1975).3 Given the validity of the main sequence, one useful application of this property of microsaccades is to check detection algorithms. Deviations from the main sequence might reflect noise in the detection algorithm.

In a larger study of fixational eye movements, 37 participants were required to fixate a small stimulus (black square on a white background, 3 3 pixels on a computer display with a spatial extension of 0.121). Each participant performed 100 trials with duration of 3 s. Eye movements were

3The astronomical term ‘‘main sequence’’ refers to the relationship between the brightness of a star and its temperature.

recorded using an EyeLink-II system (SR Research, Osgoode, Ont., Canada) with a sampling rate of 500 Hz and an instrument whose spatial resolution was better than 0.011 (for details see the methods section in Engbert and Kliegl, 2004). Figure 6a shows the main sequence for about 20.000 microsaccades generated by all participants in the simple fixation task. Corresponding distributions of amplitude and peak velocity are shown in Figs. 6b and 6c, respectively. The analysis of the large number of microsaccades indicates that our detection algorithm reproduces the main sequence well. The smallest microsaccade detected in the set of about 20.000 microsaccades had an amplitude of 0.03611 or about 2 min arc. We conclude that

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video-based recording techniques can be applied to detect even small-amplitude microsaccades. The distribution of microsaccade durations (Fig. 6d) is less smooth with a lower cutoff at 6 ms (or three samples) owing to the detection criteria.

A straightforward hypothesis on their function is that microsaccades help to scan fine details of an object during fixation. This hypothesis would imply that fixational eye movements represent a search process. According to this analogy, the statistics of microsaccades can be compared to other types of random searches. An important class of random-search processes are Le´vy flights, which have been found in foraging animals (Viswanathan et al., 1996). Moreover, it has been shown that this

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class of random searches is optimal, if target sites are sparsely distributed (Viswanathan et al., 1999). With respect to research on eye movements, Brockmann and Geisel (2000) suggested that inspection of saccades during free picture viewing represent an example of a Le´vy flight. Given these results, we check whether the amplitude distribution of microsaccades follows a similar law.

Le´vy flights are characterized by a certain distribution function of flight lengths lj. The flight lengths correspond to microsaccade amplitudes in fixational eye movements. For a Le´vy flight, the distribution function of flight lengths has the functional form

where the exponent m is limited to the range 1omr3. If the distribution decays with mZ3, we obtain a normal distribution for the search process, owing to the central limit theorem (Metzler and Klafter, 2000).

To investigate the distribution of microsaccade amplitude in our dataset of 20.000 microsaccades, we plot the tail of the distribution in Fig. 7 on a double-logarithmic scale. This plot clearly indicates a power-law decay of the tail of the distribution for

Fig. 7. Power-law distribution for amplitudes. The tail of the amplitude distribution obeys a power-law with an exponent given by the slope in the log–log plot.

amplitudes ranging from 0.31 to 11 of visual angle. The exponent, however, has a value of m ¼ 4:41; which rejects the hypothesis of a Le´vy flight. Thus, we conclude that even if the statistics of microsaccades during free viewing of a stationary scene might represent a Le´vy flight (Brockmann and Geisel, 2000), this law does not transfer to the small scale in fixational eye movements.

Temporal correlations

While kinematic properties of microsaccades have long been investigated from the beginnings of eyemovement research (e.g., Zuber et al., 1965), the question of temporal correlations did not receive a similar amount of attention. The main reason is obviously that a typical fixation duration in free viewing or reading is roughly between 200 and 500 ms. Therefore, the probability of observing more than one microsaccade in a single fixation will be rather small. Temporal correlations in the series of microsaccades, however, might also be indicative of specific functions and/or neural mechanisms underlying microsaccades. In the simplest case, the probability that a microsaccade is generated is time-independent. More precisely, the probability of observing a microsaccade in an arbitrary time interval ðt; t þ DtÞ is rDt, where r is the rate constant and Dt a small time interval, i.e., Dt-0, so that only one event can happen in the time interval of length Dt. This assumption constitutes a Poisson process. It is important to note that the number of events found in time interval ðtt þ DtÞ is completely independent of the number of occurrences in (0,t). Experimentally, a simple observable parameter is the waiting time between two events of the process. For the Poisson process, the corresponding probability density of waiting time t is an exponential function (Cox and Miller, 1965),

as in the general case of Markov processes. The waiting-time distribution is normalized in the sense that with certainty an event will occur, if we wait infinitely long, i.e., R01 pðtÞ dt ¼ 1:

To check whether the temporal patterns of microsaccades represent a Poisson process, we

IMSI [ms]

computed inter-microsaccade intervals (IMSI) for the microsaccade data shown in Fig. 8. This procedure is only possible if at least two microsaccades occur during a single trial. Obviously, this method is only an approximation to the problem of estimating the probability density, Eq. (7), which would ideally require recordings for several minutes to extract many IMSIs from a single time series. The rate constant r can be read off from the slope of the plot and has a numerical value of 1.86 s 1, which is equivalent to a mean IMSI interval of 538 ms. Thus, we conclude that the temporal pattern of microsaccades represents a Poisson process, i.e., there are no temporal correlations of the numbers of microsaccades during two different time intervals. In a non-stationary situation with changing visual input and/or attentional shifts, however, the microsaccade rate will no longer be constant (see the section on modulation of microsaccades below). In this situation the temporal pattern of microsaccades can be described by an inhomogeneous Poisson process.

Dynamic properties: time-scale separation

A typical trajectory generated by the eyes during fixational movements shows the clear features of a random walk (Fig. 1). Different classes of random walks can be distinguished by their

statistical correlations between subsequent increments (Metzler and Klafter, 2000). Such correlations can be investigated, if we plot the mean square displacement Dx2 of the process as a function of the travel time Dt. A key finding related to Brownian motion is that the mean square displacement Dx2 increases linearly with the time interval Dt (Einstein, 1905). This result is equivalent to the property of Brownian random walks in which the increments of the process are uncorrelated.

A generalization of classical Brownian motion was introduced by Mandelbrot and Van Ness (1968) to account for processes showing a power-

law of the functional form

Dx2 / DtH (8)

where the scaling exponent H can be any real number between 0 and 2. In classical Brownian motion, we find H ¼ 1, which is a direct consequence of the fact that the increments of the random walk are uncorrelated. When H41, increments are positively correlated, i.e., the random walk shows the tendency to continue to move in the current direction. This behavior is called persistence. In the case Ho1, the random walk generates negatively correlated increments and is anti-persistent.

Motivated by the study of Collins and De Luca (1993) on human postural data, we applied a ran- dom-walk analysis to fixational eye movements

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(Engbert and Kliegl, 2004). To characterize the behavior in the eye’s random walk during fixation, we introduce a displacement estimator (Collins and De Luca, 1993),

which is based on the two-dimensional time series f~x1; ~x2; ~x3; . . . ; ~xN g of eye positions. The scaling exponent H can be obtained by calculating the slope in a log–log plot of D2 vs. lag Dt ¼ m T0; where T0 ¼ 2 ms is the sampling time interval. The analysis of 100 trials generated by one subject indicates two different power-laws by linear regions in the log–log plot (Fig. 9). On a short time scale (2–20 ms), the random walk is persistent with H ¼ 1:28; whereas on a long time scale (100–800 ms), we find anti-persistent behavior. Thus, we observe a time-scale separation with two qualitatively different types of motion.

The fact that microsaccades are embedded in the drift and tremor components of fixational eye movements poses a difficult problem for the investigation of potential behavioral functions of

Fig. 9. Random-walk analysis of fixational eye movements. Linear regions in this log–log plot of the mean square displacement as a function of time indicate a power-law. On a short time scale, the random walk is persistent with a slope H41, while on a long time scale, we observe anti-persistence, i.e., slope Ho1.

microsaccades, because microsaccades will probably interact with these two other sources of randomness. To this aim, we cleaned the raw time series from microsaccades and applied the ran- dom-walk analysis (Engbert and Kliegl, 2004). First, we found that microsaccades contribute to persistence on the short time scale. Even after cleaning from microsaccades the drift still produced persistence. This tendency is increased by the presence of microsaccades. Second, on the long time scale, the anti-persistent behavior is specifically created by microsaccades. Since the persistent behavior on the short time scale helps to prevent perceptual fading and the anti-persistent behavior on the long time scale is error correcting and prevents loss of fixation, we can conclude that microsaccades are optimal motor acts to contribute to visual perception.

The random-walk analysis discussed here was motivated by the successful application of the framework to data from human postural control, where the center-of-pressure trajectory is statistically very similar to fixational eye movements, the dynamics unfold on a longer timescale. In a landmark study, Collins and De Luca (1993) observed the time-scale separation with the transition from anti-persistence to persistence. This discovery generated numerous publications since then. Combined with the observation that input noise can enhance sensory and motor functions (e.g., Collins et al., 1996; Douglass et al., 1993; Wiesenfeld and Moss, 1995), this research even inspired a technical application with the construction of vibrating insoles to reduce postural sway in elderly people (Priplata et al., 2002, 2003).

Modulation of microsaccade statistics by visual attention

The dynamic properties discussed in the last section support the view that microsaccades enhance visual perception and, therefore, represent a fundamental motor process with a specific purpose for visual fixation. Recent work demonstrated, however, that microsaccades are strongly modulated by display changes and visual attention in spatial cuing paradigms (Engbert and Kliegl, 2003a; see

also Hafed and Clark, 2002). Effects were related to microsaccade rate (rate effect) and to the angular orientation of microsaccades (orientation effect). Thus, while microsaccades might be essential for visual perception, they are — nevertheless

— highly dynamic and underlie top-down modulation by high-level attentional influences.

In a variant of a classical spatial cuing paradigm (Posner, 1980), we instructed participants to prepare a saccade or manual reaction in response to a cue, but to wait for a target stimulus before the reaction was executed (Engbert and Kliegl, 2003a, b). As the rate effect related to cue onset, we reported a rapid decrease of the rate of microsaccades

from a baseline level4 to a very low level, followed by an enhancement or supra-baseline level, until the rate resettled at baseline level.

The generation of microsaccades is a point process, i.e., discrete events are generated in continuous time (Fig. 10a).5 Therefore, the problem of computing a continuously changing rate over time from many discrete events is equivalent to the

4The baseline of the microsaccade rate is generally about 1 microsaccade per second, but will depend on the specifics of the paradigm used.

5Figure 10 represents raw data and re-analyses of Experiment 1 by Engbert and Kliegl (2003a).

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estimation of neuronal discharge rates from a series of action potentials in single-cell research. Following Dayan and Abbott (2001), we can formally describe the series of i ¼ 1; 2; 3; . . . ; N microsaccadic ‘‘spikes’’ at times ti by

XN

where d(t) denotes Dirac’s d function. For the computation of a continuous microsaccade rate rðtÞ; a window function w(t) must be chosen, since any rate estimate must be based on temporal av-

eraging, i.e.,

Z 1

1

Because the approximate firing rate at time t should depend only on spikes fired before t, a causal window of the form

which is defined for tZ0 only and vanishes for to0. Figure 10b shows the estimated microsaccade rate computed from the raw data in Fig. 10a using Eqs. (10)–(12). The corresponding rate estimates from 30 participants are plotted in Fig. 10c (thin lines), which were averaged to obtain a stable estimate of the microsaccade rate (bold line). The reliability of the estimate can be seen from the relatively constant baseline over the pre-cue interval ( 300–0 ms). Microsaccadic inhibition starts 100 ms after cue onset and lasts about 150 ms. Microsaccadic enhancement starts roughly 250 ms after cue onset, until the rate resettles at baseline level approximately 450 ms after cue onset.

Table 1. Rate and orientation effects for microsaccades

As the orientation effect, Engbert and Kliegl (2003a) found a bias of microsaccade orientations toward the cue direction. While in Experiment 1 of their study, arrows used as endogenous (central) cues induced the orientation effect during the enhancement interval, the data from Experiment 2 with color cues showed a later (and weaker) orientation effect. Thus, the results of Engbert and Kliegl (2003a) already indicated that the rate and orientation effects are not mandatorily coupled. Finally, in Experiment 3, it was shown that a relatively small display change, i.e., the same stimuli applied in a simple fixation task without instructions for attentional cuing, was sufficient to replicate the rate effect without producing an orientation effect. Therefore, the rate effect alone could also be interpreted as a response to a display change.

In a series of experiments, the relation between rate modulation, covert attention, and microsaccade orientation was further investigated (Laubrock et al., 2005; Rolfs et al., 2005). Depending on the details of the task, these studies replicated the rate effect with both inhibition of microsaccades about 150 ms after the first display change related to the appearance of the cue (Table 1) and an enhancement of microsaccade rate, which was found around 400 ms after cue onset. More importantly, the rate effect was reproduced in a simple display change condition (Engbert and Kliegl, 2003a) and in purely auditory cuing, i.e., without any visual display change (Rolfs et al., 2005). Therefore, the rate effect might be interpreted as a stereotyped response to a sudden change in — possibly multisensory input. The patterns of results on the orientation effect, however, turned out to be more complex. The list of

effects for the orientation effect in Table 1 shows that there are combinations of early and late effects with both cue-congruent and cue-incongruent modulations of microsaccade orientations.

Can we explain the rate and orientation effects from our knowledge on the neural circuitry controlling saccadic eye movements? Numerous publications have contributed to the current view that multiple voluntary and reflexive pathways exist to generate saccades (Fig. 11). Most of these pathways are convergent to the superior colliculus (SC), a structure controlling brain stem saccade generation equipped with several sensory and motor maps (Robinson, 1972; Schiller and Stryker, 1972; see also Bergeron et al., 2003). Deeper layers of the SC are multisensory, which can explain the auditory effects reported by Rolfs et al. (2005). In the rostral pole of the SC, fixation neurons are activated to keep our gaze stable. According to Krauzlis et al. (2000), fixation neurons are better conceived of as rostral, i.e., small-amplitude, build-up neurons. Thus, the amount of activation of the fixation neurons in the SC will determine the rate of microsaccades.

A key dynamical feature of the spatio-temporal evolution of activation in the SC has inspired models of local excitation and global inhibition

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(e.g., Findlay and Walker, 1999; Trappenberg et al., 2001). As a consequence of the latter property, a global change in sensory input will induce a higher mean-field activation, which will lead to an increased inhibition of the fixation neurons in the rostral pole of the SC. Consequently, we can expect a decrease of the microsaccade rate after a display change (or a sudden auditory stimulus). Given the time course with the fast inhibitory part of the rate effect, we further suggest that the ‘‘direct’’ or retinotectal connection from sensory input to the SC is responsible for the inhibition effect. In addition to the inhibition, the subsequent enhancement of microsaccade rate could also be generated by the intrinsic dynamics of global inhibition and local excitation, since after the global inhibition of fixation neurons the global increase of activation will fade out with the consequence that the remaining activation of fixation neurons will locally rise. The enhancement, however, is more difficult to interpret, because a latency of 350–400 ms is sufficient for multiple pathways to contribute to this effect.

For the interpretation of the orientation effect, a primary difference between experiments is whether endogenous or exogenous cues were used (Table 1).