Eye movements during fixation as velocity noise in minimum motion detection

Authors

  • IKUYA MURAKAMI

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    1. University of Tokyo
    • Ikuya Murakami, Department of Life Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan. (E-mail: ikuya@fechner.c.u-tokyo.ac.jp)

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      This study was supported by Nissan Science Foundation and by a Grant-in-Aid for Scientific Research on Priority Areas no. 20020006 from MEXT, Japan.


Abstract

The functional roles and perceptual consequences of fixational eye movements are argued. The retinal image motions due to these eye movements are viewed as normally unnoticed velocity noise that limits performance of minimum motion detection without reference. When the motion detection threshold and the variability of eye velocity during fixation were measured for a group of normal adult observers, an interobserver correlation was established between psychophysical and oculomotor data. In particular, when both eyes were open, the threshold of unreferenced motion was positively correlated with the fixation instability of the eye, making larger drifts. Preliminary data also suggested the possibility that the fixation instability of this eye still dominates the detection threshold if this eye was occluded during the task. Possible schemes of living with such velocity noise as originating from fixation instability are discussed.

Our eyes are incessantly in motion. Even if we are looking at a stationary object with maintained fixation, the eyes are actually making tiny involuntary movements, called fixational eye movements (Steinman, Haddad, Skavenski, & Wyman, 1973). Several extensive reviews of fixational eye movements have recently been published and have promoted our scientific interest in the possible roles and perceptual consequences of these kinds of eye movements (Collewijn & Kowler, 2008; Martinez-Conde, 2006; Martinez-Conde & Macknik, 2008; Martinez-Conde, Macknik, & Hubel, 2004; Murakami, 2006). The relationship between visual perception and the statistics of fixational eye movements has also emerged as one of the exciting issues from recent progress in the vision sciences (Beer, Heckel, & Greenlee, 2008; Laubrock, Engbert, & Kliegl, 2008; Martinez-Conde, Macknik, Troncoso, & Dyar, 2006; Rucci, Iovin, Poletti, & Santini, 2007; Troncoso, Macknik, & Martinez-Conde, 2008; Troncoso, Macknik, Otero-Millan, & Martinez-Conde, 2008).

Types of fixational eye movements

Three major types of small eye movements during fixation have been identified in classical investigations. These are “tremors”, “microsaccades”, and “drifts” (Ditchburn & Foley-Fisher, 1967; Krauskopf, Cornsweet, & Riggs, 1960; St. Cyr & Fender, 1969; Steinman et al., 1973; Yarbus, 1967). Tremors are extremely small (< 1 arcmin) and rapid (> 30 Hz) oscillations, and thus seem to interact minimally with visual processing. Microsaccades are the largest of the fixational eye movements (> 10 arcmin), but also the rarest (roughly one saccade per second or less in observers trained for fixation), and their frequency is further reducible by instruction (Steinman, Cunitz, Timberlake, & Herman, 1967). Drifts, in contrast, occur constantly between every couple of consecutive microsaccades and have a relatively large positional random walk. Their position time-series can be approximated by the “1/f” amplitude spectra in frequency domain (Eizenman, Hallett, & Frecker, 1985), and result in a velocity distribution obeying the zero-centered Gaussian distribution (Murakami, 2004a).

Functional roles

Many different species, including the human, monkey, cat, rabbit, and even non-mammalian animals, have fixational eye movements or similar (Martinez-Conde & Macknik, 2008). What is the functional significance of having such eye movements during fixation?

The most fundamental effect of having small eye movements can be demonstrated by examining the most fundamental effect of losing them. In classical experiments of the stabilized retinal image, several researchers discovered that visual stimuli perceptually faded away from consciousness in the absence of eye movements during fixation or, in other words, in the absence of retinal image motions of those stimuli (Ditchburn & Ginsborg, 1952; Riggs, Ratliff, Cornsweet, & Cornsweet, 1953; Yarbus, 1967). To accomplish visual stimulation without retinal image motions, these researchers devised special optical machinery such as a slide projector attached to a contact lens (Pritchard, Heron, & Hebb, 1960). Thus, fixational eye movements are necessary oculomotor characteristics to maintain the visibility of the outer world. Tremors might participate, but their oscillation amplitude of less than our acuity makes it unlikely that tremors are the main characteristic for this purpose. Microsaccades can undoubtedly refresh the retinal image against visual fading (Martinez-Conde et al., 2006), but their necessity is weakened by the fact that our visual world does not fade away during maintained fixation with no occurrence of microsaccades. Logically speaking, it must be fixational drift that is playing a major role in counteracting the perceptual fading of visual images (at least during the fixation period that does not contain any microsaccades).

Drift is also called slow control (Steinman et al., 1973), to highlight another important functional aspect of eye movements during fixation. Fixation that occurs between two consecutive saccades is not oculomotor relaxation, but purposeful and well-controlled behavior. Good fixation has ecological benefits, for example, elite rifle shooters can produce more concentrated fixation than untrained normal adults (Di Russo, Pitzalis, & Spinelli, 2003). The oculomotor system has the difficult job of maintaining fixation at a particular visual object and simultaneously oscillating the eyes to prevent perceptual fading. To accomplish this task, a slow control mechanism is constantly monitoring retinal image slip during a fixation period and issuing feedback control signals to keep the fixated object on the fovea. During this oculomotor control, the three kinds of fixational eye movements might each play a different role. In particular, the involvement of microsaccades in this and other functional aspects has been under extensive debate (Collewijn & Kowler, 2008; Martinez-Conde, Macknik, Troncoso, & Hubel, 2009). Some researchers think that only drift controls the gaze (Kowler & Steinman, 1980; Steinman et al., 1967), while others think more positively of the functional role of microsaccades (Ditchburn, 1980; Engbert & Kliegl, 2004).

Visual stability despite unstable eyes

The typical amplitudes of fixational drifts and microsaccades are 4 arcmin and 12 arcmin, respectively (Collewijn & Kowler, 2008), and their respective velocities are typically 4 arcmin/s and 10 deg/s (Martinez-Conde et al., 2009), under strictly head-restrained conditions. With relatively moderate head restriction, as with a chin and forehead rest, head movements and/or reflexive eye movements activated by head movements will come into play, and will expand these values several times. In any case, the angular velocities of these fixational eye movements can exceed the human motion-detection threshold. However, we do not experience oscillation of our perceptual world together with incessant fixational eye movements. Clearly, there must be a certain mechanism that makes these above-threshold velocities go unnoticed in daily life.

How does the brain represent visual stability? The easiest scheme would be to reduce motion sensitivity so as to be blind to tiny oscillation of the eyes. For tremors this scheme would be the case, because their amplitudes are as small as visual acuity. Also, it may be the case that image slip by a microsaccade goes unnoticed because of saccadic suppression (Ross, Morrone, Goldberg, & Burr, 2001), which would reduce our visual sensitivity around the instant of each saccade. However, fixational drifts cannot be canceled the same way, because they occur constantly. The visual world cannot be constantly suppressed.

For large-scale movements such as smooth pursuit, the visual system may use extraretinal information such as the efference copy of oculomotor commands (Helmholtz, 1866) and proprioceptive signals from extraocular muscles (Sherrington, 1918) as reference signals for perceptual constancy (Sperry, 1950). Subtraction of the estimated eye-movement velocity from the retinal image velocity would ideally give the true object velocity in the world. For fixational eye movements, however, it is unlikely that such extraretinal information is fully used to counteract them. First, although fixational eye drifts are sometimes called slow control, not all of them are purposefully activated for fixation control, but some are driven by spontaneous activations of peripheral oculomotor mechanisms. Second, not all retinal image motions are driven by oculomotor events, as some are due to mechanical head oscillations such as in chewing behavior. Third, cancellation of random oscillations of the fixating eyes requires temporally precise and accurate synchronization between the visual and extraretinal processes, but considerable temporal imprecision has been found at least in the visual process (Kreegipuu & Allik, 2003; Murakami, 2001a; Murakami, 2001b; Whitney, Cavanagh, & Murakami, 2000; Whitney & Murakami, 1998; Whitney, Murakami, & Cavanagh, 2000). Fourth, cancellation also requires extraretinal information of the same gain as that of visual information, but psychophysical estimations have indicated a relative gain of less than one (Freeman, 1999; Freeman, Banks, & Crowell, 2000).

The remaining source of visual stabilization is the visual inputs themselves, which exhibit a systematic image change each time the eye moves (Wertheim, 1994). Specifically, a version eye movement in the orbit gives rise to rotational optic flow, which, within a restricted spatial scale such as some degrees around the fovea, could be approximated by overall image translation in the direction opposite to the eye movement. The retinal image moves at almost the same velocity when one sees a stationary world with a rotating eye. In contrast, when there is a moving object on a stationary background and the eye rotates, the retinal image contains spatially common motions and spatially differential motions as well. Therefore, the visually based stability theory posits that the visual system constantly dismisses spatially common image motions, as they are most probably derived from eye movements, and that the visual system interprets spatially differential motions as coming from external object motion (Murakami, 2003; Murakami & Cavanagh, 1998; Murakami & Cavanagh, 2001). The theory therefore raises this prediction about motion detection performance: motion without a surrounding reference frame would be indistinguishable from image motions originating from fixational eye drifts, and thus there should be a positive correlation between the detection threshold and the size of the fixational eye drifts. More specifically, to detect motion is to distinguish an external velocity signal from the system's internal velocity noises, and one of the most powerful sources of such noises would be the probabilistic distribution of instantaneous eye velocity. Thus, the testable prediction is that the motion detection threshold should positively correlate with the SD of the instantaneous velocity of fixational eye drifts; this SD is hereafter called “fixation instability” for simplicity.

Detection threshold for unreferenced motion correlates with fixation instability

This prediction has been largely supported by previous psychophysical experiments (Murakami, 2004a, 2004b; Tong, Lien, Cisarik, & Bedell, 2008). Murakami (2004a) determined the minimum motion-detection threshold for a random-dot pattern presented at 10-deg eccentricity to the left of the fixation point, recorded fixational eye movements in separate experimental sessions, and found an interobserver correlation between the detection threshold and fixation instability for 11 observers (r = 0.61). Tong et al. (2008) determined the motion-detection threshold for eight random-dot patterns symmetrically arranged in a circle at 10-deg eccentricity around the fixation point, recorded fixational eye movements in separate experimental sessions, and plotted an interobserver correlogram. Under the straight-ahead viewing condition, a positive correlation was found between the detection threshold and fixation instability for 16 observers (r = 0.58). However, when observers were instructed to fixate at a fixation point with a 45-deg lateral eccentric gaze, fixation instability was raised, but the relationship with the detection threshold disappeared. This is an interesting result because the detection threshold should also be raised accordingly if it was limited by fixation instability on a trial-by-trial basis.

It may be that fixation instability has limited the improvement of motion-detection performance during one's development (Tong et al., 2008). Observers with fixational eye movements may have had only a few opportunities to train their visual system to detect finer motions than are resolvable within the constant velocity noise originating from fixational eye movements. This hypothesis is hard to prove, and developmental and clinical studies might shed light on this (Acheson, Cassidy, Grunfeld, Shallo-Hoffman, & Bronstein, 2001; Bedell, 1992).

Which eye dominates threshold?

Though these previous studies are suggestive of motion noise originating from eye movements limiting performance of minimum motion detection, there is a shortage in the number of observers comprising the interobserver correlograms. Clearly, the relationship should be confirmed in a larger group. Also, if long-term experience with retinal image motion may be important or not, it is interesting to ask which of the two eyes dominates our perceptual limit of minimum motion. Correlations between perception and oculomotor statistics were determined for binocular viewing in Murakami's (2004a) experiment and for the left-eye viewing in Tong et al.'s (2008) experiment. However, the two eyes show different characteristics within each individual observer, partly because a major fraction of fixational eye drift occurs independently between the eyes, and partly because each observer uses one of the two eyes as the dominant eye in various visual tasks. Thus a systematic relationship may be observed between motion-detection performance and the statistics of either one of the two eyes. In addition, it is interesting to confirm the existence of a correlation under a more ecologically useful condition of central viewing; the previous experiments cited above only tested 10-deg peripheral viewing. To examine these points, in the present study the correlation between the detection threshold for unreferenced motion and the variability of fixational drift were examined by presenting stimuli at the center or at the periphery, and by recording the fixation instabilities of the left and right eyes, for a relatively large group (N = 56) of normal adult observers.

Methods

Observers

The initial participants were the author and 64 naïve observers, nine of whom were later screened out because of failure to obtain reliable eye-movement data. The analysis was based on 56 observers, including the author (aged 20–40 years, average 29.4 years old, 42 female and 14 male, normal or corrected-to-normal vision, no history of ophthalmologic disease). Each observer gave written informed consent and underwent a battery of tests of visual acuity, astigmatism, stereopsis, and sighting dominance.

Stimuli

The stimulus was presented in a dark room on a CRT monitor (Sony GDM-F520; 42.7 deg × 32 deg; refresh rate 75 Hz; 13.3 ms/frame) controlled by a computer (Apple PowerMac G4). The viewing was binocular from a distance of 54 cm, constrained by a chin and forehead rest.

On a uniform gray background with mean luminance of 36 cd/m2, a random-dot pattern (dot density 3.5 dots/deg2) blurred for subpixel animation was presented within a circular stationary window (7-deg diameter), the edge of which was softened by a cumulative Gaussian-shaped contrast modulator (SD = 1 deg). This edge could potentially work as a stationary frame of reference when the pattern speed was fast enough. However, this was not an effective cue when the pattern moved at the average detection threshold of 0.1 deg/s (see Results), because at this speed the pattern moved only by 0.085 deg per presentation, too small a fraction of the SD of the edge-blurring function mentioned above.

A fixation point was provided throughout the experiment. There were two stimulus locations: the center of the visual field and 8.5-deg eccentricity below the center. The pattern moved coherently in one of eight possible directions differing by 45 deg, and its speed was one of seven predetermined levels that adequately spanned a psychometric function.

Procedure

In each trial, the moving pattern was presented for 0.85 s. The location, motion direction, and speed of the pattern were all chosen in random order. The observer had to indicate the direction of motion by pressing a computer key. According to the method of constant stimuli, each observer did 24 repeated trials for each combination of location × speed. For each location, the correct response rate was plotted against speed and was fit with a sigmoidal psychometric function, y = 0.125 + (0.99 − 0.125) × (1 − exp (−(x/α)β)), with α and β as the free parameters. The motion detection threshold was determined as the speed corresponding to the correct response rate of 53.3%.

Eye-movement recording

Eye movements were recorded separately from the psychophysical experiment. The recording procedure and off-line analysis followed the methods used in Murakami (2004a). While the stimulus was being passively observed (for 16 s) in the same viewing condition as in the detection task, the horizontal orbit-relative eye positions of both eyes were recorded by an infrared limbus eye tracker (Iota Orbit 8) with a sampling resolution of 1 kHz. Before and after the fixation period, calibration dots at 16 different positions (within ± 2.5 deg) were presented sequentially for 2 s each, and the observer was asked to make a reaching saccade to each of them. Blink-free periods were chosen from the fixation periods and were bandpass-filtered (1–31 Hz) to obtain resampled velocity with the same resolution as the monitor (13 ms). Microsaccades were determined by the velocity criterion of 10 deg/s (Bair & O'Keefe, 1998; Snodderly, Kagan, & Gur, 2001). Data within 65 ms around each microsaccade were removed from the drift trajectory. A velocity histogram with 0.1 deg/s bin was plotted (Figure 1), and was fit with a Gaussian distribution. The SD of the best-fit Gaussian distribution was taken as the index of fixation instability. Of the three types of fixational eye movements summarized in the Introduction, this index characterized the statistics of fixational drifts, because tremors and microsaccades were removed by bandpass filtering and the saccade-removal algorithm mentioned above.

Figure 1.

Exemplar data of small eye movements. (A) Horizontal eye position during fixation. The arrows indicate the occurrences of microsaccades. (B) Histogram of drift velocity and the best-fit Gaussian distribution function.

Results

Normal distribution in log scale

For each observer, the motion detection thresholds at the center location and at 8.5 deg below were measured, and the fixation instabilities for both eyes were also obtained. The cumulative frequency distributions for these four kinds of data in 56 observers are plotted in Figure 2. When each of these curves was fit with a cumulative log normal distribution, the fit was extremely good (R2 > 0.99) for all. Thus, the subsequent correlation analysis was made in log × log scale.

Figure 2.

Frequency distributions (N = 56) of psychophysical and oculomotor data. (●) The cumulative frequencies of the motion-detection threshold at the center location, (○) the motion detection threshold at 8.5-deg below, (▴) the fixation instability of the left eye, and (□) the fixation instability of the right eye are plotted against log speed.

Correlations between fixation instability and motion-detection threshold

Figure 3 shows interobserver correlograms (N = 56) between fixation instability and minimum motion-detection threshold. The solid and open symbols indicate the thresholds at the center of the visual field and at 8.5-deg eccentricity, respectively, plotted against the fixation instability averaged across the left and right eyes. First, observers could detect motion at approximately 10−1 deg/s, consistent with the previous study using the same experimental procedure (Murakami, 2004a). Second, detection was easier at the center than at 8.5-deg eccentricity, paired-comparison t-test, t(55) = 8.28, p < .0001. Third, while there was considerable variability both in fixation instability and the detection threshold, there was a weak but significantly positive correlation between them; the correlation between the threshold at the center and averaged fixation instability was r = 0.467, t(54) = 3.88, p < .0005, and the correlation between the threshold at 8.5-deg eccentricity and averaged fixation instability was r = 0.453, t(54) = 3.73, p < .0005. Clearly, the detection threshold was poorer for those observers who made greater fixational drifts. This finding replicated Murakami's (2004a) previous conclusion that the detection threshold for unreferenced motion is positively correlated with fixation instability, and confirmed the conclusion for both peripheral viewing and central viewing.

Figure 3.

Interobserver correlogram between the motion-detection threshold and fixation instability averaged across the eyes. (● and –––) The detection threshold at the center of the visual field and (○ and ---) the threshold at 8.5-deg eccentricity are superimposed. The averaged instability was calculated as the quadratic mean of the fixation instabilities of the left and right eyes.

Which eye might be more responsible for motion sensitivity? In the threshold measurement of the main experiment, both eyes were open. Thus, the visual system received retinal image motions from both eyes, with a common visual stimulus plus their own fixational drifts, some of which were independent between the two eyes. Similar correlation analyses were repeated with oculomotor statistics of the left eye, the right eye, the dominant eye, and the nondominant eye as the abscissa, but no clear difference was observed between the left eye and the right eye, or between the dominant eye and the nondominant eye.

However, when the data were sorted according to the eye with larger fixation instability (hereafter called the “larger-drift eye”) and the eye with smaller fixation instability (called the “smaller-drift eye”), there was some indication of interesting dependences between motion sensitivity and eye movements. Specifically, at the center, the detection threshold was better correlated with the fixation instability of the larger-drift eye, r = 0.500, t(54) = 4.25, p < .0001, than with that of the smaller-drift eye, r = 0.394, t(54) = 3.15, p < .005, with a significant difference between these two correlation coefficients, t(53) = 2.18, p < .05. Moreover, when the naturally expected correlation between the fixation instabilities between eyes, r = 0.91, t(54) = 16.4, p≪ .0001, was partialed out from the raw correlation coefficients shown above, the detection threshold was still correlated with the fixation instability of the larger-drift eye, partial correlation r = 0.375, t(53) = 2.95, p < .005, but no more correlated with that of the smaller-drift eye, partial correlation r = −0.178, t(53) = 1.32, n.s. At 8.5-deg eccentricity, the threshold was correlated with larger-drift eye instability, r = 0.471, t(54) = 3.92, p < .0005, and with smaller-drift eye instability, r = 0.400, t(54) = 3.21, p < .005, although the difference between these correlation coefficients was not significant, t(53) = 1.40, n.s. Again, when the correlation between the eyes was partialed out, the detection threshold was still correlated with the fixation instability of the larger-drift eye, partial correlation r = 0.281, t(53) = 2.13, p < .05, but no more correlated with that of the smaller-drift eye, partial correlation r = −0.082, t(53) = 0.60, n.s. These results indicate that the larger of the fixation instabilities of the two eyes is one of the determinant factors of motion sensitivity. The same threshold data that are plotted in Figure 3 are replotted against the fixation instability of the larger-drift eye in Figure 4A for the center and Figure 5A for 8.5-deg eccentricity, and against the fixation instability of the smaller-drift eye in Figure 4B for the center and Figure 5B for 8.5-deg eccentricity.

Figure 4.

Interobserver correlogram between the motion-detection threshold at the center of the visual field and the fixation instability. (A) The correlation with the fixation instability of the larger-drift eye (the eye with the larger fixation instability for each observer). (B) The correlation with the fixation instability of the smaller-drift eye (the eye with the smaller fixation instability for each observer). pr = the partial correlation coefficient; r = Pearson's correlation coefficient.

Figure 5.

Interobserver correlogram between the motion detection threshold at 8.5-deg eccentricity and the fixation instability of the smaller-drift eye (the eye with the smaller fixation instability for each observer). pr = the partial correlation coefficient; r = Pearson's correlation coefficient.

The relationship between the fixation instabilities of the larger-drift eye and the smaller-drift eye is shown in Figure 6. By definition, all data points fell below the identity function, y = x. Overall, the fixation instability of the larger-drift eye was greater than that of the smaller-drift eye by 0.078 log units. There was no relationship between the larger-drift eye and either anatomical eye (left eye or right eye). Also, there was no relationship between the larger-drift eye and sighting dominance.

Figure 6.

Interobserver correlogram between the fixation instability of the larger-drift eye and the fixation instability of the smaller-drift eye. (◆) Observers whose left eye was the larger-drift eye; (◊) observers whose right eye was the larger-drift eye. The shaded line indicates the identity function (y = x).

Correlations between fixation instability and the error rate of motion detection in concurrent measurements

What if the stimulus was viewed monocularly? Preliminary data suggested that the fixation instability of the larger-drift eye was still more influential on the motion-detection threshold, whichever eye was actually opened during the detection task. For a small subset of observers (N = 21), fixational eye movements were concurrently recorded while observers were doing the same directional judgment task as in the main experiment, for a barely moving near-threshold stimulus (10−1.1 deg/s) for which observers should frequently make errors (i.e. the average error rate was 51% at the center and 55% at 8.5-deg eccentricity). To obtain the error rate at this particular stimulus speed as the index of each observer's detection performance required much fewer trials than the method of constant stimuli used in the main experiment, and thus complied with the regulation that the total time for eye-movement recording be limited within an ethically allowed length. Only one eye was open, whereas the other eye was covered by an opaque occluder. A recording was made while each observer was making a directional judgment with the larger-drift eye only open, and as a result the fixation instability of this larger-drift eye was obtained together with the error rate of motion detection with this eye open. Another recording was made while each observer was making a judgment with the smaller-drift eye only open, and as a result the fixation instability of this smaller-drift eye was obtained together with the error rate of motion detection with this eye open.

If motion sensitivity was determined by the fixation instability of the currently opened eye, the error rate would be better correlated with the fixation instability of the opened eye than with that of the occluded eye (the movements of which were recorded in a separate session). However, the actual error rate was apparently better correlated with the fixation instability of the larger-drift eye, whether this eye only was open or whether the other eye only was open during the detection task. Figure 7A shows the correlation coefficient between each combination of the 2 fixation instabilities (of larger-drift eye and smaller-drift eye) × 2 error rates (with the larger-drift eye only open and the smaller-drift eye only open) tested at the center of the visual field, and Figure 7B shows comparable data at 8.5-deg eccentricity. The differences in the correlation coefficients between the conditions were not statistically assessable because of the small sample size, but in no cases did the fixation instability of the smaller-drift eye dominate the correlation, even for the error rate that was obtained under the condition in which the smaller-drift eye only was open.

Figure 7.

Correlation coefficients between the fixation instability and the error rate. (A) Data at the center of the visual field. (B) Data at 8.5 deg eccentricity. The broken horizontal line indicates the level of statistical significance of correlation coefficient at Bonferroni-corrected p-value of .05. Error in Lg-eye open = the error rate of the motion detection task with the larger-drift eye only open; Error in Sm-eye open = the error rate of the motion detection task with the smaller-drift eye only open; Lg-eye SD = the fixation instability of the larger-drift eye; Sm-eye SD = the fixation instability of the smaller-drift eye.

Discussion

The present study recruited a reasonably large group of observers (N = 56) for correlations between perception and oculomotor statistics. It was confirmed at central viewing as well as peripheral viewing that the minimum-motion detection threshold positively correlated with the SD of the instantaneous velocity of the fixational eye drifts. Furthermore, this relationship was more strongly seen when a correlogram was made between the threshold and the fixation instability of the larger-drift eye, that is, the eye exhibiting a larger SD of instantaneous velocity for each observer. A preliminary experiment suggested that this was also the case even when the larger-drift eye was currently occluded and the task was done with only the other eye open.

These findings are consistent with the conclusion of Murakami (2004a) that poorer fixaters tend to show poorer sensitivities for minimum motion detection. The dominance of the larger-drift eye in the positive correlation also seems consistent with the proposal by Tong et al. (2008) that the limit of minimum motion detection may be based on the visual system's long-term experience with retinal image motion. We normally live with both eyes open, and thus are continuously exposed to velocity noise due to the movement of both eyes. The larger fixation instability of the two eyes would determine the velocity noise from which the minimum motion should be discriminated. This idea might explain why no causal change was observed after experimental manipulation of fixation instability (Tong et al., 2008) or of eye opening (preliminary observation of the present study). An interesting but currently open question derived from this consideration is what might happen to our motion sensitivity if we were newly exposed to long-term visual experience with the smaller-drift eye only open, and with the larger-drift eye occluded for days.

Figures 3–5 show not only positive correlations between threshold and fixation instability, but an absolute relationship, that is, the SD of fixational eye velocity of 10 deg/s roughly corresponds to the minimum detectable motion of 10−1 deg/s. Thus, the detectable signal seems to be 1 log unit smaller than the SD of velocity noise. Why? There are several reasons why the estimated fixation instability cannot be smaller, but can be larger, than the physiologically occurring instability at strict fixation. First, the time window (13 ms) used to calculate the instantaneous velocity was very narrow compared with the slow nature of fixational drifts, and emphasized higher temporal-frequency components. Not all of these components would affect the detection of slow translation lasting for 0.85 s. Second, each observer's head was not strictly, but only mildly, restrained by a chin and forehead rest for ethical reasons that were inevitable in sampling data from a large group of naïve participants. Mild restriction might have introduced compensatory eye movements related to head movements, inflating the velocity of fixational drift. Third, fixation might have become more stable when each observer was doing the detection task than when a stimulus was only passively observed, the condition under which fixational eye movements were recorded in the main experiment. Although preliminary recordings of eye movements in both active and passive viewings indicated the contrary (data not shown), this possibility is hard to disprove in the setup of the main experiment in which psychophysics and eye-movement recording were done in separate sessions.

Putting aside the issue of absolute impact of fixation instability, the present and previous studies have together revealed that velocity noise due to fixational eye movements can affect our motion perception, although we might be normally unaware of the existence of such noise. Recently, a similar positive correlation has been found between fixation instability and the strength of a powerful motion illusion seen in a static display, often called the rotating snake illusion (Murakami, Kitaoka, & Ashida, 2006), and a possible underlying mechanism relating eye noise to visual motion representation has been argued (Beer et al., 2008) as one of the possible accounts for this phenomenon (Backus & Oruç, 2005; Conway, Kitaoka, Yazdanbakhsh, Pack, & Livingstone, 2005; Hisakata & Murakami, 2008; Kitaoka & Ashida, 2003; Kuriki, Ashida, Murakami, & Kitaoka, 2008).

We are normally unaware of eye-velocity noise particularly because our motion detection in daily life is rarely made in an isolated pattern on a uniform featureless background. Our motion detection is usually made relative to some static frame of reference in normal circumstances and, in such circumstances, our performance is very good and independent of fixational eye movements. Specifically, Murakami (2004a) did a similar motion-detection experiment with a surrounding stationary texture and found no correlation between this referenced-motion detection and fixation instability. When fixational eye movements occur, the target and reference retinally move together, and thus the relative motion information between target and reference is retained irrespective of eye-velocity noise. Recently, the immunity of relative motion sensitivity to fixational eye movements has been confirmed by using high-resolution retinal imaging by adaptive optics with the spatial resolution of cone photoreceptors (Raghunandan, Frasier, Poonja, Roorda, & Stevenson, 2008). The same study also tested an unreferenced motion-detection threshold in a high-resolution retinal imaging situation and found a partial effect of eye-velocity noise. This seems consistent with the present study, in which the correlation was significant but imperfect. Interestingly, a recent report suggests that there is a tight temporal limit for two stimuli to be the reference for each other to counteract fixational eye movements (Wallis, 2006). In a perfectly aligned grid of dot elements, a stimulus-onset asynchrony as short as 12 ms was introduced between the onsets of alternate rows. Then, the rows appeared misaligned as a result of fixational eye movements that occurred within the delay. Therefore, simultaneous presentation is a necessary condition for the two relative positions to maintain perceptual constancy despite incessant fixational drifts. To identify the temporal limit of similar asynchronous presentation in relative-motion processing, rather than relative-position processing, is an interesting direction for future investigations.