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Temporal Evolution of 2-Dimensional Direction Signals Used to Guide Eye Movements

¹Department of Neurobiology, Harvard Medical School, Boston, Massachusetts; ²Harvard University, Program in Mind, Brain and Behavior, Cambridge, Massachusetts; and ³Montreal Neurological Institute, McGill University, Neurology and Neurosurgery, Montreal, Quebec, Canada

Submitted 22 December 2004; accepted in final form 6 September 2005

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
The smooth pursuit system must integrate many local motion measurements into a coherent estimate of target velocity. Several laboratories have studied this integration process using eye movements elicited by targets, such as tilted bars, containing conflicts between local motion signals measured along contours [one dimensional (1D)] and those measured at the bar's endpoints, or terminators [two dimensional (2D)]. The general finding is that 1D signals dominate early responses, whereas later components of the behavior are determined by 2D signals. We studied the dynamics of the integration process in macaque monkeys by systematically varying the relative proportions of 1D and 2D signals and the retinal eccentricities at which they appeared. Predictably, longer bars produced greater and longer-lasting contour-induced deviations. The evolution of the 2D response occurred over a period of 50–400 ms, depending on the relative proportions of 1D and 2D signals. As contours were displaced from the fovea the deviation decreased but much less so for early (1st 40 ms) than for late (subsequent 40 ms) pursuit initiation. These bottom-up effects could be overcome to a limited extent by the top-down influence of predictability. Finally, we observed that when animals were free to track any part of the bar, they spontaneously made short-latency saccades to the terminators on most trials, especially when the bars were tilted. This suggests an increased saliency of moving terminators, particularly when discrepancies exist among local motion signals.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Everything that the primate brain can know about the visual world is represented on 2 million more-or-less discrete channels—the fibers of the optic nerves. Each one of these channels contains a limited amount of information about a very small part of the visual field, defined as the receptive field of a single retinal ganglion cell. While the fine grain of this representation is essential for high acuity vision, the limited nature of the subunits poses a problem for the rest of the visual system. How are the parts of the image that belong together integrated into coherent representations of objects?

One way of thinking about the spatially limited receptive fields of retinal ganglion cells is as "apertures," which create local visual signals that are frequently ambiguous. This is easy to imagine for any moving object that has edges at oblique angles with respect to its direction of motion (Fig. 1A). A neuron with a small receptive field positioned along the contour of one of these edges can measure only the component of motion perpendicular to the contour. Such a one-dimensional (1D) measurement is inherently ambiguous because it is consistent with many possible directions of actual object motion. In contrast, neurons whose receptive fields are positioned over two-dimensional (2D) features, such as the object's corners or endpoints ("terminators") can measure the direction of object motion accurately. Thus the visual motion system is often presented with a conflict¹ between the potentially erroneous 1D signals measured along a contour and the veridical 2D signals originating from terminators. How is this conflict resolved?

View larger version (10K): [in this window] [in a new window]   FIG. 1. General methods. A: aperture problem for visual motion. The thick and thin oblique lines represent 2 successive snapshots of the bar moving to the right. The circles represent the receptive fields of neurons early in the visual pathways, such as those in V1. Due to the limited size of these receptive fields, the motion signals measured along the contour (c) are ambiguous because the observed displacement is consistent with an infinite number of possible displacements over a range of 180°. Motion signals measured at terminators (t) do not suffer from this problem. B: visual stimulus consisted of a green bar on which was superimposed an isoluminant red Gaussian blob. The subject was required to track the center of the bar to within 2–3°, indicated by the dashed square. This "target window" was not visible to the subject, and it moved with the target. C: pursuit data from a single trial from one monkey showing both the horizontal eye position (thick line) and velocity (thin line) superimposed on the trajectory of the target position (dashed line). The onset of pursuit (arrow head) is most clearly seen in the velocity trace.

Given the evidence that MT neuronal signals are important for the initiation of smooth pursuit and other smooth eye movements (Born et al. 2000; Groh et al. 1997; Komatsu and Wurtz 1989; Newsome et al. 1985), it is not surprising that a similar effect has been observed behaviorally (Masson and Castet 2002; Masson and Stone 2002; Masson et al. 2000; Pack and Born 2001). Thus smooth pursuit provided us with a tool for examining the temporal properties of motion integration as we varied different stimulus parameters, such as bar length, eccentricity, and the predictability of the direction of target motion. Some portions of this work have been described briefly in previous publications (Born and Pack 2002; Born et al. 2002; Pack and Born 2001).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Surgical preparation

Seven adult rhesus monkeys (Macaca mulatta, 6 male, 1 female) were surgically prepared for chronic behavioral experiments and then trained to perform a fixation task and a visual tracking task. Four of these monkeys were used for the various bar pursuit experiments (Table 1). The other three were used for the experiments in which we examined the nature of saccades made to moving bars (Figs. 10–14). The experimental protocols were approved by the Harvard Medical Area Standing Committee on Animals. In a sterile surgical procedure under isoflurane anesthesia, a coil of fine wire was implanted between the conjunctiva and the sclera for the measurement of eye position (Judge et al. 1980; Robinson 1963). During the same surgical procedure, stainless steel or titanium bone screws were implanted in the skull and a fixture for immobilizing the head was attached using dental acrylic.

View larger version (63K): [in this window] [in a new window]   FIG. 10. Saccades during tracking of tilted bars by "naïve" animals. A: horizontal eye position traces from 20 trials each of bars tilted either +45° (blue) or –45° (red) or nontilted (black). For these trials, the bars always moved straight upward. The rightward and leftward deflections represent saccades to one of the bar's terminators, which are shown by the dashed lines. B: polar histogram of the percentage of trials on which the animal made a saccade to within 2° of the bars' endpoints over an interval from 100 to 400 ms after the bar began to move. The direction of each set of three bars indicates the direction of target motion; the different colors represent different relative bar orientations. Solid red and blue bars indicate cases in which the number of saccades to a tilted bar was significantly greater (P < 0.01, binomial test) than would be expected by chance if the probability of a saccade was the same as that on control (nontilted bars) trials. C and D: 2-dimensional histograms of the saccade endpoints for all saccades made between 100 and 400 ms after motion onset of 9.4° bars that were either nontilted (C, 351 saccades) or tilted ±45° (D, 602 saccades). The color of each pixel indicates the number of saccades made to that location. The numbers along the color axis are small because the pixels (bins) are small. For a sense of scale, the box around the location of the leading terminator contains 246 saccades. E: angular deviation plots of smooth pursuit during the same trials, after de-saccading and aligning on the initiation of pursuit. Thick lines indicate the direction of the mean vector and thin lines represent the 95% confidence interval about the mean direction.

View larger version (53K): [in this window] [in a new window]   FIG. 14. STTs to horizontal bars moving in different directions. A: geometry of the experiment indicating the relative tilts corresponding to different directions of motion of the horizontal bar. B: raw eye position traces of 20 trials each from 3 different directions of bar motion: up-right (blue), up (black), and up-left (red) in which the position coordinates for each trial type have been rotated such that upwards on the y axis corresponds to the direction of target motion in each case. This renders the data comparable to that of Fig. 10A, even though the conditions were strictly identical only for the nontilted (black) condition. C: 2-dimensional saccade map for early saccades (between 100 and 400 ms after the bar began moving) to nontilted bars (151 saccades). D: saccade map for early saccades to tilted bars (232 saccades). E: STT latency histograms for monkey F for 9.4° long horizontal bars. Each condition of relative tilt consists of 150 trials. The median latencies are indicated by arrows.

The animals were placed on a controlled fluid intake schedule and received water or juice as reinforcement during training and experimental sessions. Monkeys were first trained to pursue a small red spot. The animals foveated the fixation point (a small red square, 11 arc-min on a side, luminance 20.6 cd · m^-2) for a randomly varied period of 500-1,300 ms at the end of which the fixation point disappeared, and, simultaneously, a red spot (0.5° diam) appeared at the fixation location and began to move in one of several possible directions and speeds. After the animals were proficient at tracking the red spot, the target was changed to a long green bar with the same red spot superimposed on its center (Fig. 1B). Initially the bar was made quite dim and the spot very bright, but even so, the natural tendency of the monkeys was to saccade to one of the bar's terminators and track this feature (see following text). To discourage this tendency, we limited the computer-controlled eye-position window to a small area (±2 or 3° for longer bars) centered on the spot. If the monkey failed to track the spot or made a saccade to one of the terminators, which were always located well outside of the target window, the visual stimulus was extinguished, no reward was given, and a brief time-out was inserted before the start of the next trial.

In a typical experiment, such as the one for which results are shown in Figs. 2 and 3, the bar could move in one of four different directions (right, left, up, or down) at 10° · s^–1 and at one of three possible relative orientations (perpendicular, or tilted +45 or –45° with respect to the direction of motion) for a total of 12 different motion conditions. For each possible trial type, we generally performed 20–30 repetitions in a blockwise random order.

View larger version (55K): [in this window] [in a new window]   FIG. 2. Bar pursuit data from monkey H for 1 direction of target motion. A and B: individual horizontal (A) and vertical (B) eye position traces for trials in which the target moved to the right at 10° · s–1 but was tilted either +45° (red, n = 20 trials) or –45° (blue, n = 19). The control trials (vertical bar) are omitted here for clarity but are shown in C and D. C: vertical eye velocity shown for the same trials as in B but with the addition of the control (green, n = 17) trials in which the bar's orientation was perpendicular to its direction of motion. D: averages (thick lines) of the data shown in C; thin lines indicate the SE.

View larger version (23K): [in this window] [in a new window]   FIG. 3. Pooled bar pursuit data from 1 experiment for monkey H. Eye velocity parallel (A) or perpendicular (B) to the direction of target motion for tilted (solid lines; n = 908 trials) vs. perpendicular (dashed lines; n = 437 trials) bars. The vertical dashed line indicates the time of pursuit onset. C: summary plot of the average angular deviation (thick lines) and the corresponding 95% confidence intervals (thin lines) for tilted bars (solid) and nontilted controls (dashed). The thick gray line is the best-fitting single-exponential decay function (see METHODS). Numbers of trials for each condition are the same as in A and B.

Visual stimuli were presented on a Mitsubishi monitor (70 x 52 cm, 57 cm away; 1 pixel subtended 0.1°) at a refresh rate of 60 Hz. The bar was dim green (4.2 cd · m^–2; u' = 0.28, v' = 0.59), its center was indicated by an isoluminant, red Gaussian blob (4.2 cd · m^–2; u' = 0.64, v' = 0.34; sigma = 0.2°), and it moved against a black background (0.06 cd · m^–2). Values for chrominance and luminance were measured with a PR-650 SpectraScan Colorimeter (Photo Research; Chatsworth, CA) (CIE 1932). The subject had to track the center of the bar to within ±2° (Fig. 1B) while eye movements were monitored using a scleral search coil. The bars used for the "naïve" experiments (Figs. 10–14) were the same color green but lacked the red spot. For the experiments involving a "precue" as to the direction of motion, the cue consisted of a bright white arrow (90 cd · m^–2; u' = 0.19, v' = 0.45) that appeared for 300 ms at the beginning of the fixation period. The tail of the arrow originated at the fixation point and its head pointed in the direction of target motion on the upcoming trial. Cued and un-cued trials were randomly interleaved.

Data analysis

Eye position and velocity (analog differentiator: low-pass, –3 dB at 50 Hz) were digitized and stored to disk at 250 Hz for off-line analysis (Fig. 1C). Saccades were automatically detected using a previously published algorithm (Krauzlis and Miles 1996), and individual trials were rejected from further analysis if a saccade occurred within the first 80 ms of pursuit. For smooth pursuit, later-occurring saccades were removed and filled in with "NaNs," which were then treated as missing values in subsequent analyses. The time of pursuit onset was detected using a modification (Madelain and Krauzlis 2003) of the algorithm published by Carl and Gellman (1987). Pursuit onset was determined as the intersection of two regression lines, one fit to the baseline and one fit to the response eye velocity data. The baseline was defined as the time from 40 ms prior to the onset of target motion to 40 ms after; the response was taken as the 40 ms of data from the point at which the eye velocity exceeded the baseline by 3 SDs. From this point of intersection, we then explored 40 ms in either direction to determine whether another hinge point provided a better fit to the data, in a least-squares sense. Each trial was then displayed with markers for saccades and the onset of pursuit so that it could be visually inspected and the markers adjusted by the operator if necessary.

For quantitative analysis of early (or late) pursuit, we used the first (or 2nd) 40 ms of eye velocity after the onset of pursuit. The data from each trial were fit with a least-squares regression line, and the slope of this line was used as the measure of eye acceleration during that period. The individual slope values (i.e., accelerations) were then used for further statistical analyses. For many experiments, this consisted of a multi-way ANOVA using the "anovan" function in Matlab (The Mathworks, Natick, MA) with a constrained (Type III) sums of squares. Post hoc comparisons were made with the "multcompare" Matlab function using the "Tukey-Kramer" correction for critical values. Comparisons across subjects were performed using a one- or two-factor repeated measures ANOVA (RMANOVA) (Trujillo-Ortiz et al. 2004a,b).

For the analyses of the angular deviation of pursuit, the direction of the eye velocity vector was determined for each successive pair of time points (t = 4 ms) on each trial. The directional components of the velocity vectors across many trials were then analyzed using methods of circular statistics (Zar 1996) to determine the mean angle and the corresponding 95% confidence intervals. Significance testing of angular data were performed using the Watson-Williams two-sample test for circular data. We also fit each curve of angular deviation over time (e.g., Fig. 3C) with exponential decay functions of the general form

where D is the observed angular deviation over time, t, and the free parameters are the initial amplitude, A₀, a constant offset, C, and the various time constants, _1-n. Fits were optimized with a least squares criterion using the Levenberg-Marquardt algorithm (Matlab's "lsqcurvefit"). Each data set was first fit with a single and double exponential, and the errors of the two fits were compared using a sequential F-test (Draper and Smith 1966). If the addition of the second exponential significantly improved the fit (P < 0.05), a third exponential was added, the sequential F-test repeated, and so on. In practice, no more than two exponential terms were ever justified. Once the optimal model was determined in this way, 95% confidence intervals for each parameter were determined using a bootstrap procedure (Efron and Tibshirani 1993) in which the raw data were re-sampled, a new angular deviation curve was generated and re-fit. By repeating this procedure 1,000 times, we generated a distribution of bootstrap parameters from which SEs and confidence intervals were derived.

For the "naïve" bar-pursuit experiments (Figs. 10–14), latency distributions were compared using the Wilcoxon rank-sum test ("ranksum" function in Matlab), and probabilities of making saccades to terminators were compared directly using the binomial distribution. In general, we determined the probability, P, of observing x or more saccades on n trials for tilted bars, if the underlying probability, p, of making such a saccade was that determined from the nontilted bar trials. Using the Matlab statistics toolbox, this corresponds to: P = 1 – binocdf(x – 1, n, p). Two-dimensional saccade histograms (Figs. 10, 11, and 14) were generated by counting the number of saccades made to each location (spatial bins: 0.05 x 0.05°) and smoothing with a 2D Gaussian of sigma = 0.35°. The location of each saccade was plotted relative to the location of the bar at the time of the saccade, and the coordinates were rotated so that saccades to leading terminators were upwards and those to trailing terminators were downwards. For maps in which data were pooled for bars of different lengths (Fig. 11), saccade distances were scaled by bar length prior to binning and smoothing.

View larger version (62K): [in this window] [in a new window]   FIG. 11. Two-dimensional histograms for all saccades made by all 3 monkeys (I, J, and K). A: map of early saccades (between 100 and 400 ms after the bar began moving) to nontilted bars (1,543 saccades). B: map of early saccades to bars tilted ±45° with respect to their direction of motion (2,987 saccades). C: map of late saccades (between 400 and 1000 ms after the bar began moving) to nontilted bars (2,353 saccades). D: map of late saccades to tilted bars (4,233 saccades).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

For each trial, we determined the perpendicular eye acceleration (see METHODS) over the first 40 ms of pursuit and used this as a measure of the effect of local, contour-related motion signals. For the experiment shown in Figs. 2 and 3, we randomly interleaved four different directions of bar motion (right, left, up, or down) at one of three possible relative tilt angles (no tilt or a tilt of +45° or –45°) for a total of 12 different conditions. After aligning the eye velocity data on the initiation of pursuit, we analyzed the deviation across all conditions using a two-way ANOVA. For this experiment, there was a highly significant effect of bar tilt (P < 0.0001) and a nonsignificant effect of direction of motion (P > 0.1) as well as a nonsignificant interaction between the two factors (P > 0.1). The mean pursuit deviations for the different bar tilts are summarized in Table 2. The pursuit deviations induced by the +45 and –45° bar tilts were, on average, nearly identical in magnitude but opposite in sign (Fig. 2D), so that the absolute values of the effects were not significantly different (t-test, P > 0.3).

The actual direction of the initial deviation in pursuit velocity is rendered explicitly in Fig. 3C. To combine the direction of pursuit deviation across trials having different absolute directions of bar motion, we again calculated the direction of the eye movement relative to the direction of motion of the bar. In these plots, zero deviation always corresponds to veridical pursuit (i.e., in the direction of bar motion). As we would expect, the pursuit of the nontilted control bars shows no angular deviation (dashed line of Fig. 3C). For each time bin, we calculated the mean directional deviation across trials and the 95% confidence interval (thin lines in Fig. 3C) based on the von Mises distribution (Zar 1996; p. 604–605). Prior to the onset of pursuit (<100 ms after the onset of target motion), the measured directions of eye movement are essentially random, thus producing extremely large confidence intervals, and are not shown. This picture of the data indicates that the earliest pursuit deviates nearly 45°, that is, perpendicular to the orientation of the bar, presumably as a consequence of the aperture problem. Comparing this vector plot with the more traditional Cartesian representation in Fig. 3, A and B, reveals an important feature of the data, which is that the angular deviation decreases over time initially because the component of eye speed parallel to the bar's direction of motion is increasing more rapidly than is the perpendicular component—note the difference in velocity scales for the two components. Even 150 ms after pursuit onset there is an appreciable perpendicular component (Fig. 3B), which, for the long bar (34°) used in this experiment did not disappear completely for another 350 ms. The time course of the angular deviation was well described (r² = 0.994) by a single exponential with a time constant of 180 ms (Fig. 3C, gray line). Finally the same initial deviation in pursuit was seen under less-constrained conditions during experiments in which the green bar contained no red spot and the animals were free to make saccades to any part of the bar (as described in the following text; Fig. 10E).

Effect of bar length

The data presented in the preceding text, as well as that previously published for perception (Lorençeau et al. 1993), smooth pursuit in monkeys (Pack and Born 2001) and humans (Masson and Stone 2002), and ocular following in humans (Masson and Castet 2002; Masson et al. 2000), are consistent with the idea that early responses reflect the contributions of both contour- and terminator-related motion signals. If this idea is correct, one straightforward prediction is that the behavior should be affected by the relative proportion of contour and terminator present in the stimulus. A simple way to test this is to vary the length of the bar used as a pursuit target. Any single bar has only two terminators, but increasing the length adds progressively more contour-related signal. As a result increasing the bar length should increase the magnitude of the initial pursuit deviation or prolong its time course or both.

To test this prediction, we repeated the previous experiment with bars of different lengths presented on randomly interleaved trials. Increasing bar length had the expected effect of increasing the contour-based deviation according to several different measures of the behavior (Fig. 4). We performed this experiment in each of three monkeys (C, G, and H), and all showed a similar increased deviation with increased bar-length. A two-way RMANOVA (bar length and tilt) on the perpendicular pursuit acceleration revealed a nonsignificant main effect of bar-length (P > 0.5), a highly significant effect of tilt (P < 0.001), and, most critically, a highly significant interaction between bar length and tilt (P < 0.00001).

View larger version (39K): [in this window] [in a new window]   FIG. 4. Results of varying bar length. A: average eye velocity perpendicular to the direction of target motion for bars of different lengths for monkey H. Each thick line is the average of 900 trials; thin lines represent SE. B: initial (from 0 to 40 ms after pursuit onset) perpendicular eye acceleration as a function of bar length for 3 different monkeys (C, green; H, red; G, black) for bars that were either tilted (solid lines) or not (dashed lines). The error bars indicate SE. C: time course of the angular deviation for bars of different lengths in monkey H (same data as in A). The thick lines represent the direction of the mean vector and the thin lines represent the 95% confidence interval about the mean direction. The cyan circles plot the P values of a 2-sample test (Watson-Williams test) at successive time points comparing the deviation induced by the longest tilted bar (solid black line) with the nontilted bar of the same length (dashed black line). The time at which the difference becomes nonsignificant (arrows) was defined as the duration of the deviation. The significance criterion, P = 0.01, is represented by the horizontal dash-dot line. Symbols near the bottom of the plot correspond to a P < 10–14. D: time constants of the best-fitting single-exponential decay as a function of bar length for the same 3 monkeys (colors as in B). Error bars indicate 95% confidence intervals determined using a bootstrap procedure (see METHODS). The filled blue circle indicates the best-fitting time constant for the population data for 60 MT cells recorded from 2 alert macaque monkeys. The fit was to the angular deviation of the mean neuronal direction vector in response to fields of tilted bars, each bar being 3° long (Fig. 2C from Pack and Born 2001).

This effect on the duration of the angular deviation was also clear in the exponential functions fit to the curves of angular deviation versus time (Fig. 4C). The majority of these curves (37/48) were adequately described by a single exponential (sequential F-test, P > 0.05). For experiments in which the addition of a second exponential significantly improved the fit, the difference between the two fits was extremely subtle and bore no systematic relationship with bar length (² test for homogeneity, P > 0.3). We thus used the best-fitting first-order exponential for comparisons across conditions and found, as for the other measures, that the time constants generally increased with bar length (Fig. 4D). This was not true, however, for the two shortest bar lengths (4.25 and 8.5°) for which the distributions of time constants were not significantly different (paired t-test, P > 0.3). For comparison, we have also plotted the time constant of an exponential fit to the population data for 60 MT cells recorded from two alert macaque monkeys (Fig. 2C of Pack and Born 2001).

Effect of eccentricity

If the contour-induced deviation in pursuit is caused by the spatially delimited receptive fields of visual neurons, then one might predict that increased stimulus eccentricity would diminish the tilt effect. The rationale for this prediction is illustrated in Fig. 5A, which shows why the larger receptive field sizes at greater eccentricities, e.g., (Daniel and Whitteridge 1961; Gattass and Gross 1981) might have the effect of tipping the balance in favor of the terminator-based motion signals. Put another way, presenting a bar of constant length at a greater eccentricity effectively shrinks the visual representation of the stimulus, making it more like a spot or a blob (Lorençeau et al. 1993), which might also be expected to reduce deviation due to the aperture effect.

View larger version (20K): [in this window] [in a new window]   FIG. 5. A: logic of the eccentricity experiments. As a bar of constant length is presented at greater distances from the fovea, the apertures (receptive field sizes, indicated by circles) grow larger and give progressively greater weight to terminators (t) relative to contours (c), according to the relative numbers of "units" of each type activated. This might be expected to progressively diminish the contour induced deviation, as indicated by the direction of the arrows. B: visual stimuli (not drawn to scale) used for the bar width experiments shown in Fig. 8. Each stimulus was a parallelogram centered on the fixation point, was of the same uniform (green) color, and had the same fuzzy, red spot at its center. In this type of stimulus, the edges defining the contour are symmetrically displaced from the fovea, and the top and bottom edges (except at the corners) give no motion information since they are parallel to the direction of motion (indicated by the arrow).

Results for two eccentricities and three different bar lengths are shown for one monkey in Fig. 6. It is immediately apparent that the effect of bar length described in the preceding text (Fig. 4) is reproduced at both eccentricities as the deviated component (Fig. 6, A and B, bottom) increases with increasing bar length. In addition, a comparison of the two families of curves suggests that eccentricity had the expected effect—the curves produced by bars presented 4° off of the fovea (Fig. 6B) clearly have decreased slopes compared with their counterparts at 2° of eccentricity (Fig. 6A). However, as is apparent in Fig. 6, A and B, top, the component of eye velocity parallel to the direction of target motion also decreased with eccentricity. This had the net effect of rendering the angular deviation roughly equivalent across different eccentricities, at least for the early period of open-loop pursuit.

View larger version (24K): [in this window] [in a new window]   FIG. 6. Effects of eccentricity on the contour-induced deviation of smooth pursuit initiation. A and B: direct comparison of parallel (top) and perpendicular (bottom) eye velocities presented at 2 different eccentricities (2°, A, and 4°, B) for 3 different bar lengths (8.5°, red; 17°, blue; 34°, black) in monkey H. Each thick trace represents the average of 80 trials; thin lines are ±SE.

View larger version (39K): [in this window] [in a new window]   FIG. 7. Effects of eccentricity on the angular deviation of pursuit initiation. A: for experiments in which 2 different eccentricities were randomly interleaved, single-exponential decay functions were fit to the angular deviation curve for each eccentricity. Each filled circle (n = 31) indicates the time constant of the fit to the angular deviation curve for the lesser (abscissa) vs. the greater (ordinate) eccentricity. Eccentricity differences ranged from 2 to 6°. Error bars show SE for each fit, determined using a bootstrap procedure. B: time constants of the exponential decay function fit to the pooled data for each monkey (monkey B, blue; C, green; H, red; G, black) at each eccentricity tested. Error bars represent SE. C and D: angular deviation as a function of time for the pooled data from monkey H comparing the deviation for foveally presented 34°-long bars vs. the same bars presented at 2° (C) or 4° (D) from the fovea. The 0° eccentricity data are based on 470 trials, and the 2° and 4° data are based on 232 and 352 trials, respectively. Eye-movement data were first de-saccaded and then aligned on pursuit onset. The magnitude of the deviation was significantly reduced for eccentrically presented bars, but the two curves do not diverge significantly until >50 ms after pursuit onset (arrows). Thick lines represent the direction of the mean vector; thin lines show the 95% confidence interval. The filled cyan circles plot the significance values for the Watson-Williams test comparing the 2 angular distributions at each time point. The horizontal dash-dot line represents the significance level of P = 0.01; symbols near the bottom of the plot correspond to a P value of 10–5 (C) or 10–10 (D).

The preceding results suggested that eccentricity had very little effect on the early period of pursuit initiation, but that it did alter later phases of the response. However, the geometric limitations of the experiment made it difficult to reach a firm conclusion for later periods of pursuit—due to the intrusion of saccades—and for greater eccentricities. We therefore conducted a second series of experiments using bars of a single length (34°) but of varying widths, which had the effect of symmetrically displacing the edges of the bars various distances from the fovea (Fig. 5B). The "bars" for these experiments were actually parallelograms—the end contour was parallel to direction of bar motion—so that we did not add potentially disambiguating contour signals along the ends. As before the parallelograms were a uniform green color, but contained an isoluminant red gaussian blob at its center. These experiments were performed with three of the four pursuit monkeys (C, H, and B).

Increasing the bar's width had the effect of diminishing contour-induced deviations at greater eccentricities, while leaving the component parallel to the direction of bar motion relatively constant (Fig. 8 A, top; RMANOVA, P > 0.1). This produced more reliable differences in the pursuit behavior over longer time periods because the animals made very few saccades. As in the previous experiment, the earliest phase of pursuit showed only a very small effect of eccentricity, with larger differences emerging after the first 40 ms of pursuit. This can be seen in the averaged perpendicular eye velocity traces (Fig. 8A), which nearly superimpose over the first 40–50 ms of pursuit and only diverge after this point (arrow). A two-way RMANOVA (tilt and bar width) revealed the expected significant main effect for tilt and a highly significant interaction term (P < 0.00001) for both early (1st 40 ms) and late (2nd 40 ms) pursuit. That the effect of bar width on early pursuit was small is shown more clearly by plotting the perpendicular eye acceleration as a function of contour eccentricity for the early versus late phases of pursuit initiation. For early pursuit initiation, this function is nearly flat, whereas for the later period the effect is considerably greater (Fig. 8B). The difference in slopes was highly significant (t-test, P < 0.001) both for the pooled data shown in Fig. 8 as well as for each individual experiment in all three monkeys (P < 0.05; 4 each in monkeys B and H; 6 in monkey C). The same trend was seen in the vector plots, with subtle—but significant—effects of eccentricity in all three animals (Fig. 8, C and D; linear regression, P < 0.05). Thus this second experiment confirms the main result of the first, which is that eccentricity does diminish the contour effect for tilted bar pursuit, but predominantly for the latter half of pursuit initiation.

View larger version (34K): [in this window] [in a new window]   FIG. 8. Results of bar width experiments. A: magnitude of the eye velocity parallel (top) or perpendicular (bottom) to the direction of target motion for parallelograms of different widths corresponding to different contour eccentricities : 0.4°, black; 0.8°, blue; 1.6°, red; 3.2°, green; 6.4°, magenta. For example, the stimulus for the condition listed at an eccentricity of 6.4° was a parallelogram that was 12.8° wide and centered on the fovea at the time of motion onset. The long side of each parallelogram measured 34°. Each thick line is the mean of 970 trials, and thin lines represent the standard error of the mean. B: effect of eccentricity on the early (black, 1st 40 ms of pursuit) and late (red, 2nd 40 ms of pursuit) phases of pursuit initiation. In each subplot, the slope of the eye velocity data shown in A is plotted against the eccentricity of the parallelogram's contours for both tilted (solid lines) and nontilted (dashed lines) targets. Error bars represent SE. C: mean angular deviation of pursuit over time for the same stimuli. Conventions are as for A. Thick lines show the direction of the mean vector during each 4-ms bin; thin lines represent the 95% confidence interval of the mean direction. D: time constants of the exponential decay function fit to the pooled data for each monkey (monkey B, blue; C, green; H, red) at each eccentricity tested. Error bars represent SE.

The preceding experiments indicate that ambiguous local motion signals emanating from contours are manifest in the initiation of smooth pursuit eye movements and that these ambiguities exist because of the limited size of receptive fields at early stages of the visual pathways. Thus the contour effect for pursuit can be thought of as a signature of "bottom-up" motion processing. It is also clear, however, that both pursuit behavior (e.g., Deno et al. 1995) and motion perception (e.g., von Grunau et al. 1998) are subject to more cognitive, "top-down" influences, such as those following from the predictability of target motion. Given this duality of influences on the behavior, we thought it would be interesting to pit them against each other to ask to what extent prior knowledge of target direction could reduce the ambiguities inherent in early visual motion processing.

We did this by giving the monkeys information regarding the true direction of target motion well before it began to move. Insofar as this information can influence pursuit, it should diminish the deviation caused by the orientation of the tilted bars. For this experiment, bar motion on any given trial could be in one of four possible directions and at one of three possible relative orientations as described in METHODS. The new feature was that on a randomly chosen half of the trials, target onset was preceded by a cue—an arrow pointing away from the fixation spot—that indicated the upcoming direction of target motion. The cue appeared during the first 300 ms of the fixation period, and was then extinguished prior to an additional 500–1,300 ms of fixation before target onset. Thus although the direction of target motion was predictable on these trials, the time of its appearance was not. This experiment was performed in each of two monkeys (5 experiments in monkey B and four in monkey H).

The cue had a statistically significant effect for both monkeys but only for the early phase (1st 40 ms) of pursuit initiation (Fig. 9, A and B; 2-way RMANOVA, P < 0. 001). Importantly, in every case the effect of the cue was to decrease the perpendicular component (Fig. 9A, Table 3), while leaving the parallel component of pursuit unchanged (cue-tilt interaction P > 0.3 for both early and late pursuit initiation). The cue effect was quite subtle, however, producing only a very small and short-lived (from 0 to 12 ms after pursuit onset) decrease in the angular deviation (Fig. 9B).

View larger version (24K): [in this window] [in a new window]   FIG. 9. Effect of directional predictability on the contour effect. For all plots, black lines indicate trials in which the direction of motion was unpredictable, red lines indicate trials in which a direction cue preceded the appearance of the target, and green lines indicate trials that were performed in blocks containing the same direction of motion on every trial. A: perpendicular eye velocity for the different cue conditions from 1 monkey (H); mean ± SE. (uncued, 1,020 trials; cued, 1,014 trials; blocked, 316 trials). B: angular deviation for the same data in A. Thick lines indicate the direction of the mean vector and thin lines represent the 95% confidence interval about the mean direction.

To address this issue, we performed an additional experiment in which target motion predictability was created by repeating the same direction of target motion in blocks of trials. In these experiments, we continued to vary the relative orientation of the bar, but the speed and direction were constant within a block of 200–300 trials. In separate blocks of trials, we collected data from different directions of target motion so that the overall data set was matched to that for the cued versus un-cued experiments. This manipulation had the effect of greatly reducing the contour-induced deviation as shown by the green traces in Fig. 9, A and B. Both the initial perpendicular eye acceleration (Fig. 9A) and the angular deviation (Fig. 9B) were considerably smaller. For angular deviation, this difference, with respect to both the cued and the un-cued data, was highly significant (P < 0.01, Watson-Williams test) for all time points out to 300 ms after pursuit onset. Exponential fits to the angular deviation curves revealed a similar story: the time-constants for both monkeys were nonsignificantly reduced by the presence of the cue, and there was a large and statistically significant effect of the block design (_nocue = 124 ± 9 ms; _cue = 116 ± 7 ms; _blocked = 100 ± 6 ms).

Saccades to tilted bars: the salience of terminators

For all of the experiments presented thus far, we required the animals to track the approximate center of the bars and enforced this by using an eye-position window centered on the spot. We did this because it was obvious in our first training attempts that, regardless of the salience of the spot, the monkeys tended to make saccades to the endpoints of the bar. This tendency seemed potentially interesting because it suggested a particular visual salience of terminator-related motion signals. We therefore studied it in three additional animals (monkeys F, I, and J), who were naïve to the bar-pursuit task. All three animals were well trained on the pursuit of small spots but had never before pursued bars. For these experiments, we made the eye-position window large enough so that eye movements made to any point along the bar were permitted. We used bars of moderate length (9.4° for monkey F; 9.4 and 18.8° for monkeys I; and 8.5 and 17° for monkey J) and, as in previous experiments, randomly interleaved four different directions of target motion and three different relative bar orientations.

Representative eye traces from monkey F for the subset of trials on which the bars moved upwards at 10° · s^–1 are shown in Fig. 10A. The traces show the horizontal eye position over time for cases in which the bar was tilted either +45° (blue) or –45° (red) with respect to the direction of bar motion, or not tilted (black). On almost every trial, the animal made an early saccade to one of the bar's endpoints. For this particular direction of motion, the saccade was made to a leading terminator on nearly every trial—that is, when the bar was tilted +45° (blue lines), the saccade was made to the right-hand terminator, which was displaced from the bar's center in the same direction as the bar was moving. This was not always the case, however, as most monkeys had general directional biases for saccades. For example, monkey F showed a mild, but significant, bias for left- over rightward saccades (measured across all trial types, P > 0.05, binomial test) and an extremely strong tendency to make upward over downward saccades (P < 0.0001, binomial test). This meant that, for rightward bar motion, for example, he made saccades nearly exclusively to the trailing terminator for +45° tilts (73 of 74 trials) and to the leading terminator for –45° tilts (61 of 62 trials). In both cases, the terminator chosen was the one above the center of the bar regardless of whether it was leading or trailing with respect to the direction of bar motion. However, when the different directions of bar motion were balanced, all three monkeys did show a weak overall tendency to saccade to leading terminators: monkey F, 58% leading (P < 0.0001, binomial test); monkey I, 57% leading (P < 0.0001, binomial test); monkey J, 52% leading (P = 0.13, binomial test).

Another feature of the data in Fig. 10A is that the saccades appear to occur earlier and with greater frequency when the bar was tilted compared with when it was not. To examine this tendency across different directions of bar motion, we determined the percentage of trials on which the animal made a saccade to within 2° of one of the bars' endpoints within a time window from 100 to 400 ms after the onset of bar motion. The data for the 9.4° long bar are shown as a polar histogram in Fig. 10B in which different directions around the circle indicate the direction of bar motion, and the differently colored symbols indicate the relative orientation of the bar. The data indicate that the animal frequently made short-latency saccades to the bars' endpoints when the bar was tilted but was less likely to do so when the orientation of the bar was perpendicular to its direction of motion. To assess the significance of this difference, we used the binomial distribution to determine the probability of obtaining a number of saccades equal to or greater than the number observed for the tilted bar condition if the underlying probability were that observed for the corresponding nontilted bar (see METHODS). For seven of the eight possible comparisons in Fig. 10B, this difference in saccade behavior evoked by perpendicular bars versus tilted bars was highly significant (binomial test, P < 0.01). Only for rightward moving bars tilted –45° was the number of saccades to terminators not significantly greater than for perpendicular bars (P = 0.13, indicated by the unfilled red bar in Fig. 10B).

The enhanced salience of the terminators of tilted bars is shown even more clearly in 2D maps of saccade frequency (Figs. 10, C and D, and 11 ). We generated these maps by plotting the location of every saccade made by the monkey as a function of the position of the center of the bar with all coordinates rotated so that, for tilted bars, saccades to leading terminators were upward and those to trailing terminators were downward. Figure 10, C and D, shows saccade maps for monkey F for a bar length of 9.4° for all saccades made between 100 and 400 ms after the onset of bar motion. For nontilted bars, most of the early saccades were made to regions near the center of the bar, whereas for tilted bars, the endpoints were more often targeted. This was true for all monkeys and both bar-lengths as shown in Fig. 11. For all of the tilted bars, the vast majority of saccades, whether early or late, were made to terminators (Fig. 11, B and D). For the nontilted bars, only at later times after motion onset were a significant proportion of saccades made to the terminators (Fig. 11C).

The differences in the timing of the animals' tendency to make saccades to terminators are shown in more detail in Fig. 12. For each trial, we detected each saccade and determined whether or not the eye landed within 2° of one of the bar's terminators. For trials containing saccades to terminators, we then measured the time of initiation of the first such saccade with respect to the beginning of target motion and defined this as the "saccade-to-terminator (STT) latency." Figure 12A shows histograms of these latencies for monkey F for bars 9.4° long. The blue and red distributions, reflecting STT latencies for bars tilted +45 and –45°, respectively, are clearly well to the left of the distribution for nontilted bars. This can be better appreciated in a normalized cumulative distribution plot (Fig. 12B), which shows the curve for nontilted bars (black line) well to the right of those for tilted bars. Both distributions, however, fail to indicate the trials on which the animal made no saccades to the terminators at any time. The proportion of trials with no STT are shown as insets in Fig. 12, B–D, and they indicate another major feature of the data, which is that monkeys are much less likely to saccade to a terminator when the bar is not tilted. Data from the other two monkeys are shown in Fig. 12, C and D, for two different bar lengths: monkey I (Fig. 12C) 9.4° (solid lines and bars) and 18.8° (dashed lines, hollow bars); monkey J (Fig. 12D) 8.5° (solid lines and bars) and 17.0° (dashed lines, hollow bars). In each case, note that the black curves lie to the right of their colored counterparts and the black bars indicating trials with no STTs are larger. Thus all three monkeys showed the same tendency to make early STTs far more frequently when the bars were tilted compared with when they were not (P < 0.01, Wilcoxon rank-sum test; median values in Table 4) and to make STTs on a far greater proportion of trials with tilted bars (P < 0.01, binomial test).

View larger version (42K): [in this window] [in a new window]   FIG. 12. Latency of saccades-to-terminators (STTs). The time of initiation of each saccade made to a point within 2° of one of the bar's endpoints was determined for each trial. For all plots, blue indicates trials on which the bar was tilted +45°; red, –45°; and black, nontilted. A: STT latency histogram for monkey F. The bars were 9.4° long for all trials, and each condition's histogram is based on 360 trials. B: cumulative density functions for the data shown in A. C: cumulative density functions of STT latency for monkey I for each of two different bar lengths: 9.4° (solid lines and filled bars) and 18.8° (dashed lines and hollow bars). D: cumulative density functions of STT latency for monkey J for each of 2 different bar lengths: 8.5° (solid lines and filled bars) and 17° (dashed lines and hollow bars). For monkey J, the control (nontilted) bars were shortened to 6° and 12°, respectively. The bar plots of each inset (B–D) indicate the proportion of trials on which no saccade was made to a terminator (no STT). Values for the median of each distribution and the number of trials on which it is based are given in Table 4.

The preceding results show that monkeys are more likely to saccade to a terminator when there is a discrepancy among local motion measurements (tilted bars) compared with when there is no discrepancy (nontilted bars). This could result either because such a discrepancy actively promotes saccades or because consistency actively suppresses them. In either case, the behavior would require a rapid estimate of the reliability of local motion signals. Alternatively, it is possible that there is something inherently more interesting about corners of oblique objects. Recall that our stimuli always moved in one of the four cardinal directions of motion. Thus nontilted bars were oriented either vertically or horizontally, whereas tilted bars always had an oblique orientation.

To distinguish between these possibilities, we performed two additional control experiments. In the first, we randomly interleaved trials on which the bar appeared centered on the fovea but remained stationary. On these trials, the bars' shapes and orientations were identical to the corresponding trials on which the bar moved, but there were no motion signals, hence no discrepancy. We reasoned that insofar as motion signals were the basis of the differences between STTs of tilted versus nontilted bars, the difference should disappear on the static trials. This prediction was borne out by the data (Fig. 13, Table 5). The distribution of STT latencies for nontilted bars largely overlapped with those of tilted bars on the static trials (Fig. 13; moving bar data are represented by dashed lines and hollow bars; stationary bar data are represented by solid lines and solid bars) and the difference in the probability of making a STT disappeared (P > 0.1, binomial test). The manner in which the differences disappeared, however, was not as we had predicted. If the earlier, more frequent STTs seen for tilted bars were driven solely by factors related to motion signals, we would have expected to see the tilted bar distributions shift rightward to look more like that for the nontilted bars. But, in fact, the opposite occurred: the nontilted bar distribution shifted to the left to match that of the tilted bars.

View larger version (22K): [in this window] [in a new window]   FIG. 13. Comparison of STTs to moving and stationary bars. Data are from monkey I and show STT cumulative distribution functions (as described in the legend to Fig. 12) for 2 different bar lengths, 9.4° (A) and 18.8° (B) for trials on which the bars either moved (dashed lines, hollow bars) or remained stationary (solid lines and bars). For all plots, blue indicates trials on which the bar was tilted +45°; red, –45°; and nontilted, black. Saccade probabilities and numbers of trials for the nontilted bar distributions (black) are given in Table 5.

As a second test of the role that geometry might have played, we performed a series of experiments in one monkey (F) in which the moving bar was always the same shape—a horizontally oriented bar—but it moved in one of six directions on any given trial, thus creating different relationships between the direction of motion and its relative orientation. The various relationships are upward and downward motion, corresponding to the no-tilt condition, up-right and down-left motion, corresponding to +45° tilt, and up-left and down-right motion, corresponding to –45° tilt (Fig. 14A ).

Again, the data reveal the same basic pattern of STTs (Fig. 14, B–D). The raw eye movement traces (Fig. 14B) are from the same monkey (F) and correspond approximately in direction to those from Fig. 10A, and the similarity of the result is apparent. This was also true for the corresponding 2D saccade maps (compare Fig. 10, C and D, with Fig. 14, C and D). One significant difference that we did not see in our previous experiments was that the STT latency distribution for bars tilted +45° was shifted to the right of that for –45° (Fig. 14E, P < 0.0001 Wilcoxon rank-sum test). However, given that, for this experiment, the different relative tilts were confounded with different directions of bar motion, it is likely that the aforementioned directional biases for saccades combined with the bias toward leading terminators, contributed to this result. And although the latency histograms showed a difference between the +45 and –45° conditions, there was no difference with respect to the probability of never making a STT (Fig. 14E; P = 0.29, binomial test) even though each tilted condition differed dramatically from the nontilted condition (P < 0.01, binomial test).

In general, then, these results and those obtained with stationary bars, argue against a major contribution of static geometry and support the idea that the differences in saccade behavior engendered by bars of different relative tilts is largely produced by the discrepancy in local motion signals they present to the visual system.

	DISCUSSION

TOP ABSTRACT INTRODUCTION