The tangent space of a bundle

In dynamic environments, it is crucial to accurately consider the timing of information. For instance, during saccades the eyes rotate so fast that even small temporal errors in relating retinal stimulation by flashed stimuli to extra-retinal information about the eyes' orientations will give rise to substantial errors in where the stimuli are judged to be. If spatial localization involves judging the eyes' orientations at the estimated time of the flash, we should be able to manipulate the pattern of mislocalization by altering the estimated time of the flash. We reasoned that if we presented a relevant flash within a short rapid sequence of irrelevant flashes, participants' estimates of when the relevant flash was presented might be shifted towards the centre of the sequence. In a first experiment, we presented five bars at different positions around the time of a saccade. Four of the bars were black. Either the second or the fourth bar in the sequence was red. The task was to localize the red bar. We found that when the red bar was presented second in the sequence, it was judged to be further in the direction of the saccade than when it was presented fourth in the sequence. Could this be because the red bar was processed faster when more black bars preceded it? In a second experiment, a red bar was either presented alone or followed by two black bars. When two black bars followed it, it was judged to be further in the direction of the saccade. We conclude that the spatial localization of flashed stimuli involves judging the eye orientation at the estimated time of the flash

Is Mislocalization during saccades related to the position of the saccade target within the image or to the gaze position at the end of the saccade?

A stimulus that is flashed around the time of a saccade tends to be mislocalized in the direction of the saccade target. Our question is whether the mislocalization is related to the position of the saccade target within the image or to the gaze position at the end of the saccade. We separated the two with a visual illusion that influences the perceived distance to the target of the saccade and thus saccade endpoint without affecting the perceived position of the saccade target within the image. We asked participants to make horizontal saccades from the left to the right end of the shaft of a Müller-Lyer figure. Around the time of the saccade, we flashed a bar at one of five possible positions and asked participants to indicate its location by touching the screen. As expected, participants made shorter saccades along the fins-in (<->) configuration than along the fins-out (>-<) configuration of the figure. The illusion also influenced the mislocalization pattern during saccades, with flashes presented with the fins-out configuration being perceived beyond flashes presented with the fins-in configuration. The difference between the patterns of mislocalization for bars flashed during the saccade for the two configurations corresponded quantitatively with a prediction based on compression towards the saccade endpoint considering the magnitude of the effect of the illusion on saccade amplitude. We conclude that mislocalization is related to the eye position at the end of the saccade, rather than to the position of the saccade target within the image

Moving your head reduces perisaccadic compression

Flashes presented around the time of a saccade appear to be closer to the saccade endpoint than they really are. The resulting compression of perceived positions has been found to increase with the amplitude of the saccade. In most studies on perisaccadic compression the head is static, so the eye-in-head movement is equal to the change in gaze. What if moving the head causes part of the change in gaze? Does decreasing the eye-inhead rotation by moving the head decrease the compression of perceived positions? To find out, we asked participants to shift their gaze between two positions, either without moving their head or with the head contributing to the change in gaze. Around the time of the saccades we flashed bars that participants had to localize. When the head contributed to the change in gaze, the duration of the saccade was shorter and compression was reduced. We interpret this reduction in compression as being caused by a reduction in uncertainty about gaze position at the time of the flash. We conclude that moving one&apos;s head can reduce the systematic mislocalization of flashes presented around the time of saccades

Schematic overview of two example trials in Experiment 1.

<p>A black fixation dot appears on the screen. After a random interval (range 1100–1300 ms), it is replaced by a black target dot that appears on the screen 7 cm to the right of the fixation dot. Around the time at which the participant makes a saccade to the target dot, a rapid sequence of five bars is presented (one red and four black; 10 ms intervals; one frame each at different locations). The red bar was presented second (left part of the figure) or fourth (right part of the figure) in order. In both these example trials, the red bar was presented about 135 ms after the presentation of the target dot. The target dot had always disappeared by the time the saccade ended. Participants had to indicate where they had seen the red bar, by touching its location with their index finger. The insets show the spatial configurations of these example trials, with numbers indicating orders of presentation.</p

Averaged mislocalization curves for each flash location and figure configuration.

<p>The flash locations are indicated by dashed black lines. Each of the curves was first determined for each participant and shaft length, and then the curves were averaged. The instruction was to make saccades to the end of the shaft of the Müller-Lyer figure (solid black line at 100%). The horizontal arrows at the right side of the figure indicate the average saccade landing positions for the fins-out configuration (dashed arrow) and the fins-in configuration (solid arrow). The grey area shows the average saccade duration.</p

Two examples of saccades in trials in which the participant did not perceive the flash.

<p>Both are for a figure with a 7 cm shaft length in the same session. The primary saccade (grey area) is influenced by the illusion. About 220 ms later, a secondary (corrective) saccade brings the eye to the end of the shaft. The fixation cross was at 0 cm, and t = 0 corresponds to the onset of the primary saccade. The green bar at the top of the figure represents the time for which the Müller-Lyer figure is on the screen.</p

Schematic overview of an example trial.

<p>A fixation cross appears on the screen. After a random interval (range 900–1100 ms), one of the two configurations of the Müller-Lyer illusion (upper right corner) appears on the screen (and remains visible for 500 ms). Around the time at which the participant makes a saccade to the right end of the shaft of the Müller-Lyer figure (about 160 ms after the figure appears), a vertical green bar is presented on the screen for one frame. Participants indicated where they had seen the bar by touching that location with their index finger.</p

A mislocalization curve for one flash location and configuration of the Müller-Lyer figure.

<p>The dots represent the localization of individual flashes presented at various times relative to saccade onset. The curve is a smoothed average of these dots. This example shows data for one participant for flashes at 110% (dashed black line) of a 6.5 cm shaft length of the Müller-Lyer figure with a fins-in configuration. The solid black line at 100% represents the end of the shaft and the grey area shows the average saccade duration.</p

Averaged mislocalization curves for each flash location in the control experiment.

<p>Mislocalization was quantified relative to the equivalent shaft length. Dots were 10% nearer or further than the shaft ends in the main experiment (filled and open circles at the right side of the figure). The flash locations are indicated by dashed black lines. Each of the curves was first determined for each participant and dot position and then the curves were averaged across the two nearer and across the two further dots. The horizontal arrows at the right side of the figure represent the average saccade landing positions for the nearer target locations (solid arrow) and the further target locations (dashed arrow). The grey area shows the average saccade duration.</p

Average mislocalization curves in Experiment 1.

<p>Each thick curve is a smoothed average of the perceived locations of the red bar as a function of its time relative to saccade onset. The transparent areas surrounding these curves indicate the between-subjects standard error of the mean. The horizontal locations of the bars are indicated by dashed thin lines. Subjects made saccades from a fixation dot (at 0 cm) to a target dot (continuous thin line at 7 cm). The grey area shows the average saccade duration. The inset at the lower left shows that subjects were accurate in identifying the red bar: they indicated the vertical location accurately (symbols and error bars indicate the means and standard deviations of the indicated vertical locations when the red bar was presented at each of the five vertical locations that we used, only considering trials in which the red bar was presented during the saccade).</p