Stimulus dependence of the flash-lag effect

Abstract

When two moving objects are presented in perfect alignment, but are not visible for the same amount of time, the briefer object will often be perceived as "lagging" the object of greater duration. Most investigations of this flash-lag effect (FLE) employ high velocity broadband stimuli, such as lines or dots with sharp boundaries and flashes with rapid onset and offset. We introduce a stimulus paradigm with narrow-band stimuli and measure the stimulus dependence of the FLE when basic stimulus parameters of spatio-temporal frequency and temporal duration are varied. We suggest that this dependence is consistent with the involvement of early visual mechanisms and interpret our results in the context of existing theories of the FLE.

Figure 1. Stimulus Construction and Spatio-temporal Frequency Content

(A) Our Gabor FLE stimulus as seen by the observer in a sequence of screenshots. The briefer stimulus is presented above the fixation point, while more continuous stimulus is presented below. The observer’s task is to judge the vernier offset between the two gratings. In these images, the gratings are perfectly aligned and moving to the right, but due to the Flash-lag effect, the observer would probably perceive the top grating as displaced to the left (the bottom grating leading in the direction of motion). (B) Space-time schematic representation of the stimulus construction (in one spatial dimension) of the Gabor FLE stimulus, as compared to a typical FLE stimulus. The space-time (XT) plots on the left represent two 1D patterns drifting at a fixed velocity. The typical FLE stimulus is a drifting line (or bar). The Gabor stimulus is a drifting sine wave windowed with a stationary Gaussian spatial envelope. In the middle panel, the XT plots are windowed with temporal envelope profiles to generate the “flash” and “moving” object. In the Gabor FLE paradigm, the profiles are temporal Gaussians of differing widths, while the typical FLE paradigm uses a single-frame exposure vs. a continuous presentation of the “moving” object. This windowing produces the stimulus representations (pairs of XT plots) in the right panel. (C) The stimulus construction in (B) is shown in the Fourier (frequency) domain to give an idea of the spatio-temporal energies in the stimuli and how they are produced. The typical FLE stimulus is spatially broadband to begin with (left panel) whereas the Gabor FLE stimulus has a very narrow concentration of energy (left panel). The temporal envelopes used in windowing the stimulus spread energy along the temporal frequency axis. This causes a large smearing of the energy spectrum for the “flashed” stimulus in the typical FLE paradigm (middle and right panels). Compared to the typical FLE stimuli, the Gabor FLE paradigm allows us to concentrate the spatio-temporal energy in the stimuli, in order to target subsets of low-level visual mechanisms.

Figure 2. Velocity Dependence of the FLE

(A) Data for three subjects is plotted as a function of log temporal frequency and velocity. The thick line represents the grand average of their observations. Stimuli have a carrier spatial frequency of 0.5 cpd, and maximum contrast was 50% with a background luminance of 5.8 cd/m². Measured in temporal units, the magnitude of the FLE is reduced as temporal frequency or velocity increases, rather than remaining constant. (B) Data from a control experiment, plotted individually for two subjects. Maximum contrast was still 50% but we used a different background luminance (29 cd/m²). The moving object in these plots has the same duration (σ = 120 ms). Two types of flashes are used – the dashed blue line corresponds to a flashed object whose temporal envelope ramps on and off with a Gaussian profile (σ = 24 ms), while the solid red line corresponds to a stationary single-frame flash (~20 ms exposure). The results do not show significant differences between the FLE magnitudes for static single-frame flash paradigm and our Gabor FLE stimulus paradigm. The control experiment also confirms our expectation that the nature of the flash (stationary vs. moving) does not affect the pattern of stimulus dependence. Error bars represent the standard deviation of measured PSE, as returned by our adaptive staircase method.

Figure 3. Comparison of Velocity Dependence Data

Reports of linear velocity dependence (constant ETD) in the literature are based on experiments covering a large range of velocities. Here, data that address the velocity dependence of the FLE are converted into units of ETD and plotted as a function of the tangential velocity of the rotational stimulus (x-axis in log units). Two sets of data are taken from Figure 3 in Krekelberg and Lappe (1999) and one set is taken from Figure 9b in Krekelberg and Lappe (2000). The grand average of our Experiment I (open circles) is reproduced in this axis for comparison, falling in the middle of the range spanned by the other data sets. While the data sets represent results taken with different stimuli, the aggregate data shows that these studies do not contradict one another on the question of velocity dependence; instead they suggest over a low velocity ETD generally decreases, and at higher velocities, the reduced ETD remains fairly constant.

Figure 4. Effect of Relative Stimulus Duration

For a .5 cpd stimulus moving at 2 deg/sec, effects of relative stimulus duration are plotted. Durations are manipulated by changing the standard deviation of Gaussian temporal envelope of a grating patch: (A) The more continuously presented Gabor pattern is set to the longest interval: σ = 200 ms (indicated by the reference arrow in the plot). As the duration of the flashed stimulus is increased, data for all subjects shows a rapid decrease in the magnitude of the Flash Lag Effect, with the flash becoming ineffective at durations above σ = 60 ms. (B) The duration of the more transient stimulus is fixed at the briefest interval: σ = 24 ms (indicated by reference arrow in plot). When the duration of the more sustained Gabor pattern is increased, the FLE magnitude gradually increases and plateaus at values above σ = 120 ms. In both plots, when the temporal durations are equal the two patterns to be compared are completely identical, so it is technically impossible for there to be an effect. For this reason, data has not been collected for all subjects in the longest flash duration condition (the point at σ = 200 ms is not significantly different from zero). Error bars represent the standard deviation of measured PSE, as returned by our adaptive staircase method.

Figure 5. Dependence on Stimulus Spatial Frequency

Data for carrier gratings at 3 spatial frequencies (0.25, 0.5, and 1 cpd) drifting at three velocities (1, 2, and 4 deg/sec) is plotted in terms of velocity (A) and temporal frequency (B), showing that neither stimulus property accounted for variance in FLE when different spatial frequencies were used. This suggests a separate spatial frequency dependence of the FLE (in addition to the velocity/temporal frequency dependence of the effect). The data also suggest an interaction between the velocity dependence of the FLE and the carrier spatial frequency. At 0.25 cpd and 0.5 cpd the magnitude of the FLE decreases as observed in Experiment I. At 1 cpd, the stimulus dependence is no longer significant, and the profile describing velocity dependence remains fairly flat. Error bars represent the standard deviation of measured PSE when observer data is combined.