Figure 1.
Afterimage rotation in the peripheral drift illusion.
(A) The Fraser-Wilcox (FW) stimulus, which was used by Faubert and Herbert [2], [3]. (B) Illusory clockwise (light-to-dark) rotation is seen in the afterimage when the FW stimulus disappears from the light background. (C) Illusory counterclockwise (dark-to-light) rotation in the afterimage is seen on the dark background.
Figure 2.
A visual time-series stimulus (I(t)) was assigned to a certain receptive field of the retina. The retinal units (neurons) included in the receptive field, which have a biphasic temporal impulse response (TIR) function (g(t)), produced two types of time-series responses: ON- and OFF-type (fON (t) and fOFF(t), respectively). These responses are assumed to be integrated at higher levels of the visual system.
Figure 3.
The retinal ON/OFF model produced afterimage rotation of the FW stimulus on the light background.
(A) Input. A quarter of the FW stimulus suddenly disappeared and was replaced by the light background at 0 s. (B) Output after the disappearance of the FW stimulus. Red lines indicate the focus lines for which the ON- and OFF-type responses showed comparable values. (C) Time courses of input. Each marked line corresponds to the input time-series (in terms of the luminance level) at the marked position in (A). (D) Time courses of outputs from the ON- and OFF-type units (top). Each colored line represents the output in response to the input with the same color as in (C). Red lines and points indicate the focus lines and points. Schematic drawings of outputs at 0 s (a), 0.15 s (b) and 0.45 s (c) (bottom). Focus lines rotated slightly counterclockwise from 0 s (thin red lines) to 0.15 s (red lines) (b), then prominently rotated clockwise from 0.15 s (thin red lines) to 0.45 s (red lines) (c). The red marked points in (c) correspond to the three red points in the top panel.
Figure 4.
The direction of the afterimage rotation was examined by varying the background luminance.
(A) Diagram of the human psychophysical experiment. In the gaze period (4 s), the FW stimulus and the fixation cross were both presented on the background with a specific luminance. After the gaze period, both the FW stimulus and the fixation cross disappeared, but the background was not changed. The participants were instructed not to move their eyes during this afterimage period (1 s). (B) Probability of seeing clockwise rotation (by the three observers: Y.H., S.S., and R.O.). Each psychometric curve was individually fitted with a cumulative Gaussian function by means of a least squares method. The means (μ) of the Gaussian functions are given with their 95% confidence intervals. (C) Representative rotation velocity of the retinal ON/OFF model when changing the background luminance (original). Those from the modified model based on Weber's law were also plotted (a = 1, a = 0.5 and a = 0.25, dashed lines). The relative luminance levels that gave a zero-rotation velocity were 0.38, 0.27 and 0.12 for a = 1, a = 0.5 and a = 0.25 respectively, and 0.5 for the original.
Figure 5.
Velocities of the afterimage rotation on the light background.
(A) Diagram of the human psychophysical experiment. In the gaze period (4 s), the still image of the FW stimulus, the reference rotating FW stimulus, and the fixation cross were presented on the light background, on which the locations of the still and reference FW stimuli were randomly allocated to the left or right. After the gaze period, the still FW stimulus disappeared, but the reference stimulus and the fixation cross remained. The observers were instructed to fixate on the fixation cross during this afterimage period (1 s) and then to report whether the perceived velocity of the afterimage of the absent FW stimulus was faster or slower than that of the reference stimulus. (B) Probability of seeing slower afterimage rotation than the reference rotation (the three observers: Y.H., Y.A., and T.M.). Each psychometric curve was fitted individually with a cumulative Gaussian function by means of a least squares method. The means (μ) of the Gaussian functions are given with their 95% confidence intervals. (C) Representative rotation velocity of the retinal ON/OFF model when changing the background luminance. The profile of the rotation velocity, which increased with time, is shown as a grey area. Three marks indicate the rotation velocities obtained in the psychophysical experiment (marks correspond to those in (B)).
Figure 6.
The focus lines correspond to specific equiluminance lines in the light adaptation model, which are characterized by small standard deviations in the performance of the retinal ON/OFF model.
Inputs to both the retinal ON/OFF model and the light adaptation model were the same (Fig. 3(A)) on the light background. (A) Outputs of the retinal ON/OFF model. Red lines indicate the focus lines, which were accompanied by small standard deviations of the ON- and OFF-type responses. (B) Output of the light adaptation model . Cyan lines represent typical equiluminance lines. (C) Time development of the angles (rotations) of the focus line (red line) and equiluminance lines (blue lines, for different equiluminance levels) where the angle θ was specified in the left panel. The thick blue line corresponds with the example equiluminance lines in (C).