Fig 1.
Panel (a) shows example stimuli with conflicting orientations, surrounded by a Voronoi texture to aid binocular fusion. Panel (b) shows example waveforms used to modulate stimulus contrasts at the five temporal frequencies used in the experiment. Panel (c) shows example trial timecourses for two repetitions of an unmodulated condition (left) and a modulated condition (right) in which the two external noise sequences were independent. Red (green) regions in the lower two plots indicate periods of time when the left (right) eye’s stimulus was perceived. Note that in the example on the right, percepts closely followed the physical contrast with a slight lag.
Fig 2.
(a) Model diagram of the two competing units. Each receives as input an independent white noise stream, bandpass filtered at one of five different temporal frequencies (see Methods). The minimum rivalry model [4] defines the oscillatory behaviour of rivalry between two units with self-adaptation and mutual inhibition. We include additive internal independent monocular noise in our model, marked by the (+) symbols. (b) Examples of the five different internal noise spectral slopes (ɑ = 0–2.0) of the model for the left (green) and right (red) responding units. Noise streams with steeper slopes have an increased relative amplitude of low temporal frequencies relative to high, which leads to slower changes in the noise amplitude. (c) Example oscillatory behaviour of the model for a given trial (60s). The colours represent the responses of the left (green) and right (red) responding units.
Fig 3.
Traditional rivalry measures for all conditions, averaged (or pooled) across all participants (N = 5).
Panel (a) shows histograms of pooled dominance durations at five temporal frequencies (i-v) and a range of contrast levels (standard deviations of 0–16% contrast, increasing down each plot). The grey histogram, duplicated in each plot, shows the baseline condition with no contrast modulation. For low temporal frequency, high contrast modulations, there were more very long dominance periods (the positive skew of the red histogram increases). For high temporal frequency, high contrast modulations there were more short dominance periods, and the histograms shifted left. Panel (b) shows mean dominance durations for all conditions, plotted as a function of modulation contrast. The grey horizontal line shows the baseline (no modulation) condition. Error bars (and dotted lines) show ±1SE across participants. Panel (c) shows autocorrelation functions (e.g. the correlation between a participant’s percept at a given moment, as in Fig 1C, with their percept at subsequent moments) averaged across participants for the baseline condition (grey curve) and the highest contrast modulation at each temporal frequency (curves, see panels a,b for colour legends). Panel (d) shows the cross correlation between the participants’ responses and the difference in noise modulations at the highest modulation contrast, averaged across all modulation frequencies. The thin grey lines denote individual participants and the thick black line is the average.
Fig 4.
Response consistency across two passes through the experiment.
The same data are plotted in both panels, as a function of modulation contrast (a) or temporal frequency (b). In each panel, the thick grey line represents the baseline (no modulation) condition, colours represent different temporal frequencies, and symbol types represent different contrasts. All data points are averaged across participants, with error bars indicating ±1SE of the mean. The dashed horizontal line at y = 0.5 indicates a theoretical baseline in the absence of any response bias or eye dominance effects.
Fig 5.
Summary of model behaviour for internal noise amplitude and spectral slope estimation.
(a) The histograms of dominance durations for each spectral slope (ɑ = 0.0–2.0) and level of internal noise (SD = 1%– 64%). Within each subplot, the uppermost (green shaded) histogram shows the equivalent human data for a stimulus temporal frequency of 1/8Hz and a contrast modulation of SD = 16%. The solid vertical green line marks the average dominance duration for human observers. Histograms below show model dominance duration distributions for each internal noise level. (b) Average dominance durations of the model for each spectral slope (coloured lines). The green line and shaded area mark human average dominance duration and ±1SE of the mean, respectively. Average dominance duration was affected by internal noise once its standard deviation was equivalent to 4% contrast. Noise with steeper slopes (ɑ = 1.5–2.0) increased mean dominance duration as a function of noise contrast, while noise with shallower slopes decreased mean dominance duration. (c) Response consistency decreased as a function of internal noise contrast for all spectral slopes. The green line and shaded area mark human observer average consistency and ±1SE of the mean, respectively. For all ɑ>0, response consistency reached human levels at an internal noise contrast of 16%.
Fig 6.
(a) Histograms of dominance durations of the model with pink (ɑ = 1) internal noise of with a standard deviation of 16% for each stimulus temporal frequency (i-v) and contrast SD. The solid line colour serves as a legend for the stimulus noise temporal frequency (red = 1/16Hz, green = 1/8Hz, blue = 1/4Hz, yellow = 1/2Hz, purple = 1Hz). The histogram marked in grey represents baseline dominance durations with no contrast modulation. (b) The mean dominance durations of the histograms in (a). Marker colour represents the modulation temporal frequency, while the x-axis gives the modulation contrast. The grey line marks the baseline dominance duration of the model (3.18s), slightly slower than that of the human data. (c-d) Model response consistency plotted in the same manner as Fig 4. In (c), marker colour indicates the modulation temporal frequency while the x-axis indicates the modulation contrast. For all stimulus frequencies, response consistency increased according to modulation contrast, and was greatest when the stimulus temporal frequency was 1/8Hz. (d) Identical data but plotted with modulation temporal frequency on the x-axis. The grey line (c,d) marks response consistency at baseline with no external noise fed to the model (0.49).
Fig 7.
Summary of further conditions testing antiphase modulation and monocular rivalry.
Panel (a) shows response consistency predictions of the model for independent (green circles) and antiphase (brown squares) external noise (modulation temporal frequency = 1/8Hz). Panel (b) shows the human response consistency for the same conditions as (a). Panel (c) shows histograms of human dominance durations in the same format as Fig 3A, with the unmodulated rivalry condition shown at the top in grey. Panel (d) shows the response consistency of the model when the oscillatory mechanism is removed and modulations are driven by internal and external noise only (cyan diamonds) versus the response consistency for the main model (green circles). Panel (e) shows human response consistency to the monocular rivalry condition (cyan diamonds) compared with that of the main experiment (green circles). Panel (f) shows human dominance duration histograms for the monocular rivalry condition. Error bars and dotted lines show ±1SE across participants (N = 4; for the conditions from the main experiment, we omitted results from the participant who did not complete the additional conditions when constructing this figure).