We performed the experiments with 149 healthy subjects (62 men and 87 women). Their mean age was 23 ± 1 years (a minimum of 17, a maximum of 63, mode of 19). Most participants were right-handed (>88%), with normal or corrected vision, and with no record of auditory, tactile, visual and motor disorders; also without detectable neurological disorders or history of drug abuse. The participants had different educational degrees (elementary school, n = 7; secondary school, n = 5; high-school, n = 64; college degree, n = 46; master’s degree, n = 16; doctorate degree, n = 7; post-doctorate, n = 4). We performed the experiments with the informed consent of each participant and with the approval of the ethics committee of the Instituto de Neurociencias, Universidad de Guadalajara. Our procedures conformed to the Declaration of Helsinki (1964) established by the World Medical Association. All subjects were naïve to the tasks described in the following section.

For motion psychophysics, we employed a two-alternative, forced-choice, RDM direction discrimination task (Newsome and Pare, 1988; Newsome et al., 1989; Shadlen and Newsome, 2001; Gold and Shadlen, 2003). We programmed the RDM task using the psych-toolbox (Brainard, 1997; Pelli, 1997) for Matlab (TheMathWorks, Inc.; Natick, MA, USA) running on Windows 7 (Microsoft) installed on two standard desktop machines (Dell Precision T3610 Tower Workstation; AMD FirePro W7000). All subjects received written instructions of the task and performed a brief training phase which consisted of obtaining 20 correct consecutive trials. During the training phase, we used auditory tones with pure frequencies to indicate right and wrong choices. We performed all experiments in a silent room.

Each subject performed two blocks of 1000 trials each with a 20 min break between blocks. Figure 1A illustrates the basic paradigm for measuring direction-discrimination consisting on a stimulus of moving dots projected on a black screen on a computer monitor (1024 × 768 pixels @ 60 Hz; viewing distance: 60 cm; we inverted the polarity of black and white colors in Figure 1 to facilitate visualization). The RDM display was black and consisted of a total of 90 white dots (dot size: 2 × 2 pixels = 0.08°) contained within an imaginary square of 13.68° per side placed at the center of the screen, and covering a projection area of 187 deg². The dots moved at 7° s^-1, a certain percentage of them with a coherent direction to either the left or right while the remainder moved with random directions. We initialized the dots with coherent or randomized directions. The dots had limited lifetimes because when they reached the edges of the projection area, they were randomly repositioned along the dimension (x- or y-axis) that was exceeded (yet keeping their trajectories constant). We changed the direction of coherent movement pseudo-randomly on every trial (Treviño, 2014; Herrera and Treviño, 2015). We controlled the strength of motion in the RDM task by changing the relative proportion of dots moving coherently from 0 to 50%. In some trials, we included the presence of additive background white noise (intensities following a uniform distribution, noise size: 1 × 1 pixel = 0.04°), which was refreshed every frame, and had a user-controlled mean luminance (in %). We manipulated the detectability and interference of the RDM stimulus by varying the luminance of the moving dots from 0 to 100% (Pilly and Seitz, 2009; Carandini and Heeger, 2012), and the luminance of the background noise between 0 and 50%, respectively. We optimized our method to sample coherence and luminance by using category intervals based on a logarithmic scale (Gold and Shadlen, 2003; Kiani and Shadlen, 2009).

We used a ‘double receptor design’ in the set of experiments illustrated in Figure 4A. We employed two identical displays separated by a black divider that blocked the line of vision between the eyes (Carmel et al., 2010). With this approach, we explored how the background noise influenced the RDM stimulus at the peripheral visual system (Mori and Kai, 2002; Kitajo et al., 2003).

We recorded the choices and RTs of the subjects on every trial. To indicate their choices, they had to press the ‘M’ button on the keyboard with their right index finger or the ‘C’ button with their left index finger when they perceived the movement to the right or left, respectively (maximum allowed RT of 4 s). We report the %correct responses as the percentage of trials with a particular combination of coherence, dot and noise luminances for which a subject identified the direction of movement in the task. We calculated a %correct choice index (%CCI) by dividing the %correct responses in the presence of noise by the %correct responses with zero noise (ZN; paired trials, see below). We interleaved all ‘noise trials’ with trials with ZN and permuted their temporal order so that the subjects could not predict the testing conditions (Pelli, 1985). This arrangement ensured that the estimation of the %CCI index was insensitive to potential variations in attention during the task because, if existent, those variations would be distributed homogeneously into trials with and without the presence of background noise, from which we extracted the index itself. We varied coherence of the dots, and the luminance of dots and background noise across trials in a pseudo-randomized fashion.

We fitted the %CCI data from individual subjects to two descriptive models (illustrated in Figure 5). Our exclusive aim of making such curve adjustments was to extract and compare individual measures linked to the SR phenomenon across subjects. The first model corresponded to an adaptation of a general SNR curve as a function of noise intensity (l_i), as follows:

where A represents the amplitude of a periodic signal, w_n is the upper cutoff frequency of the noise, Δ₀ is the difference between the mean of the subthreshold stimulus and the threshold, g is a gain variable, and l^∗ is a translation constant (Moss et al., 2004). In the second model, we approximated the SNR function by adding a logistic curve to a Gaussian distribution, as follows:

Where L is the maximum value of the logistic function, k is the slope of the curve, c^∗ is the x-value of the sigmoid’s midpoint, Amp is the amplitude of the Gaussian with a Δ mean and Δ standard deviation. We employed standard non-linear programming techniques to fit the experimental data to both of these models (Treviño, 2015).

We report and illustrate all results as averages ± SEM. We used parametric and non-parametric tests with significance set at P < 0.05 for statistical comparisons.

We established the conditions to quantify motion discrimination performance in adult humans. We employed a RDM task originally introduced by Newsome and Pare (1988; see Materials and Methods). It consisted on projecting 90 white moving dots on a black screen and requesting the experimental subjects to report their perceived direction of overall movement when a fraction of the dots moved coherently to the left or right, while the remainder of the dots moved in random directions (Figure 1A). We manipulated the task difficulty by adjusting the percentage of coherently moving dots (Gold and Shadlen, 2007) and plotted the averaged psychometric curves as a function of stimulus coherence (x-axis) and luminance (colored lines in Figures 1B,C; legend on the inset of Figure 1C). The psychometric curves of the subjects had an average peak performance of 91.93 ± 2.50%, a midpoint of 8.65% ± 1.05% luminance and a slope of 23.78 ± 2.52 (%c/%luminance). The peak performance of these response curves had a marked sensitivity to gradients in the luminance of the stimulus at or below 12% (blue line in Figure 1B).

We conducted these initial experiments under a ‘free response’ paradigm: we instructed the subjects to discriminate motion direction as best as they could and allowed them to control their decision time autonomously (Treviño et al., 2012, 2013; Treviño, 2014). Under this condition, accuracy rates and RTs vary as a function of task conditions, leading to predictable changes in the probabilities of these two output parameters (Smith and Ratcliff, 2004; Treviño et al., 2013). For example, a shift from speed to accuracy instructions can result in slower yet more accurate responses, whereas the opposite instructions usually decrease the choice accuracy but involve shorter sampling intervals (‘speed-accuracy tradeoff’). We found that the averaged RTs exhibited a monotonic decrease linked to an increase in the stimulus coherence and luminance (Figure 1C). Indeed, the mean RTs dropped with increasing coherence from 5 to 50% (RT with 5% coherence: 1.01 ± 0.05 s; RT with 50% coherence: 0.80 ± 0.02 s; Kruskal–Wallis test, F_1,12 = 6.20, P < 0.001). This result reflects that the rate of accumulation of discriminative information depends on the difficulty of the task (Gold and Shadlen, 2007; Treviño et al., 2013). Hence, decreasing stimulus discriminability increased the error rates, delaying and dispersing the RT distributions (Smith and Ratcliff, 2004).

We wondered how the averaged RTs (extracted from those randomized trials with identical coherence and luminance levels) related to the probability of making correct choices under conditions with variable difficulty. We plotted the averaged RTs derived from correct (green dots) and incorrect (red dots) choices as a function of the probability of making a correct choice (‘%Correct,’ i.e., the number of correct choices divided by the total number of trials for that combination of stimulus attributes; Figure 1D). This plot revealed an inverted bell-shaped pattern of RTs vs. %correct choices, with smaller averaged RTs associated with ‘easy’ and ‘difficult’ task conditions (Smith and Ratcliff, 2004). The peaks of both of these bell-shaped curves occurred at 71% of correct choices and had a 12–20% increase in the averaged RTs compared to those obtained when choosing randomly (i.e., at chance level). We also confirmed that the subjects made all their choices in steady-state throughout the course of the experiment (repeated measures ANOVA test, P > 0.5; red dots: stimulus coherence = 50%, stimulus luminance = 100%; black dots: an average of all conditions; Figure 1E). Using this task, we were able to indirectly control the steady-state response accuracy of the subjects by simply adjusting the coherence levels of the RDM stimulus.

To explore how external visual noise interacted with visual motion perception, we developed the computational tools that allowed us to combine dynamic background pixel-noise (refreshed every frame) with the standard and widely used RDM task (Newsome and Pare, 1988; Figure 2A; see Materials and Methods). We asked how adding such noise with different luminance levels influenced the choice performance of naïve subjects solving the RDM task. We tested 13 new participants in conditions where the visual stimulus barely produced a perception of global motion (coherence = 5%; luminance = 25%; correct choices: 63.20 ± 2.48%, one way ANOVA test, P = 0.03; Figure 1B; Newsome et al., 1989). After performing the experiments, we calculated the group averaged %correct choice index (%CCI) as a function of the luminance of the additive background noise. We took the %CCI index as the amount of %correct choices obtained in the presence of noise divided by those obtained in its absence. The group averaged %CCI revealed a bell-shaped distribution with a peak sensitivity of 6.5 ± 1.8% at a moderate noise luminance of 5% (paired t-test, P < 0.001; Figure 2B; green dot, upper panel). This response pattern resembled a SR-like phenomenon, and the peak value in the %CCI function was consistent with previous SR observations (Zeng et al., 2000; Ward et al., 2002). Regarding the stimulus presentation sequences, we paired the test trials for each specific noise luminance condition with trials lacking noise (see Materials and Methods). This arrangement ensured that the task provided no temporal information about the stimulus (Pelli, 1985), and allowed us to estimate the %CCI independently of possible variations in choice performance due to attentional shifts (or any other factors; Smith and Ratcliff, 2004; Treviño, 2014). We used 100 repetitions per noise luminance.

Because the performance solving the RDM task was highly variable across subjects, we quantified the group response variability by using an index of dispersion known as the Fano factor (the variance of the %CCI values extracted from single subjects divided by their mean). The Fano factor is a normalized measure of the dispersion of a distribution and is useful to capture the degree of randomness of a given phenomenon, as it quantifies how clustered or dispersed are a set of observations. This analysis revealed that the luminance of the visual noise strongly modulated the Fano factor of the %CCI in the RDM task. Indeed, the index was close to 1 when using ZN, yet it dropped and had a local minimum with a background luminance of 5% (under-dispersed values) and then increased above 1 for larger background luminance levels (over-dispersed values). The reduction in the Fano factor was maximum around the same background luminance noise value that elicited the %CCI peak (Figure 2B; middle panel). Moreover, as an increase in RTs could explain the improved choice performance (Smith and Ratcliff, 2004), we compared the averaged RTs from trials performed under different noise luminances but found no differences across them (Figure 2B; lower panel; paired t-test, P > 0.05 for all cases).

We next wondered whether this SR-like phenomenon in motion discrimination operated at a perceptual level. We reasoned that if a small amount of perceived visual noise is capable of improving the subjects’ performance in the RDM task, then this effect should be absent in those trials that led to incorrect choices. Such lack of effect should be particularly evident in those error trials with smallest RTs, when the subjects made their choices at random (Smith and Ratcliff, 2004; Treviño, 2014). We calculated the %incorrect choice index (%ICI) from error trials produced in the presence and absence of background noise, but only from those that had RTs below the median. Confirming our hypothesis, we found that the %ICI extracted from these error trials was insensitive to the external noise (gray squares in Figure 2B, upper panel). Notably, the frequency distributions of RTs for correct and incorrect choices had similar shapes (Figures 2C,D). Therefore, we can discard possible misrepresentations of the averaged RTs due to their skewed distributions because (i) the number of trials involved in calculating the %errors in the presence and absence of noise was practically identical, and (ii) both distributions exhibited similarly skewed distributions before the computation of %CCI and %ICI indexes (Whelan, 2008). Altogether, these results demonstrate that an intermediate amount of background noise can increase the %CCI but not the %ICI in the RDM task via a SR-like phenomenon.

We explored whether the SR phenomenon was reproducible across two new variants of the RDM task. The first variant consisted in fixing the stimulus viewing interval to 1 s (i.e., the test trials involved a whole second of stimulus projection, w. coherence = 5% and luminance = 25%). With this setting, we sought to narrow down the variance in the RT distributions, and thereby reduce the possibility that RTs and %CCI were correlated. We conducted experiments in new subjects and obtained a similar bell-shaped %CCI curve with a maximum increase of 5.5 ± 1.5% at a noise luminance of 5% (n = 13 subjects; paired t-test, P < 0.001; Figure 3A). Next, we explored whether and how the noise affected the RTs from subjects. Many data distributions can lead to similar appearances when represented with bar-plots, which further invalidates their usage for small datasets. We therefore decided to illustrate the choice and RT data by using scatter plots with the reference (i.e., ZN), on the left, and noise condition, on the right, connected with lines representing each subject (Figures 3B,D). In these plots, we can visualize the variability in the performance with the ZN condition across subjects (i.e., each dot represents information from a single subject). Using a paired t-test, we confirmed the lack of change in the RT distributions for all levels of noise luminance tested (P > 0.05 for all cases; Figure 3B). Therefore, the improvement in the %CCI of the RDM task produced by adding background noise cannot be explained by increased sampling intervals.

For the second variant of the task, we first tested four additional stimulus coherence values (two above, and two below 5% coherence) and four additional stimulus luminance levels (two above, and two below 25% luminance). We found that switching the stimulus coherence from 5 to 8% boosted the %CCI by about 4.5 ± 0.3% (Kruskal–Wallis test F_4,494 = 392.38, P < 0.001; 25 subjects bootstrapped to 100 cases; not illustrated) whereas using a 50% stimulus luminance increased the %CCI by 2.9 ± 0.3% (against a stimulus luminance of 25%; Kruskal–Wallis test F_4,494 = 253.56, P < 0.001; 25 subjects bootstrapped to 100 cases; not illustrated). Taking this information into account, we conducted a new round of experiments on 19 naïve subjects and characterized their %CCI curves when solving the RDM task with 8% of motion coherence and a stimulus luminance of 50% (i.e., ‘optimized’ stimulus parameters; Figure 3C). The corresponding averaged %CCI curve had a peak of 7.4 ± 1.2% at a noise luminance of 5%, but a decrease of 4.9 ± 2.6% with 25% noise luminance (paired t-test, P < 0.0001). There was no change in averaged RTs for all levels of noise luminance tested (paired t-test, P > 0.05; Figure 3D). Remarkably, the %CCI peaks for open RT (Figure 2B), fixed RT (Figure 3A) and ‘optimized conditions’ (Figure 3C) were quite similar to each other (Kruskal–Wallis F_2,41 = 1.33, P = 0.51). These results demonstrate that the SR-like phenomenon in the RDM task is reproducible across different experimental settings. It is likely that the %CCI peaks were already saturated at 5% luminance noise in the three conditions tested.

In the previous experiments, we presented noise and stimulus signals identically to both eyes. This arrangement is commonly referred to as a ‘single receptor design.’ Under these conditions, the noise and signal interact in the retina and throughout the entire peripheral visual system. A possible explanation for the SR improvement in visual motion discrimination is that the noise enhances the peripheral receptors sensitivity (Mendez-Balbuena et al., 2012), increasing the amplitude of the signal which then percolates to the entire visual system (Moss et al., 2004; Flores et al., 2016), and improves sensorimotor integration (Rodriguez et al., 1999). An alternative, however, could be that this form of SR takes place at a non-retinal location. Interestingly, studies on humans have shown that some forms of visual perceptual learning can be detected by the confluence of inputs from separate eyes (Ball and Sekuler, 1987; Gilbert et al., 2001). These empirical observations motivated us to explore the anatomical locus of the SR-like phenomenon in the RDM task. We first implemented the conditions to conduct an experiment with a so-called ‘double receptor design’ (Mori and Kai, 2002; Kitajo et al., 2003). We modified the montage of the first RDM apparatus by using two monitors, separated by a black divider centered at the midline of the viewing field. We applied the noisy signal to one eye, and the stimulus signal to the other eye, excluding the possibility of peripheral SR elicited in the eyes or retinas (‘optimized’ stimulus parameters: coherence = 5%; luminance = 25%; Figure 4A; see Materials and Methods). This approximation guaranteed that if the choices of the volunteers still exhibited SR under these conditions, then it would be centrally produced, in relays located after the optic chiasm, presumably in the primary visual cortex where the noise and stimulus signals first converge (Mori and Kai, 2002).

We performed experiments in 28 new subjects some of which received the visual stimulus to their left eye (n = 16) while others received it on their right eye (n = 12). We found similar %CCI peaks when providing the RDM stimulus to either the left (gray circles) or right (black circles) eye, indicating that the side of the eye that received stimulation did not affect the SR phenomenon (Figure 4B). We averaged the %CCI curves associated with the RDM projected to both eyes to obtain a global signature of the SR phenomenon using the double receptor design (Figure 4C). The resulting averaged %CCI curve had a peak of 5.3 ± 1.6% at a noise luminance of 5% (paired t-test, P < 0.0001) but an %CCI ≈1 when using 25% noise luminance. We quantified the amount of ‘inter-ocular SR’ by taking the ratio of the peak from the averaged %CCI curve obtained with the double receptor design (Figure 4C) to the one we observed with the single receptor design (Figure 3C). The amount of ‘inter-ocular SR’ was 70%, indicating that this phenomenon had monocular and binocular components, yet the latter was considerably larger (Ball and Sekuler, 1987). Therefore, the SR-like phenomenon in the RDM task mainly occurred at (or after) a stage in the visual system where binocular inputs interact (i.e., a stage higher than layer IV of the primary visual cortex Schoups and Orban, 1996).

Our results demonstrate that the peak amplitude of the averaged SR curves depends on both the coherence of the RDM stimulus and the luminance of the background noise. Does the %CCI data from subjects contain individual differences in their corresponding measures for noise luminance and %CCI peaks? We compared our experimental results with the theory of SR by using an equation that describes the SR phenomenon itself. We did these adjustments exclusively to extract and compare SR-dependent measures across subjects. Thus, we adapted a model proposed by Moss et al. (2004; model 1; see Materials and Methods) and made non-linear fits to the %CCI data from 45 subjects that were involved in the experiments described and illustrated in Figures 2 and 3. We show the non-linear fits to nine sample cases in Figure 5B (shaded panels). From these analyses, we took the optimized parameters from each subject and constructed the cumulative probability distributions for the obtained fits for w_nA² (proportional to the peak of the %CCI curve) and Δ₀ (proportional to the luminance at which the %CCI curve peaked; see Materials and Methods for more details). These two parameters spanned over a broad range of values and displayed a variance of normalized indexes of 5.6 and 4.9%, respectively, revealing strong differences in the SR-like phenomenon across subjects. We included a second descriptive model to extract direct measures for the peak amplitude and noise luminance linked to the %CCI peak from each subject (see Materials and Methods). We made a non-linear fit (black trace) that involved the sum of a Gaussian distribution (blue trace) with a logistic function (red trace; Figure 5D). From these fits, we extracted the luminance peaks and %CCI amplitudes for all the subjects. In Figure 5E, we illustrate the non-linear fits to data from nine sample subjects (shaded panels; same data as in Figure 5B). Although, these fits produced smaller errors (Kruskal–Wallis F_2,86 = 66.75, P < 0.001), they still presented a broad range of peak values and optimal noise luminance, confirming the strong diversity in the underlying %CCI curves (variance of normalized indexes of 4.9 and 2.5%, respectively; Figure 5F). Notably, the %CCI peak amplitudes (Figure 5F, upper panel) and mean noise luminances at peak (Figure 5F, lower panel) were poorly correlated (R² = 0.06, n = 45). These results indicate that the %CCI curves exhibited different profiles, with strong diversity among individuals. The existence of small peak %CCI amplitudes reveals that at least some subjects did not display strong SR-like effects.

Finally, we tested the contribution of 19 individual characteristics such as age, sex, and years of education (among other factors; see Table 1) on the estimated peak amplitude and noise luminance at peak %CCI derived from the second predictive model (see Materials and Methods). We asked whether any of these characteristics from the subjects could predict properties from their %CCI curves. We indexed and grouped these properties by using a median split of the amplitude at luminance (Table 1A) or the noise luminance at peak (Table 1B) extracted from each subject and made statistical comparisons between ‘lower’ and ‘higher’ performers (Treviño, 2014). We found no differences between groups indicating that none of the individual factors that we characterized predicted the SR-like phenomenon in the RDM task (Table 1).