Spatial frequency tuned covariance channels for red-green and luminance-modulated gratings: psychophysical data from human infants

Sensorimotor mechanisms selective to numerosity derived from individual differences

We have previously shown that after few seconds of adaptation by finger-tapping, the perceived numerosity of spatial arrays and temporal sequences of visual objects displayed near the tapping region is increased or decreased, implying the existence of a sensorimotor numerosity system (Anobile et al., 2016). To date, this mechanism has been evidenced only by adaptation. Here, we extend our finding by leveraging on a well-established covariance technique, used to unveil and characterize 'channels' for basic visual features such as colour, motion, contrast, and spatial frequency. Participants were required to press rapidly a key a specific number of times, without counting. We then correlated the precision of reproduction for various target number presses between participants. The results showed high positive correlations for nearby target numbers, scaling down with numerical distance, implying tuning selectivity. Factor analysis identified two factors, one for low and the other for higher numbers. Principal component analysis revealed two bell-shaped covariance channels, peaking at different numerical values. Two control experiments ruled out the role of non-numerical strategies based on tapping frequency and response duration. These results reinforce our previous reports based on adaptation, and further suggest the existence of at least two sensorimotor number channels responsible for translating symbolic numbers into action sequences.

Applying Resampling and Visualization Methods in Factor Analysis to Model Human Spatial Vision

Purpose

Studies have reported different numbers of spatial frequency channels for chromatic and achromatic vision. To resolve the difference, we performed factor analysis, a multivariate modeling technique, on population data of achromatic and chromatic sensitivity. In addition, we included resampling and visualization methods to evaluate models from factor analysis. These routines are complex but widely useful. Therefore we have archived our analysis routines by building smCSF, an open-source software package in R (https://smin95.github.io/dataviz/).

Methods

Data of 103 normally-sighted adults were analyzed. They included blue-yellow, red-green, and achromatic contrast sensitivity. To obtain the confidence interval of relevant statistical parameters, factor analysis was performed using a resampling method. Then exploratory models were developed. We then performed model selections by fitting them against the empirical data and quantifying the quality of the fits.

Results

During the exploratory factor analysis, different statistical tests supported different factor models. These could partially be reasons for why there have been conflicting reports. However, after the confirmatory analysis, we found that a model that included two spatial channels was adequate to approximate the chromatic sensitivity data, whereas that with three channels was so for the achromatic sensitivity data.

Conclusions

Our findings provide novel insights about the spatial channels for chromatic and achromatic contrast sensitivity from population data. Also, the analysis and visualization routines have been archived in a computational package to boost the transparency and replicability of science.

When illusions merge

We recently found only weak correlations between the susceptibility to various visual illusions. However, we observed strong correlations among different variants of an illusion, suggesting that the visual space of illusions includes several illusion-specific factors. Here, we specifically examined how factors for the vertical-horizontal, Müller-Lyer, and Ponzo illusions relate to each other. We measured the susceptibility to each illusion separately and to combinations of two illusions, which we refer to as a merged illusion; for example, we tested the Müller-Lyer illusion and the vertical-horizontal illusion, as well as a merged version of both illusions. We used an adjustment procedure in two experiments with 306 and 98 participants, respectively. Using path analyses, correlations, and exploratory factor analyses, we found that the susceptibility to a merged illusion is well predicted from the susceptibilities to the individual illusions. We suggest that there are illusion-specific factors that, by independent combinations, represent the whole visual structure underlying illusions.

Individual Variability in Simultaneous Contrast for Color and Brightness: Small Sample Factor Analyses Reveal Separate Induction Processes for Short and Long Flashes

In classic simultaneous color contrast and simultaneous brightness contrast, the color or brightness of a stimulus appears to shift toward the complementary (opposite) color or brightness of its surrounding region. Kaneko and colleagues proposed that simultaneous contrast involves separate "fast" and "slow" mechanisms, with stronger induction effects for fast than slow. Support for the model came from a diverse series of experiments showing that induction by surrounds varying in luminance or color was stronger for brief than long presentation times (10-40 vs. 80-640 ms). Here, to further examine possible underlying processes, we reanalyzed 12 separate small data sets from these studies using correlational and factor analytic techniques. For each analysis, a principal component analysis of induction strength revealed two factors, with one Varimax-rotated factor accounting for brief and one for long durations. In simultaneous brightness experiments, separate factor pairs were obtained for luminance increments and decrements. Despite being based on small sample sizes, the two-factor consistency among 12 analyses would not be expected by chance. The results are consistent with separate fast and slow processes mediating simultaneous contrast for brief and long flashes.

Individual differences in visual science: What can be learned and what is good experimental practice?

We all pass out our lives in private perceptual worlds. The differences in our sensory and perceptual experiences often go unnoticed until there emerges a variation (such as 'The Dress') that is large enough to generate different descriptions in the coarse coinage of our shared language. In this essay, we illustrate how individual differences contribute to a richer understanding of visual perception, but we also indicate some potential pitfalls that face the investigator who ventures into the field.

Thresholds for sine-wave corrugations defined by binocular disparity in random dot stereograms: Factor analysis of individual differences reveals two stereoscopic mechanisms tuned for spatial frequency

Threshold functions for sinusoidal depth corrugations typically reach their minimum (highest sensitivity) at spatial frequencies of 0.2-0.4 cycles/degree (cpd), with lower thresholds for horizontal than vertical corrugations at low spatial frequencies. To elucidate spatial frequency and orientation tuning of stereoscopic mechanisms, we measured the disparity sensitivity functions, and used factor analytic techniques to estimate the existence of independent underlying stereo channels. The data set (N = 30 individuals) was for horizontal and vertical corrugations of spatial frequencies ranging from 0.1 to 1.6 cpd. A principal component analysis of disparity sensitivities (log-arcsec) revealed that two significant factors accounted for 70% of the variability. Following Varimax rotation to approximate "simple structure", one factor clearly loaded onto low spatial frequencies (≤0.4 cpd), and a second was tuned to higher spatial frequencies (≥0.8 cpd). Each factor had nearly identical tuning (loadings) for horizontal and vertical patterns. The finding of separate factors for low and high spatial frequencies is consistent with previous studies. The failure to find separate factors for horizontal and vertical corrugations is somewhat surprising because the neuronal mechanisms are believed to be different. Following an oblique rotation (Direct Oblimin), the two factors correlated significantly, suggesting some interdependence rather than full independence between the two factors.

Variations in normal color vision. VI. Factors underlying individual differences in hue scaling and their implications for models of color appearance

Observers with normal color vision vary widely in their judgments of color appearance, such as the specific spectral stimuli they perceive as pure or unique hues. We examined the basis of these individual differences by using factor analysis to examine the variations in hue-scaling functions from both new and previously published data. Observers reported the perceived proportion of red, green, blue or yellow in chromatic stimuli sampling angles at fixed intervals within the LM and S cone-opponent plane. These proportions were converted to hue angles in a perceptual-opponent space defined by red vs. green and blue vs. yellow axes. Factors were then extracted from the correlation matrix using PCA and Varimax rotation. These analyses revealed that inter-observer differences depend on seven or more narrowly-tuned factors. Moreover, although the task required observers to decompose the stimuli into four primary colors, there was no evidence for factors corresponding to these four primaries, or for opponent relationships between primaries. Perceptions of "redness" in orange, red, and purple, for instance, involved separate factors rather than one shared process for red. This pattern was compared to factor analyses of Monte Carlo simulations of the individual differences in scaling predicted by variations in standard opponent mechanisms, such as their spectral tuning or relative sensitivity. The observed factor pattern is inconsistent with these models and thus with conventional accounts of color appearance based on the Hering primaries. Instead, our analysis points to a perceptual representation of color in terms of multiple mechanisms or decision rules that each influence the perception of only a relatively narrow range of hues, potentially consistent with a population code for color suggested by cortical physiology.

The symmetry detection mechanisms are color selective

We investigated the role of color in the feature integration process for global form perception. For this, we used a 2AFC noise masking paradigm to measure the color selectivity of the symmetry detection mechanism. In each trial, a vertical symmetric target was randomly presented in one of the two intervals while a random dot control, in the other. The observers' task was to determine which interval contained the symmetric target. The image elements varied in chromaticity. The target density threshold was measured at various combinations of target and mask chromaticity. A noise mask with the same chromaticity as the target always produced the largest masking effect (threshold increment) on the detection on that target. The masking effect decreased as the difference in chromaticity between the target and mask increased. This suggests that the symmetry detection mechanisms are color selective and only extract local image features of a specific chromaticity.

Effects of gestational length, gender, postnatal age, and birth order on visual contrast sensitivity in infants

To investigate effects of visual experience versus preprogrammed mechanisms on visual development, we used multiple regression analysis to determine the extent to which a variety of variables (that differ in the extent to which they are tied to visual experience) predict luminance and chromatic (red/green) contrast sensitivity (CS), which are mediated by the magnocellular (M) and parvocellular (P) subcortical pathways, respectively. Our variables included gestational length (GL), birth weight (BW), gender, postnatal age (PNA), and birth order (BO). Two-month-olds (n = 60) and 6-month-olds (n = 122) were tested. Results revealed that (1) at 2 months, infants with longer GL have higher luminance CS; (2) at both ages, CS significantly increases over a approximately 21-day range of PNA, but this effect is stronger in 2- than 6-month-olds and stronger for chromatic than luminance CS; (3) at 2 months, boys have higher luminance CS than girls; and (4) at 2 months, firstborn infants have higher CS, while at 6 months, non-firstborn infants have higher CS. The results for PNA/GL are consistent with the possibility that P pathway development is more influenced by variables tied to visual experience (PNA), while M pathway development is more influenced by variables unrelated to visual experience (GL). Other variables, including prenatal environment, are also discussed.

Infant photometry: are mean adult isoluminance values a sufficient approximation to individual infant values?

Individual differences in isoluminance values were studied in infants and adults using a motion nulling paradigm. Two luminance-modulated sinusoidal grating components (spatial frequency=0.25 cpd, temporal frequency=5.6 Hz, speed=22.4 deg/s) were superimposed and moved in opposite directions across a color video screen. The contrasts of the two components were traded off to determine motion nulls. Two conditions were used: red/black vs. green/black, and red/black vs. blue/black grating components. An eye movement based response measure was used for infant subjects, and an average of 308 trials per infant were obtained. As observed in earlier studies, the mean motion null values for infants and adults were highly similar in each condition. The standard errors of motion null values for individual subjects were very small. Individual differences among infants were also small, and were clearly measurable only in the red/black vs. blue/black condition. The close similarity of mean null values, combined with the small individual differences among infants, supports the idea that under the right circumstances mean adult isoluminance values can be used as a sufficient approximation to individual infant isoluminance values in studies of infant color vision. These circumstances are discussed and evaluated in detail.

Development of psychophysically-derived detection contours in L- and M-cone contrast space

In order to investigate the development of color mechanisms in infants we fitted elliptical detection contours to psychophysically-derived contrast thresholds plotted in L- and M-cone contrast space. Detection ellipses were obtained for 47 infants (ages 2-5 months of age), and were compared to those of six adults tested under nearly identical conditions. The parameters of the fitted ellipses allowed us to address several aspects of color development. First, the lengths and widths were used to assess the relative development of chromatic, with respect to luminance, sensitivity. The results of these analyses revealed a sharp increase in chromatic sensitivity between 3 and 4 months of age, suggesting an accelerated development of chromatic mechanisms around this time. Second, the angles of the ellipses provided estimates of individual red/green isoluminance points. In line with previous reports, we found that isoluminance points do not vary significantly with age. Finally, our ellipse-fitting procedures were used to assess whether color sensitivity is best described by a model that assumes independence between post-receptoral chromatic and luminance mechanisms. Similar to previous results of Kelly and Chang [Kelly, J. P. & Chang, S. (2000). Vision Research 40, 1887-1906] obtained using steady-state visually evoked potentials, only a proportion (approximately half) of our infants exhibited detection contours that were consistent with independent mechanisms, a finding that most likely results from statistical noise in the infant data sets.

Spatial frequency tuned covariance channels for red-green and luminance-modulated gratings: psychophysical data from human adults

Both chromatic and luminance-modulated stimuli are served by multiple spatial-frequency-tuned channels. This experiment investigated the independence versus interdependence of spatial frequency channels that serve the detection of red-green chromatic versus yellow-black luminance-modulated stimuli at low spatial frequencies. Contrast thresholds for both chromatic and luminance-modulated gratings were measured within 12 individual subjects using a repeated-measures design. Spatial frequencies ranged from 0.27 to 2.16 c/deg. A covariance structure analysis of individual differences was applied to the data. We computed statistical sources of individual variability, used them to define covariance channels, and determined the number and frequency tuning of these channels. For luminance-modulated gratings, two covariance channels were found, including one above and one below 1 c/deg [cf. Peterzell, & Teller (1996). Individual differences in contrast sensitivity functions: the coarsest spatial pattern analyzer. Vision Research, 36, 3077-3085]. For chromatic gratings, correlations between thresholds for most spatial frequencies were uniformly high, yielding a single covariance channel covering all but the highest spatial frequency tested. A combined analysis of both data sets recovered the same three covariance channels, and showed that detection thresholds for low-frequency red-green chromatic and luminance-modulated stimuli are served by separate, statistically independent processes.

What covariance mechanisms underlie green/red equiluminance, luminance contrast sensitivity and chromatic (green/red) contrast sensitivity?

In order to investigate the mechanisms underlying green/red equiluminance matches in human observers and their relationship to mechanisms subserving luminance and/or chromatic (green/red) contrast sensitivity, we tested 21 human subjects along these dimensions at 16 different spatial and temporal frequencies (spatial frequency, 0.25-2 c/deg; temporal frequency, 2-16 Hz) and applied factor analysis to extract mechanisms underlying the data set. The results from our factor analysis revealed separate sources of variability for green/red equiluminance, luminance sensitivity and chromatic sensitivity, thus suggesting separate mechanisms underlying each of the three main conditions. When factor analysis was applied separately to green/red equiluminance data, two temporally-tuned factors were revealed (factor 1, 2-4 Hz; factor 2, 8-16 Hz), suggesting the existence of separate mechanisms underlying equiluminance settings at low versus high temporal frequencies. In addition, although the three main conditions remained separate in our factor analysis of the entire data set, our correlation matrix nonetheless revealed systematic correlations between equiluminance settings and luminance sensitivity at high temporal frequencies, and between equiluminance settings and chromatic sensitivity at low temporal frequencies. Taken together, these data suggest that the high temporal frequency factor underlying green/red equiluminance is governed predominantly by luminance mechanisms, while the low temporal frequency factor receives contribution from chromatic mechanisms.