Inefficiency of orientation averaging: Evidence for hybrid serial/parallel temporal integration

How are local orientation signals pooled?

Visual perception is capable of pooling multiple local orientation signals into a single more accurate summary orientation. However, there is still a lack of systematic inquiry into which summary statistics are implemented in that process. Here, the task was to recognize in which direction, clockwise or counter-clockwise, the mean orientation of a set of randomly distributed Gabor patches (N = 1, 2, 4, and 8) was rotated from the implicit vertical. The mean orientation discrimination accuracy did not improve with the increase of the number N of elements in proportion to the square-root-N, as could be expected if noisy internal representations were arithmetically averaged. The Proportion of Informative Elements (PIE), defined as the percentage of elements having an orientation different from the vertical, also affected the discrimination precision, violating the arithmetic averaging rules. The decrease in the orientation discrimination precision with the increase of the PIE would suggest that the orientation pooling could be more adequately described by a quadratic or higher power mean. Thus, we parameterized the averaging process for the power parameter of the generalized mean formula. The results indicate that different pooling rules in different trials may apply, for example, the arithmetic mean in some and the maximal deviation rule in others. It is concluded that pooling of orientation information is a relatively inaccurate process for which different perceptual cues and their combination rules can be used.

A method for detection of inattentional feature blindness

In ensemble displays, two principal factors determine the precision with which the mean value of some perceptual attribute, such as size and orientation, can be discriminated: inefficiency and representational noise of each element. Inefficiency is mainly caused by biased inference, or by inattentional (feature) blindness (i.e., some elements or their features are not processed). Here, we define inattentional feature blindness as an inability to perceive the value(s) of certain feature(s) of an object while the presence of the object itself may be registered. Separation of the effects of inattentional (feature) blindness and perceptual noise has escaped traditional analytic methods because of their trade-off effects on the slope of the psychometric discrimination function. Here, we propose a method that can separate the effects of inattentional feature blindness from that of the representational noise. The basic idea is to display a set of elements from which only one contains information relevant for solving the task, while all other elements are "dummies" carrying no useful information because they do not differ from the reference. If the single informative element goes unprocessed, the correct answer can only be given by a random guess. The guess rate can be modeled similarly to the lapse rate, traditionally represented by λ. As an illustration, we present evidence that the presence versus lack of inattentional feature blindness in orientation pooling depends on the feature types present in the display.

Multiple concurrent centroid judgments imply multiple within-group salience maps

Subjects viewed a brief flash of 8-24 dots of either two or three colors randomly arrayed. Their task was to move a mouse cursor to the centroid (center-of-gravity) of each color in a pre-designated order. Conventional and idea-detector analyses show that subjects accurately judged all three centroids utilizing an astounding 13/24 stimulus dots, with only a modest loss of accuracy compared to judging a single-predesignated color centroid. The ability to concurrently compute three centroids is important because it is believed that centroid judgments are made on salience maps that record only salience and are ignorant of the features that produced the salience. Our explanation, instantiated in a computational model of salience processing, is that subjects have three salience maps. Dots are initially segregated into three groups according to color, then each color-group is recorded on a different salience map to compute a centroid. In Part 2, the data are analyzed in terms of Attention Operating Characteristics to characterize impairments in subjects' color-attention filters (mostly insignificant) and encoding efficiency (20% drop for the hardest task) in making multiple versus single centroid judgments. A new, more sensitive analysis measured five sources of subject error variance, four independent, additive sources of error variance: imperfect color-attention filters; a Bayesian-like bias towards a central tendency; storage, retrieval, and cursor misplacement error; a large residual error due mostly to inefficient encoding; and fifth, an interactive source - error in all four components that increases when multiple centroid judgments versus a single centroid judgment are required on each trial. SIGNIFICANCE STATEMENT: An important brain process is a salience map, a representation of the relative importance (salience) of the locations of visual space. It is needed to guide where to look next, for computing the center (technically "centroid") of a cluster of items, and for other important computations. Here we show that in a brief flash of dots of three different colors, randomly interleaved, subjects can compute all three centroids. As a single salience map cannot discriminate dots of different colors, accurately reporting three centroids demonstrates that subjects have not just one, as is commonly believed, but at least three salience maps.

Ensemble perception: Extracting the average of perceptual versus numerical stimuli

Recent research has established that humans can extract the average perceptual feature over briefly presented arrays of visual elements or the average of a rapid temporal sequence of numbers. Here we compared the extraction of the average over briefly presented arrays, for a perceptual feature (orientations) and for numerical values (1-9 digits), using an identical experimental design for the two tasks. We hypothesized that the averaging of numbers, more than of orientations, would be constrained by capacity limitations. Arrays of Gabor elements or digits were simultaneously presented for 300 ms and observers were required to estimate the average on a continuous response scale. In each trial the elements were sampled from normal distributions (of various means) and we varied the set size (4-12). We found that while for orientation the averaging precision remained constant with set size, for numbers it decreased with set size. Using computational modeling we also extracted capacity parameters (the number of elements that are pooled in the average extraction). Despite marked heterogeneity between observers, the capacity for orientations (around eight items) was much larger than for numbers (around four items). The orientation task also had a larger fraction of participants relying on distributed attention to all elements. Our study thus supports the idea that numbers more than perceptual features are subject to capacity or attentional limitations when observers need to evaluate the average over an ensemble of stimuli.

The averaging of numerosities: A psychometric investigation of the mental line

Humans and animals are capable of estimating and discriminating nonsymbolic numerosities via mental representation of magnitudes—the approximate number system (ANS). There are two models of the ANS system, which are similar in their prediction in numerosity discrimination tasks. The log-Gaussian model, which assumes numerosities are represented on a compressed logarithmic scale, and the scalar variability model, which assumes numerosities are represented on a linear scale. In the first experiment of this paper, we contrasted these models using averaging of numerosities. We examined whether participants generate a compressed mean (i.e., geometric mean) or a linear mean when averaging two numerosities. Our results demonstrated that half of the participants are linear and half are compressed; however, in general, the compression is milder than a logarithmic compression. In Experiments 2 and 3, we examined averaging of numerosities in sequences larger than two. We found that averaging precision increases with sequence length. These results are in line with previous findings, suggesting a mechanism in which the estimate is generated by population averaging of the responses each stimulus generates on the numerosity representation.

Calculation Efficiencies for Mean Numerosity

Relative numerosity is traditionally studied using texture pairs. Observers must decide which member of each pair has the greater total number of texture elements. In the present experiment, textures were segregated into nonoverlapping "sectors" containing between zero and four elements, and our observers were asked to select the texture containing the greater average number of texture elements (per sector). If observers were more sensitive to total numerosity than average numerosity, their performance (quantified by the just-noticeable Weber fraction) should have been better when the two textures occupied the same number of sectors than when they occupied unequal numbers of sectors. However, we recorded Weber fractions between 11% and 13% for all observers in all conditions. This performance was comparable with an otherwise-ideal observer whose decisions were based on between three and five sectors in each texture. We conjecture that traditional numerosity discriminations are based on similarly small numbers of element clusters.

Orientation-defined boundaries are detected with low efficiency

When compared with other summary statistics (mean size, size variance, orientation variance), visual estimates of average orientation are inefficient. Observers act as if they use information from no more than two or three items. We hypothesised that observers would attain greater sampling efficiency when their task did not require an explicit representation of mean orientation. We tested this hypothesis using a texture-segmentation task. Two arrays of 32 wavelets each were presented; one left and one right of fixation. Orientations in the target array were sampled from wrapped normal distributions having two different means with the same variance. One distribution defined orientations above the horizontal meridian, the other defined orientations below the meridian. All orientations in the other array were defined by a single wrapped normal distribution having the same variance as each of the distributions in the target array. Contrary to our hypothesis, results indicate that observers effectively ignored all but one item from the top and bottom of each array. In fact, we found no change in the threshold difference between the target's two means when all but one item from the top and bottom of each array were removed. We are forced to conclude that the visual system does not compute the average of more than a few orientations, even for texture segmentation.