Grouping of contextual elements that affect vernier thresholds

Abstract

To reveal the mechanisms of spatial interference in the fovea, we examined the capacity of a variety of lateral flanking configurations to interfere with alignment thresholds of a vertical vernier. A single line on each side of the vernier, at the optimal separation of 2–3 arcmin, raises thresholds threefold or more and masks most effectively when its length equals that of the vernier. For an array of equal lines whose length differs from that of the vernier, masking is reduced but not when vernier and flanks have the same length. The reduction for shorter and longer flanks can be reversed by inserting a gap in the row of flanks. By comparing the masking effect of arrays of mixed line lengths, we show that when a pair of flanks, which by itself masks strongly, becomes a component of a coherent contextual configuration, it loses much of its effectiveness to interact. Observers' ranking of the conspicuity of the vernier test pattern among the flanking elements is negatively correlated with the threshold elevation. We conclude that clustering of contextual patterns influences their capacity to mask. Discrimination of a target deteriorates when the target is grouped within an array of surrounding elements.

Introduction

There is a class of fine localization abilities in which the spatial threshold by far transcends the grain of the receptor mosaic (e.g., see Westheimer, 1981, for a review). Thresholds for detecting the alignment of two abutting lines, vernier acuity, are of the order of arc seconds, and those for the related task of detecting the smallest difference in orientation of a short line are less than a degree of orientation difference. Of the various means of gaining insight into the neural operations underlying these abilities, a favorite is the examination of the manner in which contextual stimuli, that is, spatially and temporally surrounding elements, raise thresholds, for example, by interference, desensitization, inhibition, or masking. 

In this study, we extend the topic of vernier masking by examining whether masking by a given flanking stimulus can be modified, in turn, by changing the flanks' own neighborhood. An early indication of this kind of phenomenon was seen in the orientation discrimination of short foveal lines, where the threshold elevation produced by a surrounding mask was lessened by increasing its area (Li, Thier, & Wehrhahn, 2000; Wehrhahn, Li, & Westheimer, 1996). In the spirit of Gestalt theory, it seemed that the more a textured surround assumes its own identity as a configuration, the less is its interfering influence. We report here on experiments that demonstrate grouping properties in the realm of contextual stimuli in their capacity to mask vernier thresholds. 

General methods

In foveal vision, thresholds were measured in normal observers for vertical verniers presented alone or accompanied by a variety of configurations of flanking lines. Stimuli were generated on a Pentium-based computer and displayed on a high-resolution X–Y monitor (Tektronix 608, P11 phosphor; spatial resolution, <1 arcsec). Luminance of stimuli was approximately 80 cd/m ². Observers viewed the monitor from a distance of 2 m in a dimly illuminated room (∼0.5 lx). Stimuli were presented with a refresh rate of 100 Hz. Each trial started with the presentation of one marker at each corner, presented for 1 s, followed by a blank screen for 200 ms. 

The vernier target consisted of two vertical bars, each 10 arcmin long, and separated by a vertical gap of 1 arcmin, making the total vertical extent 21 arcmin. In each trial, the vernier was randomly offset either to the left or to the right. For each block of 80 trials, a different pseudorandom sequence of left and right offsets was chosen. Not more than four offsets of one direction were presented in a row, and the number of left and right offsets was balanced. In a binary task, observers had to indicate the direction of the horizontal offset by pressing one of two buttons. After each trial, consisting of a 200-ms stimulus presentation, the screen remained blank for a maximum period of 3,000 ms during which the observer was required to make a response. The screen was blank for 500 ms between response and the next trial. 

We used an adaptive staircase procedure to determine the threshold for which an observer reached a score of 75% correct responses (PEST; Taylor & Creelman, 1967). The starting offset was 150 arcsec. Thresholds were determined after fitting a cumulative Gaussian to the data using probit and likelihood analyses. Auditory feedback was given for errors and omissions. 

In most conditions, the vernier was flanked by neighboring vertical lines. The number and length of the flanks varied depending on the experiments and are described separately in each. Flanks were presented simultaneously with the vernier and remained on the display for the same duration as the vernier, that is, 200 ms. Flank configurations were centered on the vernier stimulus and were symmetrical in the horizontal dimension. 

In each experiment, the order of conditions, for example, number of flanks, was randomized individually for each observer. After every condition had been measured once, the order of conditions was reversed to compensate for possible learning effects. Both measurements were collapsed in the figures. Hence, thresholds were measured twice in each condition. As a baseline, we determined vernier thresholds without flanks in all experiments. 

In each set of experiments, except for the pilot study described next, five observers (with ages between 20 and 32 years) were tested. All observers had normal or corrected-to-normal visual acuity, and at least three were naive as to the purposes of the experiments. Observers gave their written consent and were paid for their participation. 

Pilot study

A pilot study was conducted on three observers to determine the vernier-to-flank distance for which interference was most prominent. One flanking line was presented equidistant to the left and to the right of the vernier, respectively. The length of the flanking lines was 10 arcmin. We determined vernier acuity thresholds with flanking lines separated from the vernier by distances of 1.67, 2.5, 3.3, and 4.16 arcmin. We duplicated the results of earlier investigations very well (Westheimer & Hauske, 1975; Westheimer, Shimamura, & McKee, 1976). Alignment discrimination is maximally degraded when flanks are situated at a distance of about 3.3 arcmin (see Figure 1). Therefore, we used a flank distance of 3.3 arcmin in the following experiments. 

Figure 1

 

Vernier offset discrimination thresholds as a function of the vernier-to-flank distance. The experiment is a replication, with the current instrumentation and on three observers, of the results in Figure 6 of Westheimer and Hauske (1975). Here, as in all subsequent experiments, unflanked vernier thresholds in the same observers are included as controls and illustrate the severe reduction in performance for flank distances in the range of 2–4 arcmin (dashed line, baseline condition).

Results

Experiment 1: Threshold change with increasing number of lateral flanks

We first asked what might happen if there were more than just one flank on each side. Accordingly, the experiment was extended by sequentially increasing the number of flanks, all of which were 10 arcmin in length, separated by 3.3 arcmin from each other and placed symmetrically on each side (see insets of Figure 2). Their interfering effect is seen to decrease with an increase in the number of flanks, which was only about half as much when there were 16 flank pairs than when there was only 1 (see Figure 2). The next experiment will show that such a flank size effect is also found for longer lines but not for flanks with identical length as the vernier. 

Figure 2

 

Offset discrimination as a function of the number of flanking lines. A vernier was flanked by a various number of lines. Lines were located on each side of the vernier. The inset shows a typical example with four flanking lines, that is, two on each side of the vernier. Performance improves, that is, thresholds decrease, as the number of flanks increases. The dashed line shows the threshold for the vernier without flanks.

Experiment 2: Changing flank length

In the first experiment (see Figure 2), the flanks were only about half the length of the whole vernier configuration. The experiment was now repeated with three flank lengths: about half (10 arcmin), equal (21 arcmin), and double the length (42 arcmin) of the whole vernier configuration with one or eight flank pairs (see Figure 3). Flank interference is most pronounced when the flanks have the full length of the vernier pattern (21 arcmin). Surprisingly, performance shows a clear reduction when the length of flanks is further increased (42 arcmin). The highest thresholds occur when the vernier pattern is embedded in an extended grid of lines of equal length as the vernier. 

Figure 3a, 3b

 

Vernier acuity was determined for 2 or 16 flanking lines of various lengths. The length of flanks was 10 arcmin (A), 21 arcmin (B), and 42 arcmin (C). Longer flanks yield lower thresholds compared with equal-length conditions.

The results so far demonstrate that flanking stimuli interfere with vernier thresholds in a more nuanced manner than by linear addition of the masking influence of their individual constituents. In particular, it is seen in Figures 2 and 3 that masking can be reduced by adding to the basic single flank pair components that, by themselves, are either inert or mask to some lesser degree but certainly do not facilitate thresholds. 

The strongly deteriorated performance in the equal-length condition with 16 flanks may result from an uncertainty of location of the vernier target. Observers may simply be confused to which line to attend to. To test for such an uncertainty, we added single collinear lines, 6.66 arcmin long, below and above the vernier target separated by a vertical gap of 3.33 arcmin. The vernier was flanked by 16 equal-length lines (see Figure 4, Configuration C). Adding these lines still yields a strong threshold elevation, arguing against location uncertainty as the cause of threshold elevation in the equal-length conditions in Figure 3. 

Figure 4

 

As in Figure 3, vernier thresholds raise when flanked by 16 lines of length equal to the vernier (B). Thresholds remain strongly elevated if the vernier location is highlighted by collinear lines (C). Nor does Configuration D help, where there is an indirect pointer to the location of the vernier. In this configuration, the length of flanks was increased in steps of 100 arcsec per line from the center.

Moreover, we designed a configuration, shown in Figure 4 (Configuration D), with a layout of flanks that gives the observer an indirect pointer to the location of the vernier. However, this produced little improvement of performance and further denies location uncertainty a role in threshold elevation when the target is embedded in an array of flanks. 

Experiment 3: Breaking regularity

We wondered whether isolating the inner flank pair, which, as has been shown, is the most potent masking stimulus, from those accompanying stimuli that lessen its masking would restore its masking potency. Flanks' length was 10 arcmin. In Figure 5, we present data for the situation in which a gap is inserted in the uniform row of flanks. When the gap separates the single inner flank pair from the remaining flanks, thresholds rise strongly (see Figure 5, Gap@2). Here is another example of the main phenomenon emphasized in this study: The removal of a flanking line enhances the masking. This effect decreases as the gap becomes more remote from the vernier and as the length of the regular inner row of flanks increases. 

Figure 5a, 5b

 

We removed 1 of 16 lines on each side of the vernier at different positions, thus creating a gap. Offset discrimination is maximally deteriorated when flanks at Position 2 were removed on each side of the vernier. It seems that the fewer flanking lines there are next to the vernier, the higher the thresholds are. The dashed line indicates vernier acuity without flanking lines.

Experiment 4: Spatial layout of lateral flanks

We designed a series of configurations in which the inner flanks, short or long, were themselves flanked by rows of either short or long flanks (see Figure 6). Among the configurations used here, the most powerful masking occurs when only the central portion of the test vernier is flanked by a pair of short lines that itself is either unflanked (Condition B) or flanked by rows of lines of different height (Condition F). On the other hand, when the inner flanks become part of a row of similar height, either short (Condition C) or long (Condition E), their masking influence is reduced. 

Figure 6

 

(A) Vernier without flanks. (B) A pair of two short lines (10 arcmin) flanked the vernier. (C) Twenty-four short lines (12 at each side) flanked the vernier. (D) The vernier stimulus was flanked by two long vertical lines (42 arcmin). (E) The vernier was presented with 12 long flanking lines on each side. (F) The vernier was flanked with 12 flanking lines at each side. All lines are 42 arcmin in height except for the flanking lines next to the vernier, which were 10 arcmin in length. (G) Twelve flanking lines were located at each side of the vernier. The lines next to the vernier were 42 arcmin long, whereas all the other lines had the same length as the vernier (21 arcmin).

Discussion

Vernier offset discrimination is compromised by closely neighboring flanks. Interference is strongest when a single flank is placed on each side at a distance of 2–3 arcmin and is less for smaller or larger separations (see Figure 1; Westheimer & Hauske, 1975). We have here demonstrated how both the length and the pattern of the flanks influence this masking. Except for the equal-length condition in Figure 3, in almost all configurations we tried, the threshold elevation due to a single pair of flanks is reduced when the flanks become part of a more extended configuration. 

Originally, vernier interference was explained in terms of local interactions between the vernier stimulus and the flanks (Levi, Klein, & Aitsebaomo, 1985; Westheimer & Hauske, 1975; Westheimer et al., 1976). The simplest form of interaction, light summation within the optical image on the retina can be quickly discounted. If optical overlap between target lines and flanks were the cause of the rise in threshold, then the effect ought to diminish monotonically with increasing target–flank separation. This is not what the data in Figure 1 show (also, see Westheimer & Hauske, 1975). 

Once optical factors are ruled out, one turns to the properties of the neural circuits utilized in fine spatial localization tasks. Those involved in vernier acuity remain to be fully elucidated, and the first structure to be examined in this connection is the retina. At the outset, it is clear that the magnitude of the thresholds precludes reliance solely on the local signs of individual elements of the retinal mosaic. Hence, processing from ensembles of neurons is required for a signal to emerge with the few arc second precision of alignment acuity. The evidence is overwhelming that the earliest location in the visual stream of the phenomena under study here is the visual cortex. First, the change with eccentricity in the visual field is different from that of retinal structure and functional organization of ganglion cells, and second, masking is dichoptic (Westheimer & Hauske, 1975). 

Once it is accepted that the primary visual cortex is involved, one can examine the properties of the neurons there, a subject that has been thoroughly investigated even in the preparation most germane to human performance, the alert primate. Here, a great deal of information has been accumulated recently about neural interactions, specifically about the influence of contextual stimuli on the firing of individual orientation-selective neurons. Exploration has been extended from the receptive field, that is, the spatial region in which explicit stimuli induce firing of the neuron, to the so-called “nonclassical receptive fields,” a surrounding zone from which stimulation, which, by itself, does not affect the neuron, nevertheless will influence the response to stimulation within the receptive field (Allman, Miezin, & McGuinness, 1985; Kapadia, Ito, Gilbert, & Westheimer, 1995; Knierim & van Essen, 1992; Levitt & Lund, 1997; Li et al., 2000; Sillito, Grieve, Jones, Cudeiro, & Davis, 1995). Such findings invite comparison with interaction phenomena in the realm of flank masking of visual thresholds in the spatial hyperacuity range. 

A class of explanations argues that there is signal averaging within small spatiotemporal windows and a subsequent pooling of information (Badcock & Westheimer, 1985; Baldassi & Burr, 2000; Parkes, Lund, Angelucci, Solomon, & Morgan, 2001; Pelli, Palomares, & Majaj, 2004). There are also long-standing proposals of contour interactions either in the context of metacontrast masking (e.g., Werner, 1935) or in a more general manner (e.g., Blachowsky, 1912). None of these concepts, however, can accommodate our findings that extending the number of flanking lines improves performance dramatically. Nor can the improvement of performance be explained by any kind of energy mechanisms because longer and shorter flanks yield an improvement of performance, which is more pronounced in the longer line conditions (see Figure 3). Even more surprisingly, worst performance is reached if the flanks have the same length as the vernier. This nonmonotonic dependence of performance on flank length imposes serious restrictions on many models of spatial processing. 

Other explanations invoke lateral inhibition between elements to explain vernier threshold elevation postulating that the flanks fall into the inhibitory region of the vernier offset detector mechanism, introducing a desensitization. Additional flanks might then reduce such inhibition. The gap experiments of Figure 5 would then be interpreted as examples of breaking a hypothetical chain of inhibition/disinhibition. A credible model with the nuanced set of parameters to cover the range of effects revealed in this study with reasonable verisimilitude is beyond the scope of this article. 

Whereas our results tend to support a role of target conspicuity in crowding research, other researchers have denied such a role (Chung, Levi, & Legge, 2001; Felisberti, Solomon, & Morgan, 2005). Their results were obtained in peripheral vision; we presented stimuli foveally. Because spatial visual processing in the retinal periphery may differ in significant respects from that for foveal stimuli, comparison between such results may be difficult. For example, improved performance with increases in the number contextual elements was reported previously in foveal vision (e.g., Li et al., 2000; Wehrhahn et al., 1996), whereas in peripheral vision, performance does not seem to improve with an increasing number of flanks (e.g., Felisberti et al., 2005; Parkes et al., 2001; Pelli et al., 2004; Strasburger, Harvey, & Rentschler, 1991; Wilkinson, Wilson, & Ellemberg, 1997). 

Here, we are taking the first steps to examine the proposition that the results of the experiments described above warrant interpretation in terms of grouping processes in which the flanks, if their number is small or if they share the target lines' length (e.g., Figure 3, “equal length”), join cluster with the target and mask it, whereas when their number is large and they are of different length, they form their own configuration and allow the target to stand out by itself (e.g., Figures 2, 3, and 6). 

We see reinforcement of this view in the observation that on casual inspection of the configurations, it appears that the more conspicuous the vernier pattern, the lower is the threshold. The impression that the more the actual test pattern stands out from its laterally flanking surround, the better its vernier acuity, can be given numerical expression by comparing the thresholds with the subjective ranking of conspicuity: The lower the score is, the more conspicuous the vernier pattern is. Five observers were asked to rank the eight configurations in Figure 7A in the order of how conspicuous the central test vernier pattern appeared to them. The averaged rank order was plotted as a function of the average vernier threshold. Figure 7B shows that there is indeed a strong tendency for the threshold to be higher the less the test vernier stands out from the whole display. 

Figure 7a, 7b

 

A set of eight patterns in which the vernier test line was embedded. Five observers ranked the patterns according to how well the vernier appeared to be standing out from the surround from most conspicuous (1) to least conspicuous (8). Patterns are shown in the order of their average conspicuity ranking (A), and their thresholds were plotted against this conspicuity ranking (B). The correlation coefficient is 0.7.

The data presented here open up the vista of formulating rules that grouping of feature elements obey in masking vernier acuity and, by extension, in acting as modules in perception. 

Acknowledgments

Maka Malania was supported by the Volkswagen Foundation Project “Between Europe and the Orient—A Focus on Research and Higher Education in/on Central Asia and the Caucasus.” 

Michael H. Herzog was supported by the Swiss National Fund. 

Commercial relationships: none. 

Corresponding author: Maka Malania. 

Email: [e-mail]. 

Address: Laboratory of Vision Physiology, I. Beritashvili Institute of Physiology, Georgian Academy of Sciences, 14, Gotua Street, 0160, Tbilisi, Georgia.