The Boynton Illusion: Chromatic edge attraction to a luminance contour

Abstract

In the Boynton Illusion, the perceived location of a low-contrast chromatic edge is altered by a nearby high-contrast luminance contour. Our study explores this color spreading effect across different chromatic directions using a position judgment task. We used the gap effect stimulus, which consists of a box evenly divided by a central contour, in half of the conditions. The suprathreshold chromatic test area embedded in the box provided a horizontal chromatic edge parallel to the central, high-contrast luminance contour that varied in its distance from the contour. An attraction effect of the nearest high-contrast contour on low-contrast chromatic and achromatic edges was observed. Specifically, when the test area is smaller than the region defined by the outer and middle contours, the edge is perceived to be closer to the middle contour (the colored area is perceived to be larger), a filling-in effect; conversely, when the test area extends beyond the middle contour, the edge is perceived to be closer to the middle contour (the colored area is perceived to be smaller), indicating a filling-out of color. Achromatic directions exhibit a relatively smaller effect than chromatic directions, whereas S-cone and equiluminant red and green edges show the same magnitude of positional displacement. The results can be interpreted as the visual system attempting to assign a single hue or brightness to a demarcated region.

Introduction

Edges are an important feature of the natural visual world, and the human visual system is shaped to process edge and border information early (Fang, Boyaci, & Kersten, 2009; Hubel & Wiesel, 1962; Marr & Hildreth, 1980; McIlhagga, 2018). Edges can be formed by abrupt changes in luminance or color, but rarely do color edges occur without co-located luminance edges in natural scenes (Hansen & Gegenfurtner, 2009). 

In the laboratory, studies of chromatic edge effects have focused on two types of interactions between clearly visible edges and weak, poorly visible stimulus regions. First, a suprathreshold edge or contour can alter the detectability of a weak test region. An example of this change in visibility is the gap effect, the enhancement of chromatic discrimination produced by adding a gap or contour between two abutted fields (Boynton, Hayhoe, & MacLeod, 1977; Danilova & Mollon, 2006; Eskew, 1989; Eskew & Boynton, 1987; Hilz & Cavonius, 1970; Hilz, Huppmann, & Cavonius, 1974). Figure 1 shows the basic idea: when two small fields are abutting (Figure 1a), with only a weak or invisible edge between them, sensitivity for the color difference may be reduced compared to the example in Figure 1b, where a gap or contour is added to the chromatic edge. The contour or gap may constrain the visual system from filling-in across the two small fields, which would enhance the discriminability of the top and bottom fields (Eskew, 1989). 

Figure 1.

 

Gap effect. (a) Two colored regions are juxtaposed. (b) A gap is added between two colored regions which enhances the discriminability between the fields (Boynton et al., 1977).

A second type of edge effect has to do with the effect of a suprathreshold contour on the localization of a weaker edge. A classic example is the Boynton Illusion (Boynton, 1980), shown in Figure 2. This simple illusion demonstrates that achromatic signals override the weak chromatic signal to function as boundaries and outline feature information, and produce a uniform percept. In Figure 2, the yellow square on the right is not veridically perceived due to the presence of the high-contrast luminance contour: the white area in between the yellow edge and the black contour seems to be filled with yellow color, and the yellow area outside of the black contour is not well perceived—both filling-in and filling-out. A dramatic example of this type of effect is the change in afterimages produced by a contour (Van Lier, Vergeer, & Anstis, 2009). 

Figure 2.

 

Illustration of the Boynton Illusion. The yellow areas on the left and right are same squares. With a black squiggly contour drawn on top of the right square, the yellow edge appears to be defined by the black contour when viewing from a certain viewing distance.

Although the original gap effect was found with a luminance gap or contour and chromatic discrimination, in fact the effect can be obtained with equiluminant contours (Eskew, 1989; Montag, 1997); the key seems to be that the clearly visible contour demarcates regions to be discriminated (Eskew, Stromeyer, Picotte, & Kronauer, 1991), regardless of what visual attributes create the contour. There are chromatic as well as luminance edge detection mechanisms, as shown by McIlhagga (2018) and McIlhagga and Mullen (2018) using classification images. Shapley, Nunez, and Gordon (2019) suggest that these chromatic edge detectors belong to less sensitive mechanisms that are apparent only above threshold, and that these mechanisms resemble double-opponent cortical neurons. The different edge detectors differ in their precision, and the higher acuity provided by luminance information suggests that luminance should be weighted more than chromatic information in border detection (Sharman, McGraw, & Peirce, 2013; Zhou & Mel, 2008). This weighting by precision is consistent with other examples of cue combination (Ernst & Bülthoff, 2004; Zhou & Mel, 2008). Evidence from a localization task also contributes to this argument. Rivest and Cavanagh (1996) tested how different attributes were combined to localize a contour with all attributes kept at approximately equal precision. Interactions between the attributes were observed, but with no privileged role of luminance found, which suggests that all attributes were equally integrated at a common site (see also Greene & Brown, 1995). 

Here we direct our attention to the interaction between the luminance contour and chromatic edges in the specific case of a simplified Boynton Illusion, while incorporating the threshold-level change due to the gap effect. We have adopted the stimulus configuration used in Boynton et al. (1977) that has two juxtaposed rectangular half-fields. Two experiments were conducted to investigate the effect of a highly visible luminance contour on the contrast detection sensitivity of a rectangular region in the box stimulus, and localization of a suprathreshold edge. 

Experiment 1 measured the thresholds for the stimuli with and without the added black contour to reflect interactions at threshold level and across color directions. This experiment is a systematic replication of Eskew (1989), except that in the earlier study the tests were pairs of opponent chromaticities (e.g., red–green), whereas in the present study each chromatic test was discriminated from gray (e.g., red–gray and green–gray were both used), and here we use a forced-choice method instead of method of adjustment. The gap effect has not always been found with forced-choice methods (cf. Boynton et al., 1977; Danilova & Mollon, 2006; Montag, 1997). The goal of Experiment 1 was to, first, investigate the threshold-level sensitivity enhancement effect of a luminance contour across color directions with the current stimulus spatial configuration, and second, set baseline contrasts for Experiment 2. We confirmed a small chromatic sensitivity enhancement by adding a co-located luminance contour, except that one luminance test condition showed very minimal effect. 

The second experiment estimates whether and how much the perceived position of a suprathreshold chromatic edge deviates from its physical position, and how that deviation is affected by the presence of suprathreshold contours as in the Boynton Illusion. One specific hypothesis is that the degree to which the edge position is altered by the luminance contour will vary with the chromaticity of the edge, with the largest effect for S-cone edges, a smaller effect for equiluminant red–green ones, and a still smaller effect for the achromatic edges, mimicking the pattern of spatial resolution for these chromatic directions (Wuerger et al., 2020). The obtained results show that in general the test edge is perceptually attracted to the nearest high-contrast contour, with a smaller spread of attraction for achromatic compared both red–green and S-cone edges. The extent of the two chromatic spreading effects were about equal in magnitude, contrary to expectation. 

General methods

Observers

Five students (23.4 ± 5.3 years; two females) from Northeastern University participated in the experiment. All observers had normal or corrected-to-normal visual acuity, and normal color vision as tested by the Hardy–Rand–Rittler plates for all and by Rayleigh matches for three observers. Informed consent was provided by all observers. This study was approved by the Northeastern University Institutional Review Board and the procedures were in accordance with the Declaration of Helsinki. 

Apparatus

Stimuli were created on a Macintosh system (Apple Inc., Cupertino, CA) connected to a Bits# display controller (Cambridge Research Systems, Rochester, UK) providing 14-bit resolution in the RGB channels. Stimuli were presented on a Sony GDM-F520 CRT monitor (Tokyo, Japan) at an 85-Hz frame rate. Experimental procedures were programmed in MATLAB (MathWorks, Natick, MA) using the Psychtoolbox (Kleiner, Brainard, & Pelli, 2007). The monitor was carefully calibrated. The mean luminance background was 93.2 cd/m² (x = 0.284, y = 0.313). The head position of the observers was fixed 130 cm from the screen with a chin rest, and their dominant eye was used to view the screen through ophthalmic trial lenses with the other eye patched. 

Stimuli

All stimuli consisted of a black outer box (line width = 1 pixel, approximately 0.0124°; box width = 2.49°, box height = 1.24°) containing a colored rectangle (Figure 3). In half of the trials, a middle black contour was added, separating the outer box into two equal parts (the with-contour condition). The two short horizontal lines at the two sides of the box are middle-position marks (position 5 in Figure 5), which were always presented with the box (in both the no-contour and with-contour conditions). The entire stimulus flashed in a 329-ms rectangular temporal profile (28 monitor frames). A fixation mark, consisting of four radial diagonal lines with a blank center (the diagonal lines extend from 1.32° to 2.19° eccentricity) was presented continuously throughout the run. Six chromatic conditions were selected for the colored area in the box: achromatic increment (A+; appearing white), achromatic decrement (A–; appearing black), equiluminant L–M (appearing pink), equiluminant M–L (appearing cyan), S-cone increment (S+; appearing purple), and S-cone decrement (S–; appearing lime green). Contrast of the colored region in Experiment 2 was fixed at 4× each individual's forced-choice thresholds from Experiment 1. Results from a pilot experiment (He, Taveras-Cruz, & Eskew, 2018), as well as the signal detection analysis reported below, confirm that all the test patches were clearly visible. 

Figure 3.

 

Stimuli in all experimental conditions with the S+ chromaticity. The top panel shows no-contour stimulus (left) and with-contour stimulus (right) in the contrast detection task. The chromatic area in both conditions fills in the top half of the rectangular box. The bottom panel shows examples of the no-contour and with-contour stimuli in Top and Bottom conditions in Experiment 2, the position judgment task.

Determination of the S-cone isolating direction

The stimulus color direction that modulates the S-cones alone (the S-cone isolating direction), using the silent substitution method (Estévez & Spekreijse, 1982), can be calculated from published cone fundamentals for observers who have standard cone fundamentals (i.e., the Stockman–Sharpe fundamentals; Stockman & Sharpe, 2000; Stockman, Sharpe, & Fach, 1999). We used an empirical procedure (Wang, Richters, & Eskew, 2014; Webster & Mollon, 1994) to estimate the isolating direction for three of our five observers. Briefly, contrast detection thresholds were measured with and without an added field of 420 nm light of sufficient radiance to raise thresholds, using the method of adjustment. Test chromaticities were the Stockman–Sharpe isolating directions and nearby chromatic directions in RGB color space. The threshold for the RGB direction that was most elevated by the violet field was taken as that observer's S-cone isolating direction. Two of our five observers were shown to be Stockman–Sharpe observers, and for these two observers we used the standard S-cone isolating direction; one was not a standard observer, and we used the best estimated direction for that observer. The remaining two observers whose S-cone isolating directions were not tested by this procedure were assumed to be Stockman–Sharpe observers and the standard S-cone isolating direction was used for them. 

Determination of equiluminance

Equiluminant red and green directions were determined individually for each individual using heterochromatic flicker photometry, considering its high reliability and precision (He, Taveras-Cruz, & Eskew, 2020). Procedures were the same as in He et al. (2020). 

Experiment 1: Chromatic detection task

In Experiment 1, we measured thresholds for detecting the box stimuli with and without the added middle black contour for six color directions. 

Task and procedure

Each run started with a 1 min adaptation period, followed by 100 forced-choice trials. There were 12 stimuli (6 color conditions × 2 contour conditions) in the detection task in total, corresponding to 3,600 trials for each observer (3 runs for each stimulus). A two-alternative forced-choice method combined with a 3-down-1-up adaptive staircase procedure (Wetherill & Levitt, 1965) was used to vary the contrast of the test rectangle over trials. In each trial, observers were presented with two temporal intervals in sequence signaled by beeps, with one randomly selected interval showing the box and the test rectangle and the other showing the box only; the box was always presented at maximum contrast. A test stimulus in the S+ condition is shown as an example in the top panel of Figure 3. Observers were instructed to select the test interval by keypress. For each run, the frequency-of-seeing data were fitted with a Weibull psychometric function to estimate the contrast yielding 82% correct; the average of three runs was taken as the final threshold (in cone contrast vector length units) for the given color direction. 

Results and discussion

Figure 4 depicts the log of the detection threshold ratio of no-contour and with-contour stimuli. Most of the log ratios are above 0, suggesting a small increase of sensitivity produced by adding a luminance contour, although the A+ condition shows a close to zero effect. Our results therefore replicate the gap effect, in which detectability can be enhanced by adding a luminance contour (Boynton et al., 1977). However, as reported by Boynton et al., there are large individual differences. 

Figure 4.

 

Box-and-whisker plot of threshold ratio of no-contour stimulus and with-contour stimulus for six chromatic conditions. The magenta symbols represent the log detection ratios for each observer, with different symbols used to distinguish between observers' data. Each boxplot displays a median marked by a central line and quartiles at the 25th and 75th percentiles. Whiskers extend to the maximum non-outlier points. Outliers falling more than 1.5 times the interquartile range from the closest quartile are indicated with black crosses.

Boynton et al. (1977) found a positive gap effect (facilitation) of adding a luminance contour for S-cone stimuli and a negative gap effect for red/green equiluminant and achromatic stimuli. Montag (1997) reported similar results for S-cone and achromatic stimuli, but a positive gap effect for the red/green stimuli, and argued that this divergence can be ascribed to the small field used in Boynton et al. (1977). Cole, Stromeyer, and Kronauer (1990), however, demonstrated that the detectability of both chromatic and luminance flashes can be improved by a suprathreshold luminance pedestal that creates a clearly visible edge around the test spot. Our results are consistent with this last finding. Our short stimulus presentation duration might serve as the reason that the sensitivity enhancement was small (Eskew, 1989). 

Experiment 2: Position judgment task

In this experiment, we quantified the deviation of the perceived chromatic edge from its physical position for six color directions via a position judgment task. 

Task and procedure

The observers were asked to judge the vertical position of the chromatic edge in the box. There were nine possible low-contrast edge positions numbered 1 to 9, equally spaced from top to bottom, at which the chromatic edge could appear (Figure 5). The colored rectangle abutted either the upper contour of the box (Figure 5, Top condition at left), or on the lower contour of the box (Figure 5, Bottom condition at right). Figure 5 shows the Top and Bottom conditions when the middle line is present, the rectangle is colored with S+, and the chromatic edges are at position 4 (Top condition) and position 6 (Bottom condition). 

Figure 5.

 

Stimuli in the position judgment experiment. For each test rectangle, nine vertical positions were defined from Top to Bottom to indicate the location of the test edge. The Top and Bottom conditions are shown at left and right, respectively. The chromatic edge position is at “4” in the Top condition, and “6” in the Bottom condition. Two additional conditions, with no chromatic stimulus, were coded as being at position 0 or position 10. For data analysis, position responses in the Bottom condition were subtracted from 10 (see text). The dashed gray arrows and the columns of numerals were not present in the actual experiment, but solid black line segments did mark the middle of the box in every presentation (shown clearly on the right of each panel, but obscured by the gray arrow on the left).

To analyze the data from the Bottom condition, the responses were subtracted from 10, effectively flipping the stimulus upside down. In the example shown in Figure 5, a veridical judgment would be “4” in the Top condition and “6” in the Bottom condition; for analysis, the Bottom response was coded as 10 − 6 = 4, the same position in the two conditions. The purpose of having both Top and Bottom conditions was to average out any bias in responses due to having the chromatic rectangle at one end of the box. 

Blank or no-edge stimuli were included as well, designated as occurring at position 0 or 10. For a veridical response, observers would respond “0” or “10” in these conditions, in which no chromatic edge could be visible. Because there was no actual chromatic edge position to measure, these data are analyzed separately from the others (as discussed later in this section). Therefore, in each trial, the observers were instructed to attend to the chromatic edge in the box and judge the position of the chromatic edge by choosing 1 of the 11 line positions by pressing the corresponding key. 

Contrasts of the colored rectangles were fixed at 4× the corresponding forced-choice detection threshold (for the no-contour or with-contour conditions separately) measured in Experiment 1 but jittered by ±10% contrast in every trial. The vertical position of the entire box stimulus on the screen also jittered by ±10% of the box height (within the fixation lines, which were not jittered), to help make the judgment of chromatic edge position relative to the black middle lines and the box, rather than to the absolute position on the display. 

Observers performed two runs for each condition, with each run consisting of nine trials for each position (99 trials in total), in random order. In each trial, a single interval containing the stimulus was presented and observers responded to the perceived position by pressing keys 1 through 9 on the keyboard for the nine chromatic positions, and used the “∼” and “0” keys for position 0 and position 10 (no chromatic rectangle visible). A high-pitched feedback beep signaled when any of the 11 valid keys (key “∼” to key “0”) was pressed, otherwise a low pitch tone was given and the trial repeated. In total, there were 264 stimuli (6 color conditions × 2 contour conditions × 2 Top/Bottom conditions × 11 positions) in the position judgment task, requiring 4752 trials per observer. 

Observers were instructed to report the position of the chromatic edge, using numbers 0 through 10, to indicate the apparent position of the edge of the chromatic rectangle. Prior to the main experiment, observers were given practice trials in a randomly chosen chromatic condition, with the stimulus set to the highest available contrast, to help them make reliable judgments of edge position. In these runs, unlike the main task runs, valid feedback was provided, and observers were required to practice until they could complete an entire run without error. The goal of this training procedure was to minimize response error in the main task when low-contrast stimuli were shown and no feedback was given. 

In summary, the stimuli in this experiment were weak but clearly visible (4× threshold), the chromaticity being studied was blocked such that the observer knew which chromaticity to look for, observers knew whether the run was a Top or a Bottom condition, and the observers were well-practiced with the position judgment task so that the errors due to the mechanics of the task were minimized, in an effort to obtain veridical measurements of the perceived position of the edge. 

Results and discussion

One observer completed half of the conditions (S+, S–, and A+ color conditions) and the rest completed all. Data were organized to show the perceived edge position versus the actual edge position in each condition. 

As an example, in Figure 6, responses of one observer for the S+ stimuli are plotted in the left column, where curves show the mean perceived positions for each physical position, with the horizontal axis being the nine positions at which the edge was presented and the vertical axis being the nine response positions. The dotted orange curves and the solid gray curves represent the no-contour condition and the with-contour condition, respectively. If there was no filling-in effect and observers correctly judged the positions, all responses would lie on the solid black diagonals in the left panels. 

Figure 6.

 

Illustrative results of one observer in one color condition (S+). Curves in the left panels show the perceived edge position against the real edge position and curves in the right panels show the effect of adding a middle contour (with-contour minus no-contour positions), in terms of visual angle and percentage of box height. The gray quadrants represent responses showing that the edge was perceived closer to the middle position when there was a contour there. Panels are shown, from Top to Bottom, in the order of the Top condition, the Bottom condition, and the average of the two conditions. Error bars in the left panels represent standard errors, and error bars in the right panels represent standard deviations calculated with the propagation of error method. Note that data points at position 0 and position 10 are forced to converge to the diagonals for better visualization of the filling-in effect; the actual responses at those blank positions are described later in this section.

The plots in the right panels show the vertical distance between the with-contour and no-contour pairs of points in the corresponding left panels. If there were no filling-in effect, the points in the right panel would appear at a constant value of 0. Therefore, the vertical displacement of the points from the diagonal on the left, or the horizontal on the right, quantifies the magnitude of the filling-in effect. Systematic shifts of the points are observed in both Top and Bottom conditions, where most of the perceived with-contour points are larger than veridical when the chromatic area is smaller than half of the outer box (position number <5), and are smaller than veridical when the chromatic area is larger than half of the outer box. Responses of the no-contour condition manifest the opposite pattern. 

These implied percepts are illustrated schematically in Figure 7. Black arrows in the figure denote the direction the chromatic edge fills-in. In stimuli (a), (e), (g), and (k), without the middle contour, the chromatic edge is attracted to the closer luminance contour of the box, whereas in stimuli (b), (f), (h), and (l), the chromatic edge is attracted to the added middle contour. 

Figure 7.

 

Illustration of the filling-in pattern of the chromatic edge in different conditions. Left and right panels show the Top and Bottom conditions, and left and right columns in each panel are no-contour and with-contour conditions, respectively. The chromatic edge is perceptually-attracted to the nearest contour in all cases.

Responses are categorized in Top and Bottom conditions to show potential response bias. A small bias is shown for this observer in the upper left two panels in Figure 6, where the crossing points of the with-contour and no-contour curves are in different quadrants of the panel. In the Top condition panel, the crossover appears in the first quadrant which indicates that, for actual position 5 (middle position), the perceived position with no-contour is smaller than with-contour (stimulus (c) vs. (d) in Figure 7). In the Bottom condition, the opposite is observed—the crossover occurs in the third quadrant and the perceived position at position 5 with no-contour is larger than with-contour (stimulus (i) vs. (j) in Figure 7). Although opposite patterns are shown for the biases in the two conditions, they suggest the same type of color spreading effect, in which the chromatic edge tends to be attracted to the side with color when the chromatic rectangle extends to half of the box with no middle contour added. The average condition, which averages responses in the Top and Bottom conditions, corrects for this type of response bias. 

Data are further analyzed by subtracting no-contour responses from with-contour responses to illustrate the net effect of the luminance contour. As in Figure 6 right panels, the differences of the with-contour and the no-contour conditions are plotted in terms of visual angle (vertical axis on the left) and percentage of box height (vertical axis on the right). After this difference is taken, the results are not simple errors in localization, but instead reflect a change in localization owing to the nearby contour. 

On average, the filling-in effect varied as a function of the edge location (Figure 6, bottom right). The magnitude of the filling-in effect for this particular observer and color direction (S+) is 7.34 arcmin, as indicated by the average magnitude of the two peaks in the second and the fourth quadrant of the figure. With similar stimulus conditions, Rivest and Cavanagh (1996) showed that precision of localization for luminance and color was about 1 arcmin, much smaller than the filling-in effect shown here; Greene and Brown (1995) found a maximum effect of about 3.7 arcmin, approximately half of our largest effects. Feitosa-Santana, D'Antona, & Shevell (2011) compared how different types of luminance contour bound color filling-in of S-cone decrement chromatic edges inside the contours and quantified the color spreading of the weak chromatic edge to extend as far as 6 arcmin. 

The patterns of results were very similar for all observers, and are therefore averaged and shown in Figure 8, for each of the six chromatic conditions. The averaged patterns are the same for all the color directions, but with lower magnitude of effects for the achromatic increments and decrements. The S-cone conditions were expected to show the largest effect, because S-cone images are considered to be more susceptible to the filling-in process and S-cone detection has been improved most by adding luminance contours (Eskew, 1989; Montag, 1997). However, the magnitude of the color spreading effect in the present study was similar for S-cone and the equiluminant red and green conditions. Although one data point for the A– condition at position 9 (Figure 8, bottom right) increased the mean magnitude for A–, the two achromatic conditions generally show relatively less of an effect than the chromatic conditions. 

Figure 8.

 

The effect of adding the contour in six color conditions, averaged across observers and Top and Bottom conditions. Error bars are standard deviations averaged across observers derived using the propagation of error method. An illustration of the attraction effect of the middle contour is shown in the second and fourth quadrants of the top left panel. Panels S+, S–, and A+ show the average of all five observers, whereas the other panels show the average of four observers (one observer did not complete all conditions). See text for description of the dashed curves.

The data are reasonably well-described by a sinusoidal function y = −Amp · sin(ωx), where ω = 2π/10. The amplitude values estimated for Amp are reported in Table 1, second row, and the fitted curves are shown in Figure 8 as dashed curves. On average, low-contrast edges were attracted by the high-contrast middle contour, especially for the S-cone and red–green conditions. The achromatic filling-in effect is slightly weaker than the chromatic filling-in effect, likely due to the higher localization precision provided by luminance vision at this contrast level. The weaker effect for the achromatic tests is consistent with a cue combination model, in which the attributes with higher precision (achromatic edges, here) are given greater weight compared to attributes with lower precision, such as the chromatic edges (Sharman, McGraw, & Peirce, 2015). 

Table 1.

 

Average magnitude of the filling-in effect in terms of the mean of the two measured peak effects (top row) or the amplitude of the fitted sine wave (bottom row).

 

When no colored test edge was actually present (which happened on 2/11 of the trials in a given condition), perfect performance would be for observers to respond “0” or “10,” depending on whether there was no test rectangle at all or one that filled the entire box. These data were analyzed to determine how well the observers were actually seeing the stimuli, and to determine the magnitude of false alarms in this task. This analysis proceeded as follows. When the stimulus was at position 0 (Top condition) or 10 (Bottom condition), any response other than “0” or “10” was treated as a false alarm (no test edge was present but the observer said it was). When the stimulus was at positions 1 through 9, any response other than “0” (Top condition) or “10” (Bottom condition) was treated as a hit (a test edge was present and the observer said so). From the hit and false alarm rates d’ and λ_center were calculated (Wickens, 2001), and are shown in Figure 9 (see mean values in the Appendix). 

Figure 9.

 

Box-and-whisker plot for corrected d’ (left) and λ_center (right), with the correction being applied to deal with cases with no false alarms or 100% hits (Hautus, 1995; see the Appendix). For each color direction in each panel, the boxplots for the with-contour condition are on the left and the no-contour condition data are slightly shifted to the right. Colored circles correspond to the d’ or λ_center of each observer, with the median for each color direction represented as the central line. The top and bottom bounds of the gray boxes indicate the 75th and 25th percentiles, respectively. Outliers, points that lie beyond 1.5 × the interquartile range, are outside of the whiskers; the whiskers themselves indicate the maximum and minimum values within that 1.5 × interquartile range.

This analysis indicates that observers were generally quite sensitive to the stimuli, consistent with the use of 4× thresholds from Experiment 1, with most d’ values being greater than 2. There is no obvious difference in sensitivity across conditions, except that perhaps the A+ d’ values are slightly higher. The addition of the contour does not have any obvious effect in this analysis, which pools all the physical edge locations; the results of Experiment 1 (Figure 4) do indicate a small improvement of sensitivity when the contour is aligned with the physical edge of the test. 

The λ_center values are almost all negative, indicating an overall bias to name a 1 to 9 position (to say “yes,” a test edge was present). This finding is not surprising; only approximately 9% of the trials had no test edge at all. The key feature here is that there are no obvious changes in bias with-contour or color condition, with the possible exception of the A+ and A– conditions. The λ_center values averaged slightly lower when the contour was present in these two conditions (the left of the pair of box plots above A+ and A– is lower). These values indicate that the contour is at most causing a very small increase in the observer's bias toward saying yes, that there was a chromatic stimulus present at some position. Thus, our main focus is on sensitivity and especially on the perceived position of the chromatic or achromatic test edge. 

General discussion and conclusions

In Experiment 1, we found a small chromatic sensitivity enhancement by a co-located luminance contour, except for A+ tests which showed no clear effect. Overall, this finding replicates the gap effect (Boynton et al., 1977; Eskew, 1989; Eskew & Boynton, 1987). Boynton et al. (1977) did not obtain the gap effect with forced-choice methods as used here, although Montag (1997) and Danilova and Mollon (2006) did. The contour's effect is likely to depend on the spatial and temporal properties of the stimuli; in particular, the contour's effect is reduced for short duration flashes (as commonly used in forced-choice procedures), perhaps due to the time required for the chromatic smoothing or filling-in to occur (Eskew, 1989); however, see He, Mingolla, and Eskew (2024) for evidence against filling-in being slow. Here, our small contour enhancements were produced despite a relatively brief 329ms stimulus presentation and use of a forced-choice method. 

In Experiment 2, we explored interactions between a suprathreshold, high-contrast achromatic contour and chromatic and achromatic lower-contrast edges using a position judgment task. The observers’ task was to judge the position of the edge, rather than the degree of filling-in per se. It is conceivable that the test rectangle did not appear solid, and that only its edge was perceived and used in the position judgment, as if the rectangle were high-pass filtered. However, this seems unlikely, since the stimuli were 4× their thresholds, and no observer reported such a percept. Thus we take the edge position judgment as a proxy for the spatial extent of chromatic filling-in. 

We found that, like in the Boynton Illusion (Figure 2), the test edge was attracted to the nearest suprathreshold contour (Figure 7). The test rectangle became perceptually larger (quadrant II results in Figure 8) or smaller (quadrant IV results in Figure 8) than its physical size. 

The magnitude of the positional change effect observed here, from approximately 3 to 7 arcmin, is comparable to or larger than many of those reported in previous literature. It was reported that the maximal separation between achromatic test and flanking contours to induce an attraction effect can be as small as 3 to 4 arcmin or as large as 10 arcmin depending on the task (Badcock & Westheimer, 1985; Feitosa-Santana et al., 2011; Greene & Brown, 1995; Rentschler, Hilz, & Grimm, 1975; Rivest & Cavanagh, 1996). As for the interaction of different attributes, Rivest and Cavanagh (1996) showed that a chromatic test edge was attracted for 1 arcmin by a luminance contour at a distance smaller than 10 arcmin. We found 2.9 arcmin and 5.3 arcmin achromatic attraction effects for achromatic increments and decrements, respectively, at a distance of 18.6 arcmin (1/4 of the entire box height), and even larger chromatic attraction effects (Table 1). The magnitude of these effects is still more impressive considering that the observers were well-practiced with the task, and were given feedback to teach them to judge the veridical position of a high-contrast edge during the practice phase. The large positional effect observed in our study might be due to the use of relatively low contrast edges and high negative contrast contours (Greene & Brown, 1995), and the short presentation time (Badcock & Westheimer, 1985). Presumably the smaller attraction effect for achromatic tests is due to the higher acuity (McKeefry, Murray, & Kulikowski, 2001; Wuerger et al., 2020) and localization precision (McIlhagga & Mullen, 2018; Rivest & Cavanagh, 1996) for achromatic compared to chromatic stimuli. 

Achromatic edges can mask chromatic blur (Jennings & Kingdom, 2017; Sharman et al., 2015); because blur causes an apparent increase in the size of a stimulus, we might naively expect the addition of the black contour to make the low-contrast chromatic rectangle appear smaller, moving its apparent position away from the contour. The color spreading effect we observe is instead in the direction of attraction to a suprathreshold contour, such as produced by diffusive processes (Grossberg & Mingolla, 1985; Paradiso & Nakayama, 1991), but see He et al., (2024), or by multiscale filtering (Blakeslee, Cope, & McCourt, 2016; Blakeslee & McCourt, 2008; Dakin & Bex, 2003) 

The pattern of filling-in in Figure 7 can be parsimoniously understood as follows: when the middle black contour is added, it divides the box into two well-defined regions, which are interpreted by the visual system as two surfaces adjacent to each other. Our results can be interpreted as the visual system assigning a uniform hue percept to each region. 

Acknowledgments

Supported by NSF Grant BCS- 2239356. The authors thank Connor Choptij, Aanya Sehgal, and Yangyi Shi for the observing work. The current address for Jingyi He is Herbert Wertheim School of Optometry and Vision Science, University of California Berkeley, Berkeley, California. 

Commercial relationships: none. 

Corresponding author: Rhea T. Eskew, Jr. 

Email: [email protected]. 

Address: Department of Psychology, College of Science, Northeastern University, Boston, MA 02115, USA. 

Appendix: Judgment bias analysis

Signal detection analysis

This section shows the corrected d’, λ, and λ_center averaged for all observers in each condition (see Table A1). The Inf or NaN values caused by 100% hit rates or 0% false alarm rates were corrected by adding signal trial percentage to number of hits and 2 × signal trial percentage to number of signal trials, and adding noise trial percentage to number of false alarms and 2 × noise trial percentage to number of noise trials (Hautus, 1995). Subject #5 completed only three color conditions (S+, S–, and A+). 

Table A1.

 

Means of the corrected d’, λ, and λ_center averaged across observers.

 

ANOVA

Judgment bias is analyzed based upon responses to positions 0 and 10. Figure A1 exhibits the four conditions with no test edge. Large individual differences are observed in all conditions. The median responses (middle line in each individual boxplot) were quite close to the bounding box contour (i.e., they were close to veridical) when a test rectangle was actually presented (Figures A1b and A1c), but those medians deviated more from being physically correct when no test rectangle was actually shown (Figures A1a and A1d). These latter responses are likely false alarms for seeing the test chromatic rectangle at all. 

Figure A1.

 

Judgment bias at positions 0 and 10. The four panels show the four conditions where either no chromatic rectangle was presented, or the chromatic rectangle filled the box and its edge was overwritten by the box contour. The corresponding with-contour stimulus and judgment position are shown in each panel. The box-and-whisker plots show the median, the upper and lower quantiles, the non-outlier minimum and maximum values, and the outliers (data points with red outlines that are more than 1.5 × the interquartile range above and below the box). For each color direction in each panel, the boxplots for the with-contour condition are on the left and the no-contour condition data are slightly shifted to the right.

A three-way ANOVA based upon the four (of five) observers who completed all trials was conducted, in which the Top position “10” condition and the Bottom position “0” condition (Figures A1b and A1c) were converted by inverting the response positions and averaged and became “filled box” condition, whereas the Top position “0” condition (Figures A1a and A1d) and the Bottom position “10” conditions were converted and averaged and became “empty box” condition. The three-way ANOVA (2 [middle line conditions: middle line, no middle line] × 2 [box color conditions: filled box, empty box] × 6 [color conditions: S+, S–, L–M, M–L, A+, A–]) results reveal medium main effects for middle line, F(1,77) = 5.78, p < .05, η² = 0.059, and box color conditions, F(1,77) = 4.61, p < .05, η² = 0.047. Multiple comparisons show that the “with middle line” condition has higher means or judgment bias (further away from correct position), whereas the “empty box” condition has higher means compared to the “filled box” condition. The deterioration effect of adding a middle line is consistent with the negative gap effect reported in Boynton et al. (1977) that luminance discrimination is impaired with a gap, resulting in worsened judgment of the edge. This result is also consistent with the idea that, functionally, the mechanism compares the differences across contours so more effort is required when a middle contour is added, resulting in larger variance (Shapley et al., 2019). When the entire box is filled in with color, the uncertainty can be reduced owing to the presentation of color edges which coincides with the box contour, as the addition of surface attributes improves localization precision and facilitates surface recognition by reducing signal-to-noise ratio (Kingdom & Kasrai, 2006; Rivest & Cavanagh, 1996).