Journal of Vision - Crowding is unlike ordinary masking: Distinguishing feature integration from detection, by Pelli, Palomares, & Majaj

Figure	Effect of	Task	Signal and flanker (font or grating)	Signal size (deg)	Flanker size (deg)	Ecc. (deg)	Observer
3	eccentricity	Identify	Sloan	1	1	0, 2, 4, 8, 12, 20, 24	MCP, SJR, SSA
4	fovea vs. periphery	Identify	Sloan	0.32	0.32	0, 4	MCP, AG, MLL
5	size	Identify	Sloan	0.32, 0.5, 1, 2	same as signal	4	MCP, AG, SSA
6	flanker size	Identify	Sloan	0.32	0.32, 0.64, 0.96, 1.6, 3.2	4	MCP, AG
7	font	Identify	2x3 Checkers, Sloan, Bookman, Outline Sloan	0.25, 0.32, 0.50, 0.32	same as signal	4	MCP, MLL
8	# of flankers	Identify	Sloan	0.32	0.32	6	MS, MLM, MCP
9, 11	flanker contrast	Identify	Sloan	0.32	0.32	4	MCP, AG, MLL
12	task	identify, detect	Sloan	0.32	0.32	4	MCP, AG, MLL
13	eccentricity	Detect	Sloan	0.75	0.75	2, 4, 8	MLM
14	size	Detect	Sloan	0.75, 1.5, 3.0	same as signal	8	MCP, MLL
15	extent	Identify	1 c/deg grating	2, 4, 8	same as signal	20	MCP, AG
16	letter vs. grating	identify, detect	Sloan, 8 c/deg grating	0.32,0.52	0.32,0.52	4	MCP, AG, MLL

Table 1. The experiments. For gratings, “size” is the 1/e radius of the Gaussian envelope, and the observer “identified” the ±45° orientation. Regarding Figure 8, observer MCP was tested at 4 instead of 6 deg eccentricity.

The experiments were exploratory, trying to characterize the phenomenon, especially as a window into the mysterious feature integration process. The results indicate that the observer’s identification response is based on an amalgam of all the features detected in a large region we call the “integration field,” which is approximately centered on the signal (Toet & Levi, 1992). Most relevant to this conclusion are the effect of task and the combined effects of mask contrast and spacing.

2. Methods

2.1 Observers

Seven observers with normal or corrected-to-normal acuity performed these experiments binocularly (see Table 1). One observer (MCP) is an author. The other observers were paid for participating.

2.2 Tasks and stimuli

All experiments were performed on Apple Power Macintosh computers using MATLAB software with the Psychophysics Toolbox extensions (Brainard, 1997; Pelli, 1997). The background luminance was set to the middle of the monitor range, about 18 cd/m². Sloan letters were based on Louise Sloan’s design specified by the NAS-NRC (1980). (The Sloan font is available from http://psych.nyu.edu/pelli/software.html). Sloan letters were usually 0.32 deg high and wide. Sinewave gratings were 1 or 8 c/deg with a circularly symmetric Gaussian envelope with a 1/e radius that we specify as “size.”

Observers viewed a gamma-corrected grayscale monitor (Pelli & Zhang, 1991). The fixation point was a 0.15 deg black square. The position of the fixation point on the screen determined the eccentricity of the signal (always presented at the center of the display). For peripheral viewing conditions, the fixation point was displayed for the entire trial. For foveal viewing, the fixation point was presented for 200 ms, followed by a 200 ms blank and then the signal. The signal, flanked by two horizontally aligned high-contrast masks of either letters or gratings, appeared at the center of the screen for 200 ms (Figure 1). Signal eccentricity was controlled by varying the position of the fixation point on the screen. Thus the signal was presented at various eccentricities along the horizontal meridian in the right visual field. Letter contrast is defined as the ratio of luminance increment to background. Letter contrast can be greater than 1. Flanker contrast was usually 0.85. Each signal presentation was accompanied by a beep. Mask-to-signal spacing is measured center to center. Usually the signal and each flanking letter were independent random samples from the same alphabet. A response screen followed, showing all the possible signals (usually the 10 letters

of the Sloan alphabet) at 80% contrast. Observers identified the signal by using a mouse-controlled cursor to point and click on their answer. Correct identification was rewarded with a beep.

Figure 1. Typical condition for crowding. The black square is a 0.15 deg fixation mark. The signal is a faint 0.32 deg Sloan letter at 4 deg in the right visual field. Two 85%-contrast masks (S, Z) flank a signal letter (R) with a signal-to-mask center-to-center spacing of 0.64 deg. Letter contrast is defined as the ratio of luminance increment to background. Letter contrast can be greater than 1. The signal contrast changes from trial to trial.

The signal duration (200 ms) is too brief for eye movements in response to the signal to help see it. We occasionally watched the observer’s eyes while the observer was doing the task to detect anticipatory eye movements, but we never saw any. The results presented in this paper (e.g. Figure 3a) reveal a more-than-tenfold threshold elevation and a steep dependence on spacing. Anticipatory eye movements would reduce the signal eccentricity by an amount that would vary between trials and among observers. The steep dependence of threshold on spacing (e.g., Figure 3a) and the consistent critical spacing among observers (e.g., Figure 3b) indicate that anticipatory eye movements were not a problem.

Threshold contrast was measured by a modified QUEST staircase procedure (Watson & Pelli, 1983; King-Smith, Grigsby, Vingrys, Benes, & Supowit, 1994) using an 82% criterion and β of 3.5 for 40-trial runs. Log thresholds were averaged over two runs for each condition.

In the detection task, the signal letter was randomly presented in one of two consecutive intervals. The flankers were displayed in both intervals, independently randomly selected for each interval. Observers indicated their choice of interval by clicking the mouse once for first and twice for second. Correct responses were rewarded with a beep.

2.3 Clipped line fit

Strasburger et al. (1991) suggested that threshold contrast for target identification is a good way to measure the effect of crowding, and we agree. Most of our data are threshold contrast plotted against spacing, and have a generally sigmoidal shape. We fit a clipped line to the data by eye. This fit has three parts: a horizontal ceiling, a falling slope, and a horizontal floor (Figure 2). Threshold elevation (a ratio) is measured from floor to ceiling. Critical spacing is the least spacing at which there is no threshold elevation in the fit (i.e., edge of the floor).

Figure 2. Clipped line fit: threshold contrast as a function of center-to-center spacing of signal and flanker. (At zero spacing the signal and flanker are superimposed, added on top of one another.) We fit a clipped line to each data set by eye. Two parameters of that fit are of interest. Threshold elevation is the ratio of thresholds at zero and infinite flanker spacing (i.e., ceiling:floor ratio). Critical spacing is the least spacing at which there is no threshold elevation (i.e., edge of the floor).

Figure 3. Effect of eccentricity. Each symbol is the geometric average of two threshold estimates. (a). Threshold as a function of flanker spacing for a 1 deg Sloan letter between flankers at various eccentricities. The solid lines are clipped-line fits, as explained in Figure 2. The horizontal line at the bottom left, below the graph, represents the width of the signal in deg. Contrast is the ratio of increment to background, and can exceed 1. (b). Critical spacing plotted against viewing eccentricity for three observers. Like Bouma (1970), we find that critical spacing is roughly half of viewing eccentricity. Observers MCP, SJR, and SSA.

3. Results

Figures 3–16 present our results. To help the reader make sense of it all, Table 2 presents the nine empirical differences between crowding and ordinary masking. We recommend focusing on the sheer strangeness of crowding. Our intuitions, based on familiarity with ordinary masking, were defied at every turn. The single most important result is Bouma’s (1970), greatly extended here, that critical spacing is roughly half the eccentricity (distance from fixation), independent of everything else.

Fact	Ordinary masking	Crowding	Figures
a	Similar in fovea and periphery.	Normally evident only in the periphery (Korte, 1923; Stuart & Burian, 1962; Flom, Weymouth, et al., 1963; Bouma, 1970).	3, 4
b	Signal disappears, suppressed by mask.	Signal is visible but ambiguous, incorporating features from mask (Korte, 1923; Flom, Weymouth, et al., 1963; Andriessen & Bouma, 1976; Wolford & Shum, 1980; Wilkinson et al., 1997; Parkes, Lund, Angelucci, Solomon, & Morgan, 2001).	1, 10
c	Occurs for any task and signal.	So far, specific to identification of letters (Flom, 1991), orientation of tumbling E (Levi, Hariharan, et al., 2002), and fine discrimination of contrast, spatial frequency, and orientation (Andriessen & Bouma, 1976; Wilkinson et al., 1997; Parkes et al., 2001).	12 - 16
d	Similar effect on identification and detection.	Little or no effect on detection (Wilkinson et al., 1997) and coarse discrimination.	12 - 14, 16
e	Narrow critical spacing, little or no effect of nonoverlapping mask.	Wide critical spacing can be more than 10 times bigger than a small signal (Korte, 1923; Stuart & Burian, 1962; Bouma, 1970; Toet & Levi, 1992; Levi, Hariharan, et al., 2002).	3 – 5
f	Critical spacing scales with signal, independent of eccentricity.	Critical spacing is roughly half of viewing eccentricity (Bouma, 1970; Toet & Levi, 1992), independent of signalsize (Strasburger et al., 1991; Levi, Hariharan, et al., 2002), mask size, mask contrast, and number of masks.	3 – 11, 13 - 15
g	Spatiotemporal selectivity more or less consistent with a receptive field.	Remarkably unselective, showing equal effect over a wide range of flanker type (letter, black disk, or square; Eriksen & Hoffman, 1973; Loomis, 1978), flanker size (10:1), and flanker number (≥2).	6, 8
h	Shallow power-law contrast response (log-log slope of 0.5 to 1).	Steep sigmoidal contrast response. Log-log slope of 2 for close spacing. Log ceiling and log slope fall exponentially with spacing.	10, 11
i	Threshold mask contrast depends on spacing. No saturation.	Threshold and saturation mask contrasts are independent of spacing.	11

Table 2. Facts: summary of the differences between crowding and ordinary masking. We cite the authors of the known facts about crowding, many replicated here, and italicize our new findings. We take line f as the defining difference: critical spacing scales with eccentricity, not size. (a). The extremely-short-range foveal effect described by Liu and Arditi (2000) is likely to be crowding. (c). Andriessen and Bouma (1976) show a large crowding-like effect of flanking bars on fine discrimination of bar orientation, and a small effect on detection threshold, too small to account for the effect on orientation discrimination. Illusory conjunction provides evidence for crowding of conjunction of color vs. shape (Treisman & Schmidt, 1982). (d). The critical spacing for detecting a letter among letters can be as large as that for identification, but we call it ordinary masking, not crowding, because it scales with letter size (Figure 14b), not eccentricity (Figure 13b). Despite refutals of the feature vs. conjunction dichotomy in the search literature, we still expect a robust feature vs. conjunction dichotomy in crowding.³ (e). Figures 12, 16a, and 16b are examples of weak effects of nonoverlapping masks in ordinary masking. (f). At 0 deg eccentricity, Levi, Klein, et al. (2002) found that critical spacing is proportional to signal size over a 50:1 range. “Roughly half” can be as low as 0.3, as in Figure 5b. Fine (2003) also reported crowding to be independent of contrast. (g). We say “more or less consistent” because current feature detector models to explain ordinary masking have not just one but several similar receptive fields (to implement divisive inhibition) as noted earlier.¹ The spatiotemporal selectivity found by Chung et al. (2001) with filtered letters is like that for ordinary masking, unlike our summary for crowding, but it is not certain whether their paradigm elicited crowding or ordinary masking (see Section 4.6). Many studies have documented systematic effects of the similarity of target and flanker (e.g., Estes, 1982; Ivry & Prinzmetal, 1991; Nazir, 1992; Kooi et al., 1994; Donk, 1999; Chung et al., 2001).

There is a minor caveat to Bouma’s rule, but it does not affect the basic intuition. The caveat is that critical spacing is asymmetric, greater in the peripheral than in the central direction from the target (Bouma 1970, 1973; Townsend, Taylor, & Brown, 1971; Banks, Larson, & Prinzmetal, 1979; Chastain & Lawson, 1979; Wolford & Shum, 1980; Toet & Levi, 1992). It is greater in radial directions (peripheral and central) than in circumferential directions (Chambers & Wolford, 1983; Toet & Levi, 1992). It is greater in the upper than in the lower visual field (Intriligator & Cavanagh, 2001). These details matter when comparing results across conditions, but they reinforce the basic intuition that the extent of crowding depends almost exclusively on the local anatomy of the visual field, independent of the signal, unlike ordinary masking, which is co-extensive with the signal, independent of location in the visual field.

3.1 Effects of spacing and eccentricity

One of the stranger aspects of crowding is Bouma’s (1970) finding that the critical spacing is proportional to eccentricity, which we replicate here. We measured the threshold contrast for identifying a 1 deg letter as a function of signal-to-mask spacing. The signal was at 0 to 24 deg eccentricity in the right visual field (see Table 1). There were two flankers, one to the left and one to the right of the signal. Figure 3a shows that the letter masks have a very strong effect, raising threshold tenfold. For each eccentricity, the clipped-line fit provides an estimate of the critical spacing. Figure 3b shows that critical spacing is proportional to eccentricity. Our data confirm the finding (Bouma, 1970; Strasburger et al., 1991; Toet & Levi, 1992; Levi, Hariharan, et al., 2002, p. 173) that the critical spacing is roughly half of the viewing eccentricity. (Bouma, 1970, was right to say “roughly” 0.5. For some of our data, this value drops as low as 0.3, as we will see below.) Andriessen and Bouma (1976) report a critical spacing of 0.4 of eccentricity for fine discrimination of line orientation. Wilkinson et al. (1997) report a critical spacing of 0.4 of eccentricity for fine discrimination of crowded grating contrast and spatial frequency, and slightly higher for fine discrimination of orientation.

Figure 4 shows threshold for observer AG in the presence of one mask, as a function of horizontal mask offset, for a 0.32 deg signal. The width of the critical region is the sum of the critical spacings, left and right. Separate curves show results at 0 and 4 deg eccentricity. In the fovea, the critical region (i.e., the sum of critical spacings left and right) is about as wide (0.40 deg) as the signal (0.32 deg). In the periphery, the critical spacings are 1.00 deg to the left and 1.25 deg to the right, for a total critical region width (2.25 deg) about 7 times the 0.32 deg width of the signal. This replicates the asymmetry of previous findings that, for a given signal location, crowding extends farther in the peripheral direction than in the central direction (Bouma 1970, 1973; Townsend et al., 1971; Banks et al., 1979; Chastain & Lawson, 1979; Wolford & Shum, 1980; Toet & Levi, 1992).

Figure 4. Fovea vs. periphery. Threshold for identifying a 0.32 deg Sloan letter (at 0 or 4 deg in right visual field) in the presence of a single flanker of the same size, as a function of spacing (i.e., flanker position). (Positive values are positions to the right of the signal. Negative values are to the left.) At 4 deg eccentricity, the critical region is 7 times wider than the letter (indicated by the horizontal bar). Observer AG. Not shown: similar results for observers MCP and MLL. Similar results at 6 deg eccentricity appear in Figure 8.

It may seem surprising that a more peripheral mask is more effective than a more central mask equally distant from the target. However, critical spacing is proportional to eccentricity, suggesting that the relevant cortical representation of visual space is progressively more compressed at greater eccentricity. Thus the more-eccentric mask is effectively closer than the less-eccentric mask (i.e., at a smaller fraction of the ever-increasing critical spacing).

Section 3.5 will show that a single flanker is much less effective than flankers on both sides (Bouma, 1970).

3.2 Effect of size

Ordinary masking would lead one to expect that the critical spacing in crowding would be proportional to signal size, not eccentricity. What is the effect of size on critical spacing? Levi, Klein, et al. (2002) and Levi, Hariharan, et al. (2002) found that, at 0 deg eccentricity, the critical spacing is proportional to size over a 50:1 range, but that, in the periphery, critical spacing is proportional to eccentricity, independent of size. We measured threshold contrast for letters of various sizes at 4 deg viewing eccentricity. Figure 5a shows threshold contrast as a function of spacing for letter sizes of 0.32, 0.5, 1, and 2 deg. For these sizes, threshold is elevated 26-fold (geometric mean). Figure 5b shows that the critical spacing did not change with letter size, instead remaining constant at about 1.2 deg, which replicates the Strasburger et al. (1991) finding, for numerals, that the spatial extent of crowding is 1.2 deg at 4 deg eccentricity, independent of size. Threshold elevation increases as a function of size (Figure 5c) because, as Figure 5a shows, the ceiling remains fixed at about 0.7 while the floor drops with size. This is just the familiar fact that contrast sensitivity for letters depends on size (see Pelli & Farell, 1999).

Figure 5. Effect of size. Identification of 0.32 - 2 deg Sloan letter (at 4 deg in the right visual field) between 2 flankers of the same size. (a). Threshold as a function of spacing. For observer AG, the threshold contrasts for all four sizes, 0.32, 0.5, 1, and 2 deg, nearly superimpose at spacings up to 1 deg. (b). Critical spacing vs. size, for three observers, showing no effect. Average (horizontal line) is 1.2 deg. (c). Threshold elevation increases somewhat with size: log-log slope of 0.6. This replicates the familiar finding that threshold contrast depends on size (Pelli & Farell, 1999).

3.3 Effect of flanker size

We also measured the effect of mask size on critical spacing. We kept signal size at 0.32 deg and varied mask size from 0.32 to 3.2 deg. We didn’t know what to expect. On the one hand, increasing the mask’s size increases its contrast energy, which we thought might increase the mask’s effect. (For a letter, contrast energy is the product of area and squared contrast.) On the other hand, enlarging the mask makes it less similar to the signal, which might lessen its effect. Surprisingly, Figure 6 shows that the threshold curves nearly superimpose, hardly affected by mask size, retaining a critical spacing of about 1.3 deg. (Figure 6a is for one observer; Figure 6b is for another.) Unlike ordinary masking, the crowding effect is not tuned to size. The range (spatial extent) of crowding is independent of signal size (Figure 5b) and mask size (Figure 6), depending solely on eccentricity (Figure 3b).

Figure 6. Effect of flanker size. Signal is 0.32 deg Sloan letter at 4 deg in the right visual field. The two flankers were 1 to 10 times the size of the signal. One fit was made to data for all mask sizes. (a). Critical spacing is 1.3 deg for MCP. (b). Critical spacing is 1.2 deg for AG. Horizontal line at the bottom left of the graph represents the width of the signal.

3.4 Effect of font

We wondered whether perimetric complexity (perimeter, squared, over ink area; Pelli et al., in press) or some other aspect of letter shape is important for crowding. Figure 7a shows threshold as a function of spacing for several fonts, including a meaningless alphabet of twenty-six 2x3 checkers (e.g., d) and another alphabet consisting of just two letters,

and

, from the Sloan alphabet. These curves are quite similar to each other, differing from one another by large, but unimportant, vertical translations and small horizontal translations. The vertical shifts track the different threshold contrasts for different fonts, which is not of interest here. The small horizontal shifts are small differences in critical spacing, which ranged from 1 to 1.3. Pelli et al. (in press) showed that efficiency for letter identification is inversely proportional to perimetric complexity of the font, but complexity seems to be irrelevant to crowding. Figures 7b and 7c plot critical spacing and threshold elevation as a function of complexity, showing no systematic effect of complexity.

Figure 7. Effect of font. Signal is 0.32 deg letter at 4 deg in the right visual field. (a). Threshold contrast as a function of spacing for various fonts, Bookman , 2 x 3 Checkers

, Sloan

, NZ Sloan

, and Outline Sloan

. (b). Critical spacing is independent of complexity. (c). Threshold elevation as a function of perimetric complexity, perimeter squared divided by area, showing that threshold elevation does not seem to be systematically related to complexity. Observer MLL. Not shown: similar results for observer MCP.

3.5 Effect of number of flankers

Would adding more flankers increase the crowding effect? Figure 8a plots threshold for letter identification in the periphery with 1, 2, and 4 flankers. The signal and flankers are all Sloan letters, right-side up. Figure 8b shows that critical spacing is independent of number of flankers. It is about 0.4 of the eccentricity. Figure 8c shows that threshold elevation increased when flankers were increased from 1 to 2, but threshold was not further elevated when flankers were increased from 2 to 4. Consistent with this, Wilkinson et al. (1997) reported that reducing the number of flanking gratings from 14 down to 2 did not significantly reduce their effect on the discriminability of the signal. Toet and Levi (1992) report extensive measurements of the effect of two T flankers on judging orientation of a T target, adding that, in pilot measurements, they found no effect of a single flanker. However, Strasburger et al. (1991) did report an increased threshold elevation when they increased the number of flankers from 2 to 4.

Figure 8. Effect of number of flankers. Signal is 0.32 deg Sloan letter at 6 deg in the right visual field. Flankers are letters, too, also right-side up, but displaced vertically or horizontally. (a). Threshold contrast as a function of spacing, for 1, 2, or 4 flankers. Flanker position (e.g., “right”) is relative to signal position. The horizontal line at the bottom left of the graph represents the width of the signal. Note that, lacking data at zero spacing (because the flankers would have collided), it is not clear whether there is a ceiling at small spacing, so that part of the clipped-line fit is somewhat arbitrary. The one-flanker data shown here, for a signal at 6 deg ecc., are similar to the data shown in Figure 4, for a signal at 4 deg ecc. We replicate the well-established finding that the critical spacing is greater in the peripheral than in the central direction. (b). Critical spacing (estimated separately for each condition, but averaging results for 1-left and 1-right) as a function of number of flankers. (c). Threshold elevation (estimated separately for each condition) as a function of number of flankers. This last graph is tentative because it depends on the somewhat arbitrary ceilings of the clipped-line fits in panel a. Observers MS and MLM. Not shown: similar results for observer MCP at 4 deg eccentricity.

It makes sense that a single flanker would be much less effective than multiple flankers that surround the object. One imagines that when there is only one flanker the observer may use a large but offset integration field to pick off the exposed target. This strategy is not available when there are two or more flankers surrounding the target.

For a signal 6 deg to the right of fixation, we find a smaller critical spacing for flankers above and below, , instead of left and right of the signal,

, which is consistent with Toet and Levi’s (1992) finding that the critical spacing is smaller along the circumference than along a radial ray from the fovea.

3.6 Effect of flanker contrast

The experiments presented above used flankers of a high contrast, 0.85. Figure 9a shows threshold signal contrast as a function of spacing for several mask contrasts. Figure 9b shows that critical spacing is independent of mask contrast. There is an outlier, the X representing a critical spacing of 0.5 deg at a mask contrast of 0.1 for observer MLL. This is based on the fit shown in panel a to the 0.1 mask contrast data (solid diamonds). Note that threshold is elevated only when the mask overlaps the signal.

Figure 9. Effect of flanker contrast for three observers identifying a 0.32 deg Sloan letter at 4 deg in the right visual field. (a). Threshold contrast as a function of spacing for several flanker contrasts. (b). Critical spacing as a function of flanker contrast. Mask contrasts below 0.1 did not elevate threshold so they have no critical spacing. Observers MCP, AG, and MLL.

Thus the anomalous point in 9b seems to represent ordinary masking, not crowding. The rest of the data show no consistent effect of mask contrast on critical spacing: For one observer, critical spacing rises slightly with mask contrast, but it falls slightly for the other two observers. Fine (2003), too, reported crowding to be independent of contrast. So far, we have seen that critical spacing is independent of signal size, mask size, mask contrast, signal and mask font, and number of masks.

Figure 10 demonstrates the effect of mask contrast, showing an abrupt transition as mask contrast is increased. Once the mask becomes visible it soon saturates, producing its full effect on the signal.

Figure 10. Effect of flanker contrast. Starting at the top, in each row, fixate the black square, and try to identify the middle letter on the right. As you read down the chart, the contrast of the center letter is always 0.50, while the contrast of the two outer letters increases (0, 0.10, 0.15, 0.25, and 0.50). You’ll find that the central letter becomes much harder to identify as soon as the flankers are at all visible.

Based solely on this demo, one might wonder whether the crowding is determined by similarity. The flankers become more similar to the signal as their contrast approaches that of the signal. However, Chung et al. (2001) manipulated signal and flanker contrast to test this hypothesis, finding that, at least in their conditions, more mask contrast always increased masking, even when this made the masks less similar to the signal.

In another view of the same data, Figure 11a shows threshold contrast as a function of mask contrast for several spacings. For a 0.32 deg letter, the contrast response curves show that threshold elevation increases abruptly with mask contrast, going from none to full effect as the mask goes from 0.1, the threshold contrast for identifying an isolated letter, to about 3 times that, saturating at higher contrast. There are two critical mask contrasts. In our clipped-line fit, mask threshold is the mask contrast at which threshold contrast of the signal begins to increase (edge of floor). And mask saturation is the mask contrast at which threshold contrast of the signal stops increasing (edge of ceiling).

Figure 11. Effect of flanker contrast for three observers identifying a 0.32 deg Sloan letter at 4 deg in the right visual field. Same data as Figure 9. (a). Threshold contrast for identifying the target letter as a function of mask contrast for observer MLL. Clipped lines (shown) are fit to the (roughly sigmoidal) data, constrained to have equal threshold and saturation contrasts of the mask for all conditions. Threshold contrast rises at 0.1 mask contrast and saturates at 0.25 mask contrast for all spacings. Clipped lines (not shown) were also fit independently to the data for each condition for each observer, and the parameters of these fits are plotted in panel d. (b). Psychometric function. Proportion correct identification of a letter as a function of contrast. The knees (critical contrasts) of this psychometric function roughly match those of the contrast response function in panel a. This is a maximum likelihood fit of a Weibull function to the measured proportion correct (not shown) at several contrasts (see Pelli et al., in press; Strasburger, 2001). The lower asymptote is 1/10 because that is the chance of correctly guessing the identity of one of 10 letters. (c). The threshold elevation (left scale of panel c) and log-log slope (right scale) of the fits in panel a (and similar data for observers MCP and AG) are high at small spacings and fall exponentially with increased spacing. (d). Threshold and saturation contrasts of the mask as a function of spacing. Mask threshold is the first knee, where the signal threshold rises. Mask saturation is the second knee, where the signal threshold saturates. Each pair of points (solid and open) is based on an independent clipped-line fit (not shown) to the data for one condition and observer. The threshold contrast for identifying the mask may be estimated from that for the signal (0.1) at low (0.01) mask contrast (panel a). Observers MCP, AG, and MLL.

This contrast-response curve is quite unlike what is usually seen in ordinary masking. Here the function rises steeply and hits a hard ceiling, with no further increase over a wide range of high mask contrasts (0.25 – 1). In ordinary masking, the function rises with a log-log slope of 0.5 to 1 and continues to increase relentlessly. The log-log slope of the (clipped line) contrast-response function for crowding is 2 at the closest spacing and falls exponentially with spacing (Figure 11c, right hand scale). The function found here is more reminiscent of the sigmoidal form of a frequency-of-seeing curve, rising suddenly from floor to ceiling over a narrow range of contrast. For comparison, Figure 11b shows the observer’s proportion of correct identifications for an unflanked signal at this eccentricity as a function of signal contrast.

Chung et al. (2001) measured the contrast-response function for a bandpass-filtered letter among similar letters at a single separation (2.2 deg) at an eccentricity of 5 deg, obtaining shallow log-log slopes (0.3 and 0.1) that are consistent with the less than 0.4 slope found here at our maximum separation (1.5 deg at an eccentricity of 4 deg). Testing at such large (near-critical) separations (about 0.4 of eccentricity), the threshold elevation and slope are nearly gone.

The series of functions plotted in Figure 11a reveal something quite remarkable. It is hardly surprising that the threshold elevation (on the vertical scale) is reduced at greater spacings, as shown in Figure 11c. But we were surprised to find that the critical mask contrasts (0.1 and 0.25 on the horizontal scale) are unaffected by the spacing. In Figure 11a every curve (one for each spacing) turns up at a mask contrast of 0.1 and saturates when the mask contrast reaches 0.25, no matter how far away the signal is. Figure 11d shows explicitly that the critical mask contrasts are independent of spacing. We will come back to this in Discussion.

3.7 Effect of task: identification and detection of letters and gratings

Most crowding studies have used identification tasks, whereas most masking studies have used detection tasks. To determine whether crowding depends on task, Figure 12 shows identification and detection thresholds for a letter among letters as a function of flanker spacing for two observers. (Figure 16a shows similar results for a third observer.) For identification, averaging across the three observers, the threshold elevation is large (ten-fold) and extends out to 1.3 deg (four signal widths). For detection, the threshold elevation is only three-fold but extends about as far (average is 1.5 deg).

Figure 12. Effect of task. Identification or detection of a letter between letter flankers. Signal is 0.32 deg Sloan letter at 4 deg in the right visual field. Threshold curves for identifying a letter are sigmoidal with an average threshold elevation of about 1 log unit and a critical spacing of 1.2 deg. (a). Observer MCP. (b). Observer MLL. There are some observer differences, but detection threshold is always lower, with less threshold elevation. The average critical spacing for detection is 1.5 deg. Horizontal line at the bottom left of the graph represents the width of the signal. Figure 16a shows similar results for a third observer.

To distinguish crowding from masking, we assessed the effect of eccentricity and size on critical spacing.

We measured the effect of eccentricity (2, 4, and 8 deg in right visual field) on detection thresholds for 0.75 deg Sloan letters. Figure 13a plots threshold as a function of spacing for each eccentricity. Figure 13b shows that the critical spacing for detection is independent of eccentricity, unlike the proportionality found for identification (Figure 3b).

Figure 13. Effect of eccentricity on detection. Detection of a letter among letters at several eccentricities in the right visual field. Signal and flankers are 0.75 deg Sloan. (a). Threshold as a function of spacing. (b). Critical spacing as a function of eccentricity. The critical spacing for letter detection is independent of eccentricity. This is characteristic of ordinary masking, whereas in crowding the critical spacing is proportional to eccentricity, as in Figure 3b. Observer MLM.

We measured detection thresholds for Sloan letters of three sizes, 0.75, 1.5, and 3 deg, at 8 deg in the right visual field. The results in Figure 14b show that the critical spacing for letter detection is proportional to size; critical spacing for letter identification is independent of size (Figure 5b).

Figure 14. Effect of size on detection. Detection of a letter among letters at several sizes. Signal and flankers have equal size. Signal is Sloan letter at 8 deg in the right visual field. (a). Threshold as a function of spacing. (b). Critical spacing as a function of size. The critical spacing for letter detection is proportional to letter size. This is characteristic of ordinary masking, whereas in crowding the critical spacing is independent of size, as in Figure 5b. Observer MCP. Not shown: similar results for observer MLL.

To us, this is the most telling difference: In ordinary masking (e.g. letter detection), the critical spacing is proportional to signal size (Figure 14b), independent of eccentricity (13b), whereas in crowding (e.g., letter identification) the critical spacing is proportional to eccentricity (3b), independent of size (5b).

We also changed the envelope size of 1 c/deg gratings in a ±45° orientation discrimination task at 20 deg viewing eccentricity (Figure 15a). We saw earlier (Figure 5b) that changing the size of letters did not affect critical spacing. However, for gratings, the critical spacing scales with the size of the envelope (Figure 15b). There is no mystery here: The gratings mask each other only when they overlap; at their critical spacing they are abutting.

Figure 15. Effect of grating extent. Size is the 1/e radius of the Gaussian envelope. Grating (at 20 deg in the right visual field) flanked by two gratings. (a). Threshold contrast for identification of ±45° orientation of 1 c/deg grating between two flanking gratings as a function of spacing, for several envelope sizes. Signal and flanking gratings had same spatial frequency and same size envelope. (b). Critical spacing as a function of envelope size. Observer MCP. Not shown: similar results for observer AG.

3.8 Effect of letter vs. grating

Here we tried letters (0.32 deg Sloan) and gratings (8 c/deg) in every combination of target and flanker. Majaj et al. (2002) show that identification of letters is mediated by a channel with a center frequency determined by the stroke frequency of the letter. For a 0.32 deg Sloan letter the stroke frequency is 1.6/0.32 = 5 c/deg, and, by their formula, the channel frequency is 6.3 c/deg, which is very close to the 8 c/deg spatial frequency of the grating we used. Thus the identification of letter and grating in this experiment was mediated by channels tuned to similar spatial frequencies.

We measured thresholds for detection and identification of 8 c/deg sinewave gratings. Signal and flanker gratings were each randomly tilted ±45° on each trial. In the detection task the observer was required to choose which of two intervals contained the signal grating (ignoring orientation). In the identification task there was only one interval and the observer was asked, on the response screen, to identify its +45° or -45° orientation.

Figures 16c and 16d show that neither grating nor letter flankers raised the grating signal’s threshold unless they overlapped it. (Letter size is 0.32 deg; grating size is 0.52 deg; see Table 1.) Grating threshold elevation at all spacings is similar for both tasks (detection and identification) and flanker types (letter and grating). Compared with identifying a letter among letters, the grating curves show no ceiling and have a small critical spacing (about one signal width). The grating’s narrow critical spacing — threshold is elevated only when the flanker overlaps the grating — suggests ordinary masking, not crowding.

Figure 16. Effect of letter vs. grating. Identification or detection of a letter or grating flanked by letters or gratings. Signal at 4 deg in the right visual field. (a). Letter flanked by letters. Averaging across Figures 12ab and 16a, the critical spacing is about 5 letter widths (1.5 deg) for both identification and detection. (b). Letter flanked by gratings. Critical spacing is 2 times the width of the signal for identification, and 5 times the width of the signal for detection. (c). Grating flanked by letters. (d). Grating flanked by gratings. The results show that threshold is elevated only when the flankers overlap the signal. Sloan letters were 0.32 deg wide and sinewave gratings were 8 c/deg with a 0.52 deg Gaussian window (radius at 1/e). Horizontal line at lower left corner represents the width of the signal. There were always two flankers, to the right and left of the signal. Observer AG. Not shown: similar results for observers MCP and MLL.

When we originally got the grating results reported in Figures 16c and 16d, we were led to think, wrongly as it turns out, that gratings are immune to crowding. Our identification task was too coarse. We had asked the observer to distinguish orientations 90° apart. Ordinary masking studies have shown that we see gratings by means of feature detectors that have an orientation bandwidth of ±15° to ±30° (Phillips & Wilson, 1984). Thus orthogonal gratings are detected by distinct feature detectors, and we would expect the label of a single feature detector to suffice for identifying the coarse orientation of the grating. Indeed, Thomas and Gille (1979) reported that two gratings differing in orientation by 20° to 30° are identified just as accurately as they are detected. And the thresholds for detection and identification in Figures 16c and 16d seem to be identical. This is the logic that Watson and Robson (1981) applied to frequency identification. When the two signals stimulated different detectors, observers could identify at the threshold for detection. When the same feature detector picks up both signals, then the observer cannot identify based on a single feature detection and requires at least two detectors to be active. The ratio of the detector responses would presumably be a good basis for fine discrimination. (Treisman, 1991, makes the same point for other stimulus dimensions.) Thus a parametric change in the task, from a coarse (>2:1) to a fine (<2:1) frequency discrimination, results in a qualitative change in the observer’s computational algorithm, from single- to multi-feature detection and integration (also see Verghese & Nakayama, 1994, and Discussion, Section 4.3).

4. Discussion

Our seven theoretical conclusions about the difference between crowding and ordinary masking are listed in Table 3 and discussed in Sections 4.1 – 4.7. The discussion of illusory conjunctions comes last (Section 4.7), but its only prerequisite is the vocabulary established in the Introduction (Section 1). We begin the discussion by proposing a definition.

Theory	Ordinary masking	Crowding	Facts (Table 2)	Section
a	Critical spacing is proportional to size and independent of eccentricity.	Critical spacing is proportional to eccentricity (Bouma, 1970) and independent of size (Strasburger et al., 1991; Levi, Hariharan, et al., 2002).	f	4.1
b	Occurs for any task.	Specific to tasks that could not be performed based on a single detection by coarsely coded feature detectors.	b - d	4.2, 4.3
c	Same feature detector mediates the effects of mask and signal.	Distinct feature detectors mediate the effects of mask and signal.	g - i	4.4
d	Eccentricity doesn’t matter.	In the periphery, the observer uses an inappropriately large integration field because smaller fields are absent.	a - i	4.5
e	Impairs feature detection.	Impairs feature integration (Flom, Weymouth, et al., 1963; Wolford & Shum, 1980; He et al., 1996; Parkes et al., 2001; Chung et al., 2001; Levi, Hariharan, et al., 2002).	a - i	4.6
f	Selectivity is that of the feature detector.	Selectivity is that of the feature integrator.	g	4.6
g	No signal feature is detected, so the signal is invisible.	Features of both signal and mask are detected and combined, so the signal is visible, but jumbled with the mask (Korte, 1923; Wolford & Shum, 1980; Parkes et al., 2001; Levi, Hariharan, et al., 2002).	b - d	4.7

Table 3. Theory: summary of the differences between crowding and ordinary masking. We cite the authors of existing theories about crowding, and italicize our new ideas. (b). Treisman (1991) makes a similar suggestion for illusory conjunctions. (c). This idea is implicit in the models that Wolford and Shum (1980), Treisman and Schmidt (1982), Wilkinson et al. (1997), and Parkes et al. (2001) use to explain their results. (f). Current feature detector models have several receptive fields, to implement divisive inhibition, but the differences in selectivity of these various fields are too small to matter here. (g). Treisman and Schmidt (1982) make a similar suggestion for illusory conjunction.

Using published and new results, we have established that the original crowding phenomenon — impaired identification of a letter among letters in the periphery — is unlike ordinary masking. We suggest that the term “crowding” be applied to any phenomenon that exhibits the critical-spacing dependence reported by Bouma (1970).

When defining a term already in use, the desire to sharpen must be tempered by the need to respect established usage. Crowding was discovered in the course of measuring letter acuity in patients with central field loss (Korte, 1923) or amblyopia (Ehlers, 1936).⁴ Stuart and Burian (1962) coined the term “crowding” for the impairment of identification of a peripheral letter by neighboring letters. Since then the term has been used primarily, but not exclusively, to refer to lateral masking of letters by letters. Most writings on crowding — and this manuscript is no exception