Crowding is the deterioration of target identification by neighboring objects. For example, a target letter is more difficult to identify when flanked by letters (“flankers”). Crowding is particularly pronounced in the peripheral visual field (
Bouma, 1970;
Bouma, 1973;
He, Cavanagh, & Intriligator, 1996;
Levi, Hariharan, & Klein, 2002;
Levi, Klein, & Aitsebaomo, 1985;
Pelli, Palomares, & Majaj, 2004;
Strasburger, Harvey, & Rentschler, 1991), but also occurs in foveal vision (
Coates, Levi, Touch, & Sabesan, 2018;
Flom, Weymouth, & Kahneman, 1963;
Liu & Arditi, 2000;
Malania, Herzog, & Westheimer, 2007;
Sayim, Westheimer, & Herzog, 2008;
Sayim, Westheimer, & Herzog, 2010;
Sayim, Westheimer, & Herzog, 2011). There are several key factors that determine the strength of crowding, including target-flanker spacing (
Bouma, 1970;
Bouma, 1973;
Toet & Levi, 1992), similarity (
Chung, Levi, & Legge, 2001;
Kooi, Toet, Tripathy, & Levi, 1994;
Levi et al., 2002;
Nazir, 1992;
Põder, 2006;
Sayim et al., 2008), and grouping (
Banks, Larsson, & Prinzmetal, 1979;
Banks & White, 1984;
Livne & Sagi, 2007;
Manassi, Sayim, & Herzog, 2012;
Manassi, Sayim, & Herzog, 2013;
Melnik, Coates, & Sayim, 2018;
Saarela, Sayim, Westheimer, & Herzog, 2009;
Sayim et al., 2010,
Sayim et al., 2011;
Sayim, Greenwood, & Cavanagh, 2014;
Wolford & Chambers, 1983).
Crowding not only deteriorates target identification but also changes its appearance (
Greenwood, Bex, & Dakin, 2010;
Korte, 1923;
Sayim & Cavanagh, 2013;
Sayim & Wagemans, 2017). A number of recent studies used appearance-based methods to characterize in detail how target appearance changed in crowding (
Coates, Wagemans, & Sayim, 2017;
Sayim & Taylor, 2019;
Sayim & Wagemans, 2017). One of the central findings of these studies was that observers perceived fewer elements than were presented (“omission errors”;
Coates et al., 2017;
Sayim, Myin, & Van Uytven, 2015;
Sayim & Wagemans, 2017; see also
Korte, 1923). For example, when asked to draw crowded letters and letter-like stimuli presented in the periphery, participants often omitted presented target elements (
Sayim & Wagemans, 2017). Importantly, the omission error rate depended on crowding strength, with more omissions under strong compared with weak crowding (
Sayim & Wagemans, 2017). Similar omissions were also found with stimuli of higher complexity such as the Rey-Osterrieth figure (
Coates et al., 2017), abstract paintings (
Sayim et al., 2015), and letter strings in which participants frequently reported fewer letters than were presented (
Liu & Arditi, 2000;
Korte, 1923; see also
Strasburger, 2014;
Strasburger, Rentschler, & Jüttner, 2011).
Usually, it is assumed that crowding only deteriorates target identification but not target detection (
Levi et al., 2002;
Pelli et al., 2004; but see
Allard & Cavanagh, 2011). However, omission errors under crowding are akin to a deterioration of detection: although the studies that revealed omission errors did not use standard detection tasks in which observers indicate target absence and presence, omission errors can be classified as failures of detection as the presence of an element (or a subset of elements) is not reported, similar to a miss in detection tasks. Whether omission errors are an integral (and often overlooked) characteristic of crowding is still unclear.
A particularly strong case of omission errors occurred when all displayed items were the same. For example, when presented with three closely-spaced Ts in the periphery (
Figure 1), most participants verbally reported and drew only two Ts (
Sayim & Taylor, 2019; see also
Taylor & Sayim, 2018). Similarly, when subjects were asked to report all items of a letter trigram, many errors indicated the loss of a repeated letter feature (
Coates, Bernard & Chung, 2019). We termed this phenomenon when one (or multiple) of a number of identical items is not reported “redundancy masking” (
Sayim & Taylor, 2019;
Yildirim, Coates, & Sayim, 2019a; see also
Coates et al., 2019). Here, to characterize redundancy masking and to elucidate its relations and commonalities with crowding, we investigated the dependence of redundancy masking on spatial features. In particular, we investigated stimulus attributes that have been shown to be effective—or ineffective—in modulating crowding: spacing, spatial arrangement (anisotropy), size, and regularity.
One of the key characteristics of crowding is its dependence on the spacing between the target and the flankers (
Bouma, 1970;
Pelli et al., 2004): identification improves with increasing target-flanker spacing (
Bouma, 1970;
Pelli et al., 2004). The distance at which flankers cease to interfere with target identification, the critical spacing, is proportional to the target's eccentricity, and is often estimated to be approximately 0.5 times the eccentricity (in the radial direction, Bouma's law;
Bouma, 1970,
Pelli et al., 2004). However, the “crowding zone” in which flankers impair performance is anisotropic (
Greenwood, Szinte, Sayim, & Cavanagh, 2017;
Petrov & Popple, 2007;
Toet & Levi, 1992). Flankers positioned along an axis directed to the fovea, that is, radial flankers, usually impair performance over larger distances than flankers that are positioned on the tangential axis (radial-tangential anisotropy;
Chambers & Wolford, 1983;
Pelli, Tillman, Freeman, Su, Berger, & Majaj, 2007;
Toet & Levi, 1992).
A number of studies showed size invariance of crowding (
Levi et al., 2002;
Pelli et al., 2004;
Strasburger et al., 1991;
Tripathy & Cavanagh, 2002): the strength of crowding was determined primarily by the center-to-center spacing between target and flankers, not the distance between closest edges (the edge-to-edge spacing). For example, when presenting stimuli with different sizes (while keeping the target visibility constant), a five-fold increase in target size resulted in less than a 15% change in the spatial extent of crowding (
Tripathy & Cavanagh, 2002). Hence stimulus size seems to be negligible in crowding. However, size differences of the target and the flankers do play a role in crowding, for example, because of a reduction of target-flanker similarity and target-flanker grouping (
Levi & Carney, 2009;
Malania et al., 2007;
Manassi et al., 2012;
Saarela et al., 2009; but see
Pelli et al., 2004).
The strength of grouping between the target and the flankers is generally a good predictor of crowding strength, with strong (weak) target-flanker grouping yielding low (high) performance (
Banks et al., 1979;
Banks & White, 1984;
Herzog, Sayim, Chicherov, & Manassi, 2015;
Livne & Sagi, 2007;
Manassi et al., 2012; Manassi et al.,
2013;
Saarela et al., 2009;
Sayim et al., 2010;
Sayim et al., 2011;
Wolford & Chambers, 1983). For example, when the spacing between all items—the target and multiple flankers—was the same (regular spacing), crowding and grouping were strong (
Saarela, Westheimer, & Herzog, 2010). When the spacing was irregular, the target did not group with the flankers, and performance improved compared with regular spacing (
Saarela et al., 2010). As performance depends on target-flanker grouping, the effect of regularity can be reversed when irregular arrangements of flankers group more strongly with the target than regular arrangements (
Manassi et al., 2012;
Sayim, Manassi, & Herzog, 2010). Although strong target-flanker grouping is usually associated with strong crowding, a number of recent studies showed that strong grouping can also be beneficial, for example, when the target groups with an identical shape presented in the fovea (
Sayim, Greenwood, & Cavanagh, 2014) or when emergent features help to identify the target (
Melnik et al., 2018,
2020). Importantly, although crowding and grouping share many features, such as the integration of information across space and their dependence on spacing and similarity, they are different processes as shown, for example, by their different spatial extents (
Sayim & Cavanagh, 2013).
Note that these characteristics of crowding have typically been measured with flanked target identification. However, the deleterious effect of redundancy masking is easily missed when identifying a single target. For example, using a free report and drawing paradigm with displays such as in
Figure 1, most observers reported only two letters, but they correctly reported the target as a “T” when asked to identify the central letter (
Sayim & Taylor, 2019). Therefore to explicitly determine when a repeated item is lost, we used an enumeration task in which all items in the display were relevant. Previous enumeration experiments showed that accuracy is usually high up to approximately five presented items (
Bourdon, 1908;
Jensen, Reese, & Reese, 1950;
Jevons, 1871;
Kaufman, Lord, Reese, & Volkmann, 1949;
Mandler & Shebo, 1982;
Piazza, Fumarola, Chinello, & Melcher, 2011;
Revkin, Piazza, Izard, Cohen, & Dehaene, 2008;
Taves, 1941;
Trick & Pylyshyn, 1994). This so-called
subitizing when small numbers of items are presented is different than the process for larger numbers in which the number of items is not easily “seen” but needs to be (imprecisely) estimated or deliberately counted (
Jensen et al., 1950;
Kaufman et al., 1949;
Mandler & Shebo, 1982;
Revkin et al., 2008;
Trick & Pylyshyn, 1994). For example, in some of the earliest contributions, it was shown that enumeration errors start to emerge at four (
Jurin, 1738; see also
Strasburger & Wade, 2015) or five items (
Jevons, 1871). Similarly, response times were shown to be almost invariant in enumeration tasks with arrays of up to approximately four items, followed by a rapid increase with increasing numbers of items (
Jensen et al., 1950;
Kaufman et al., 1949;
Mandler & Shebo, 1982). Few studies have investigated subitizing in peripheral vision (
Chakravarthi & Herbert, 2019;
Palomares, Smith, Pitts, & Carter, 2011;
Parth & Rentschler, 1984;
Railo, Koivisto, Revonsuo, & Hannula, 2008). Here we used an enumeration task with relatively small numbers of items presented in the visual periphery to investigate redundancy masking.
In four experiments, observers were presented with arrays of small numbers of closely-spaced lines centered at 10° eccentricity in the left or right visual field. We varied the number of lines to obtain sufficient uncertainty, which is required to reveal the effect of redundancy masking (see General discussion; cf.,
Sayim & Taylor, 2019). The task was to indicate the number of lines. In
Experiment 1, we investigated the role of spacing in redundancy masking by varying the distance between adjacent vertical lines. Redundancy masking was strong with small spacings, weakened with increasing spacing, and ceased at large spacings, showing that spacing strongly modulated redundancy masking. In
Experiment 2, we investigated the effect of spatial arrangement by presenting radial (horizontally arranged vertical lines as in
Experiment 1) and tangential (vertically arranged horizontal lines) arrays of lines. We found strong redundancy masking with radial arrangements and no redundancy masking with tangential arrangements of lines. In
Experiment 3, we asked whether target size modulates redundancy masking, varying line length and width. The strength of redundancy masking was independent of the length of the lines; however, it was modulated by the width of the lines, yielding less redundancy masking with thicker compared with thinner lines. Finally, in
Experiment 4 we varied the regularity of the line arrays by introducing vertical or horizontal jitter to individual lines. We found that regularity influenced the strength of redundancy masking. High regularity of the line arrays resulted in strong redundancy masking, and a reduction of regularity decreased redundancy masking in conditions with small numbers of lines. Taken together, we revealed several key characteristics of redundancy masking by showing how spacing, spatial arrangement, size, and regularity modulated the perception of peripherally presented arrays of lines.