Academic journal article Attention, Perception and Psychophysics

Substitution and Pooling in Crowding

Academic journal article Attention, Perception and Psychophysics

Substitution and Pooling in Crowding

Article excerpt

Published online: 9 December 2011

© The Author(s) 2011. This article is published with open access at

Abstract Unless we fixate directly on it, it is hard to see an object among oTher objects. This breakdown in object recognition, called crowding, severely limits peripheral vision. The effect is more severe when objects are more similar. When observers mistake the identity of a target among flanker objects, they often report a flanker. Many have taken these flanker reports as evidence of internal substitution of the target by a flanker. Here, we ask observers to identify a target letter presented in between one similar and one dissimilar flanker letter. Simple substitution takes in only one letter, which is often the target but, by unwitting mistake, is sometimes a flanker. The opposite of substitution is pooling, which takes in more than one letter. Having taken only one letter, the substitution process knows only its identity, not its similarity to the target. Thus, it must report similar and dissimilar flankers equally often. Contrary to this prediction, the similar flanker is reported much more often than the dissimilar flanker, showing that rampant flanker substitution cannot account for most flanker reports. Mixture modeling shows that simple substitution can account for, at most, about half the trials. Pooling and nonpooling (simple substitution) together include all possible models of crowding. When observers are asked to identify a crowded object, at least half of their reports are pooled, based on a combination of information from target and flankers, rather than being based on a single letter.

Keywords Crowding . Substitution . Pooling . Mixture modeling

(ProQuest: ... denotes formulae omitted.)


In daily life, visual crowding often prevents recognition of objects in clutter. It is impossible to recognize objects that are too close together, and the critical spacing for recognition grows proportionally with eccentricity (Bouma, 1970; Levi, 2008; Pelli & Tillman, 2008). Crowding wrecks object recognition, but what remains in its wake? Analyzing observers' mistakes during crowding might elucidate how crowding happens, by revealing how the mistaken report depends on the stimulus. Observers who are asked to identify a crowded target often mistakenly report a flanking object instead (Chastain, 1982; Estes, Allmeyer, & Reder, 1976; Huckauf & Heller, 2002; Krumhansl & thomas, 1977; Põder & Wagemans, 2007; Strasburger, 2005; Strasburger, Harvey, & Rentschler, 1991; Vul, Hanus, & Kanwisher, 2009; Wolford & Shum, 1980). This basic finding is consistent with two different accounts of crowding: substitution and pooling. In the substitution account, observers merely confuse the locations of the flanker and target objects, perhaps due to positional uncertainty or failure of attentional selection, and the report is based on a single object, from the wrong place (Chastain, 1982; Estes et al., 1976; Huckauf & Heller, 2002; Strasburger, 2005; Strasburger et al., 1991; Vul et al., 2009; Wolford & Shum, 1980). In the pooling account, observers combine features across several objects and sometimes report a flanker, because that (flanker) object is similar to (i.e., shares features with) the pooled result (Dakin, Cass, Greenwood, & Bex, 2010; Greenwood, Bex, & Dakin, 2009; Parkes, Lund, Angelucci, Solomon, & Morgan, 2001; Prinzmetal, 1995; Treisman & Schmidt, 1982; van den Berg, Roerdink, & Cornelissen, 2010; Wolford & Shum, 1980).

Any model of crowding must receive the stimulus as input and produce the appropriate kind of observer response (e.g., a letter or a word). That is a vast space of possible models. Particular models-for example, substitution and pooling-have been carved out of that space. Here, we carefully define pooling to divide the space in two: pooling and nonpooling. Pooling models take input from more than one object and may perform any computation to produce the response. …

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