Substitution and pooling in crowding

Jeremy Freeman (Corresponding Author), Ramakrishna Chakravarthi, Denis Pelli

Research output: Contribution to journalArticlepeer-review

67 Citations (Scopus)


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 presented in between one similar and one dissimilar flanker. (Simple) substitution takes 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, on the basis of a combination of information from target and flankers, rather than being based on a single letter.
Original languageEnglish
Pages (from-to)379-396
Number of pages18
JournalAttention, Perception & Psychophysics
Issue number2
Early online date9 Dec 2011
Publication statusPublished - Feb 2012


  • crowding
  • substitution
  • pooling
  • mixture modeling


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