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Richard Murray, Kevin DeSimone, Minjung Kim; How do we count at a glance?. Journal of Vision 2017;17(10):400. doi: https://doi.org/10.1167/17.10.400.
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© ARVO (1962-2015); The Authors (2016-present)
Many studies have examined the ability of humans and other animals to rapidly perceive the approximate number of elements in a scene, but there has been little work on what computation underlies this ability. To address this question we measured psychophysical decision spaces for number judgements. Observers judged whether a reference stimulus or test stimulus contained more dots. The reference stimulus had fixed area and density on all trials. The test stimulus had a wide range of areas and densities across trials. From 3,300 trials we created a 2D plot showing the observer's probability of choosing the test stimulus as more numerous, as a function of its log area and log density. In fifteen such plots (five observers with three reference stimuli each; 49,500 trials total), fitted decision curves showed that number judgements were based on log-area plus log-density, i.e., they were monotonically related to true number (consistent with Cicchini et al., 2016). We fitted a generalized additive model (GAM) to this data, and found that number judgements were based on almost perfectly logarithmic transformations of area and density, again demonstrating that number judgements are tightly linked to true number. There is debate about whether number judgements are based on number, or on low-level properties like density. We implemented an ideal observer model that simply counts stimulus elements, and also Dakin et al.'s (2011) bandpass-energy model of number perception, and ran them in the same experiment as human observers. Surprisingly, both models' decision spaces were practically the same as human observers'. Thus decision spaces are highly informative in that they reveal the stimulus properties that guide observers' number judgements, but they are less useful for discriminating between current competing models. We will suggest that number adaptation aftereffect experiments have greater potential to choose between current models.
Meeting abstract presented at VSS 2017
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