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Keiji Ota, Qihan Wu, Pascal Mamassian, Laurence Maloney; Modeling visual estimation of the centers of symmetric distributions. Journal of Vision 2021;21(9):2381. https://doi.org/10.1167/jov.21.9.2381.
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Estimating the summary statistics of arrays of items is a key visual operation (see Jacoby, Kamke & Mattingley, JEP:HPP, 2013). In previous work (Ota et al., VSS, 2020), we presented human observers with 9-point samples (points on a computer screen) drawn from three families of symmetric population density functions (Gaussian, Laplace, and Uniform) and asked them to estimate the center (axis of symmetry) of the population given only the sample and knowledge of distributional family from which it had been drawn. We tested whether observers estimate the center differently if they know that the points are drawn from, for example, a Uniform. We found that the visual system treated samples from three different populations differently but that no obvious normative criterion (e.g., minimum variance) captured what observers had done. Here we describe a process model intended to capture human performance for all three distributions. We propose that the center estimate is a weighted linear combination of the nine sample points but that the weights assigned to each point depend on two factors. The first is a global agreement of each sample point with the others (a measure based on likelihood) and the second depends upon the clusters to which the point belongs. Intuitively, points within a cluster are assigned more weight in estimation. These two steps can be interpreted as two opposite constraints the visual system has to optimize, the integration of the points (likelihood) and their segmentation (clusters). We show that this two-step model can account for observed quantitative differences in performance with the three distributions. These results illustrate that our visual system is sensitive to the distributional family when estimating the summary statistics of a sample drawn from the family, and that the center estimates of symmetric distributions can be described by a single model of perceptual organization.
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