Given the birds, where is the flock? Visual estimation of the location of collections of points

Abstract

Many visual tasks resemble statistical judgments, estimating the center of a cloud of identical items for example. In statistical form, the observer sees a sample drawn from an invisible probability density function (PDF) : the observer attempts to estimate the location of the PDF. He receives larger rewards for lower variance. Optimal minimum variance estimators are different for different distributions. We evaluated performance for three location families (Gaussian, Laplacian, and Uniform). How does human perceptual organization stack up against optimal perceptual estimation? We found that observers adopted distinct estimators for distinct distribution families, each approximately minimizing variance for its family. To explain observers ability to adapt to different distributional families, we propose that observers adopt a single estimator based on clusters in the sample. This Visual Cluster Model accounted for performance across distributions, suggesting that perceptual grouping first aggregates parts into clusters and only then into a whole. Significance statementImagine a flock of birds. We can predict where additional birds might appear by estimating the probability density function (PDF) of the birds. We compared performance in estimating the location of PDFs drawn from Gaussian, Laplacian or Uniform location families, rewarding lower variance. The optimal estimators for the three families are different. Observers approximately minimized variance for each condition and used different estimators for different families. How could they do so? We propose that observers use a single estimator based on sample clusters: perceptual grouping first aggregates parts into clusters and only then into a whole.