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

A key step in perceptual organization is segmentation of a scene into wholes made of parts: birds form flocks, pedestrians form crowds. The parts have spatial locations as does the whole and we can ask, how do the locations of the parts influence the perceived location of the whole? The answer may depend on the nature of the parts, the processes that generate them: the influence of single birds on the location of a flock may be different from that of single pedestrians on the location of a crowd. We treated the parts as samples from a probability density function (PDF) and asked participants to estimate the location of the generating PDF given a sample. The generating PDFs belonged to one of three location families - Gaussian, Laplacian or Uniform. Observers received training with each family and knew which family the generating PDF came from on each trial. We compared human performance to that of the Uniform Minimum Variance Unbiased Estimator (UMVUE) for each location family. We based our analyses on the measured influence of each sample point, a measure of how the observer made use of each sample point in estimating the center. Observers used different estimators for different families and the estimator chosen for samples from each family were close to the UMVUE for that family. How does the observer calculate approximate UMVUEs for the three location families considered? We propose that a critical step is to estimate the locations of visual clusters in the sample. The Visual Cluster Model accurately captured human performance across all three distributions. Our findings suggest that the observers estimate of the location of the whole is based not directly on the locations of the parts but rather on the clusters they form.