Direction information in multiple object tracking is limited by a graded resource

Abstract

Is multiple object tracking (MOT) limited by a fixed set of structures (slots), a limited but divisible resource, or both? Here, we answer this question by measuring the precision of the direction representation for tracked targets. The signature of a limited resource is a decrease in precision as the square root of the tracking load. The signature of fixed slots is a fixed precision. Hybrid models predict a rapid decrease to asymptotic precision. In two experiments, observers tracked moving disks and reported target motion direction by adjusting a probe arrow. We derived the precision of representation of correctly tracked targets using a mixture distribution analysis. Precision declined with target load according to the square-root law up to six targets. This finding is inconsistent with both pure and hybrid slot models. Instead, directional information in MOT appears to be limited by a continuously divisible resource.

Figure 1

Method. Observers were presented with an array of identical dark gray disks on a light gray background. A variable number of targets were designated at the start of the trial (a). All disks then moved independently for several seconds (b). In Experiment 1, two probes were presented in sequence on the same probe disk at the end of each trial. When the probe disk turned blue (classification probe, c), the observer indicated whether or not the disk was a target. When a blue arrow was presented on the probe disk (d), the observer had to adjust the arrow to match the probe disk’s trajectory. The primary dependent variable was the angular error, the difference between the adjusted angle and the probe’s true direction of motion (e). In Experiment 2, observers performed the adjustment task twice on each trial, but did not perform the classification task.

Figure 2

Illustration of the mixture model procedure. Gray bars represent a histogram of the angular errors for one observer tracking two targets in Experiment 1, in 20° bins. The broken line (tracked) represents the estimated (von Mises) distribution of errors on trials on which the probed target was tracked, while the dotted line (untracked) represents the estimated (uniform) distribution of errors on trials on which the probed target was not tracked. The two distributions are mixed by multiplying the tracked distribution by P_t and the untracked distribution by (1 - P_t). See Data Analysis section for further details.

Figure 3

Proportion of targets tracked and distribution parameters as a function of tracking load for Experiment 1 (top panels) and Experiment 2 (bottom panels). Left hand panels plot σ, the standard deviation of the fitted von Mises distribution, for both targets (circles) and distractors (diamonds). Right hand panels plot measures of proportion of targets tracked: P_t, the fitted mixture parameter (triangles); and corrected classification accuracy H-F (squares, Experiment 1 only). See Data Analysis section for details. All error bars represent the 95% within-subject confidence intervals (Loftus & Masson, 1994; Masson & Loftus, 2003) based on the effect of number of targets.

Figure 4

Tracking capacity as a function of tracking load for Experiment 1 (left panel) and Experiment 2 (right panel). Triangles denote capacity derived from the distribution analysis (computed as NPt), and squares denote capacity derived from the classification probes (computed as N(H-F)). See Data Analysis section for details. All error bars represent the 95% within-subject confidence intervals based on the effect of number of targets.

Figure 5

Experiment 2 data versus models. Left panel is the pure resource model, middle column the slots + resources model, right column the slots + averaging model. Data are plotted as circles and solid lines, model predictions as squares and dotted lines. Error bars represent the within-subjects 95% confidence interval for the data X model interaction. Unconnected points in each plot are the σ data that the model is based on. Error bars for the base values are standard errors of the mean. Numbers on each plot indicate the RMS error for that model, with the standard error of the mean in parentheses.