No capacity limit in attentional tracking: Evidence for probabilistic inference under a resource constraint

Abstract

Human ability to simultaneously track multiple items declines with set size. This effect is commonly attributed to a fixed limit on the number of items that can be attended to, a notion that is formalized in limited-capacity and slot models. Instead, we propose that observers are constrained by stimulus uncertainty that increases with the number of items but use Bayesian inference to achieve optimal performance. We model five data sets from published deviation discrimination experiments that varied set size, number of deviations, and magnitude of deviation. A constrained Bayesian observer better explains each data set than do the traditional limited-capacity model, the recently proposed slots-plus-averaging model, a fixed-uncertainty Bayesian model, a Bayesian model with capacity limit, and a simple averaging model. This indicates that the notion of limited capacity in attentional tracking needs to be revised. Moreover, it supports the idea that Bayesian optimality of human perception extends to high-level perceptual computations.

A simple proximity heuristic allows tracking of multiple objects through occlusion

“…The most significant performancelimiting factor in any form of MOT may be the uncertainty associated with represented object locations, relative to the proximity of other objects that might steal the spotlight of activation and foil ongoing correspondence computations (Franconeri, Jonathan, & Scimeca, 2010;Franconeri, Scimeca, & Jonathan, 2012;Franconeri et al, 2008;Ma & Huang, 2009;Vul, Frank, Alvarez, & Tenenbaum, 2009). Our results cannot rule out a role for motion extrapolation across other types of disruptions or for tracking performance without disruptions.…”

Why do people appear not to extrapolate trajectories during multiple object tracking? A computational investigation

“…The inclusion of nontarget measurements is critical, as the typical MOT task would be trivial if the observer knew which portions of the moment-by-moment stimulus were due to targets. All of the observations are corrupted by independent noise; as is standard in Bayesian approaches to perception, we assume that the observer is aware of her own noise variance (e.g., Girshick, Landy, & Simoncelli, 2011;Kersten, Mamassian, & Yuille, 2004;Lee & Mumford, 2003;Ma & Huang, 2009;Maloney, 2002;van den Berg, Shin, Chou, George, & Ma, 2012;Vul, Frank, Alvarez, & Tenenbaum, 2009; in the case of motion, specifically, see Sekuler, Watamaniuk, & Blake, 2002;Warren, Graf, Champion, & Maloney, 2012). 2.…”

“…The Kalman filter is a basic framework for recursively estimating the values of unknown variables from noisy measurements. It is applied frequently in computer vision applications for tracking (BarShalom, & Fortmann, 1988;Boykov & Huttenlocher, 2000), and it supplies the main framework for two prior modeling efforts in MOT (Ma & Huang, 2009;Vul, Frank, Alvarez, & Tenenbaum, 2009). Using the Kalman filter as a computational foundation, we begin by implementing three models of multiple object tracking, one that does not utilize extrapolated predictions, and two models that weight extrapolations in different ways.…”

“…Actually, relatively few computational models have been implemented in the first place; we are aware of only one oscillator model (Kazanovich & Borisyuk, 2006) and two Bayesian models (Ma & Huang, 2009;Vul et al, 2009). These models have been designed to capture basic aspects of performance and, to a certain extent, assumed features of neural implementation.…”

“…Tracking errors can arise from incorrect correspondence inferences, in particular when a nontarget is mistakenly identified with a target (Bae & Flombaum, 2012;Franconeri, Intriligator & Cavanagh, 2001;Franconeri, Jonathan, & Scimeca, 2010). Two reports have explored computational models that adopt a probabilistic approach to representations of object position and correspondence (Ma & Huang, 2009;Vul, Frank, Alvarez, & Tenenbaum, 2009). These models employ Bayesian inference to infer moment-by-moment positions from noisy measurements, and to infer object correspondences between current positions and those in memory.…”