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Jeffrey Beck, Wei Ji Ma, Vidhya Navalpakkam; Bayesian theory of visual search. Journal of Vision 2008;8(6):1081. doi: https://doi.org/10.1167/8.6.1081.
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Human performance in searching for a tilted target among vertical distractors is well described by signal detection theory (SDT) models which combine the outputs of noisy detectors using a maximum or summation operation. These theories assume each detector is a neuron best tuned to the target, and a detector's response to the target or distractor follows a Gaussian distribution. However, recent work questions the validity of SDT assumptions in search tasks with more complex stimulus distributions. Instead, a saliency-based signal-to-noise ratio was proposed to measure task difficulty. A drawback of this theory is that it cannot predict receiver operating characteristics (ROCs).
We reconcile and generalize both approaches by developing a fully Bayesian model of visual search. We study detection of a target among distractors, where target and distractor features are drawn from arbitrary, but known, distributions. At each location in the display, the feature (such as orientation) is coded in a population of neurons with Poisson-like variability. Decisions are based on log odds of target presence given the responses of all neurons at each location (unlike SDT, where decisions are based on the neurons best tuned to the target). Log odds are computed via a nonlinear operation on the location-specific log odds, which incorporate the feature distributions. This model 1) reproduces behavioral effects and ROCs in simple visual search, such set size effects, target-distractor similarity, and distractor heterogeneity; 2) explains behavior in complex search conditions, e.g. flanking distractors; 3) can in special cases be approximated by the maximum or sum rule. Additionally, we show in some cases the decision variable from the Bayes-optimal computation is approximately Gaussian and can be linked to SDT. Finally, we demonstrate how the Bayesian approach can predict which neurons are most informative and argue that attention provides task relevant prior information.
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