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Jiri Najemnik, Wilson Geisler; Simple summation rule for optimal eye movement selection. Journal of Vision 2007;7(9):716. doi: 10.1167/7.9.716.
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Humans can achieve near-optimal fixation search performance when compared to a Bayesian ideal searcher constrained with the human map of target detectability (d-prime) across the visual field (Najemnik & Geisler, 2005). Yet, the computations performed by the ideal searcher to select the next fixation location are nonlinear and complex, and hence seem improbable for an implementation within a biological nervous system. Here, we present a simple summation rule for optimal fixation selection in visual search. Specifically, we show that a weighted sum across the current priors on the target's location is an accurate measure of how much information about the target' location will be obtained for any considered next fixation. This weighted summation formula (the weights are the squares of the d-primes) becomes an exact expression in the limiting case of an infinite number of independent potential target locations across the search area, but serves as an excellent approximation even when the number of independent potential target locations is relatively small. We show that the new rule generally achieves search performance equal to that of the Bayesian ideal searcher. Currently, the most prevalent candidate rule for efficient fixation selection in visual search is a maximum a posteriori (MAP) rule. A MAP searcher always fixates the location with the highest posterior probability of containing the target. The MAP rule achieves a near-optimal search performance, but has a distribution of fixation locations across the search area that is very different from that displayed by both humans and the Bayesian ideal. The simple summation rule, on the other hand, leads to a human-like distribution of fixation locations, making it a plausible candidate for use by the nervous system. Other non-search applications of the summation formula will be discussed, such as its implications for efficient coding.
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