**Visual Search: amnesic or undecided?**

Visual search involves the
deployment of attention from one item in the visual field to another. It has
recently been claimed that visual search is memoryless^{1}, or
inefficient in the sense that it re-examines items previously attended to. We
suggest here that this claim is unsupported by the evidence presented in ref.
1, that the current experimental paradigm^{1,2} is unable to
distinguish between memoryless and memory-driven search, and that some of the
evidence from the same experiments suggest that visual search does indeed show
some form of memory.

Horowitz and Wolfe asked subjects to search for a target (a letter T) among distractors (L's) and to report as quickly as possible whether the target is present in the display. To test whether visual search has memory, they used a condition (called random) which thwarted any memory that visual search might use, by moving the target to a new random position every 110 ms and therefore forcing search to begin anew with every new frame presented. The logic of the experiment was that if visual search is indeed memoryless, no difference would be observed between the control trials with a fixed target location (static) and the random trials, but if search has memory, the random condition should prove less efficient than the static one. Horowitz and Wolfe calculated how much less efficient than memory-driven search memoryless search would be by running Monte Carlo simulations to obtain reaction times (RT) for the random condition assuming serial sampling with replacement of items in the visual scene. They concluded that the slope of the relation between RT and number of items in the display (set-size, S), which represents the added cost of each additional item, in the random display should be twice that of the static condition for correct target-present trials if search has memory.

*If
search is allowed to proceed indefinitely*, the random condition slope
should indeed be twice that of a memory-driven search. But subjects were not
allowed infinite time to respond --each trial was concluded after a fixed
number of frame updates. Furthermore, even an experiment with no time limits
would not yield such a high slope because subjects do not have an infinite span
of attention. The expression for the mean reaction time as a function of the
set size and the number of objects examined before time expires (M) for correct
target-present trials in the random condition is:

_{} (1)

where K represents the time needed
to begin a search, calculated as the intercept of the RT vs. S curve; k is the
mean time required to scan one additional item, given by the slope of the
target-absent static condition; and E_{random} is the random condition
error rate. If errors consist mostly of misses, E_{random} can be
estimated from the miss rate, given by Q_{random} below:

_{} (2)

Equation 1's closed-form solution is (E. Peral, personal communication)

_{} (3)

When M tends to infinity, equation 3 reduces to:

_{} (4)

which has indeed double the slope of the static memory-driven case, modeled as sampling without replacement:

_{} (5)

Surprisingly, mean RT vs. set size
slopes are far from their limit value of twice the static slopes even when the
probability of finding the target before the final frame is 98%. This is
because the random condition is significantly different from the static one
only in those trials in which the subject takes long enough to find the target
that he/she makes a significant number of repeated visits to distractors. The
contribution of that deceivingly low 2% of the trials is significant because
among those are trials with arbitrarily long reaction times, and it is in those
few cases that the subject keeps returning to the distractors. To show that
even if search has memory, static and random conditions will yield
indistinguishable slopes, as seen in ref. 1, we have estimated the mean number
of letters sampled (M) using equation 3 (slightly modified to account for
forced guessing at the end of the trial) and the experimental data for
experiment 3^{1}. Using this estimate of M (33) and equation 3, we
could predict the value of the random condition RT vs. set-size slope in
experiment 1 (18, experimental value is 18±5; slope in the static condition is
19±4 (data shown as ms per item, mean±s.e.m.)). In summary, if visual search is
memoryless, the static and random conditions will show equal slopes by
construction; if search has memory, static and random conditions will also
yield indistinguishable slopes for the parameters in ref. 1. The measure of RT
x set-size slopes in this experimental paradigm^{1,2} thus appears
inappropriate as a means to decide between the two alternative hypotheses.

Note also that the relation between RT and set-size in the random condition (equation 3) is not linear. Therefore, a single slope is not a meaningful representation of the underlying process. This is consistent with the experimental curves for the random condition (Fig. 1; Fig. 2 of ref. 1). Other predictions of the model presented here have also recently been confirmed experimentally (Scheier, Khurana and Shimojo, personal communication).

So far, we have only presented the
data used by Horowitz and Wolfe to arrive at their conclusion, which includes
only correct target-present trials. The rest of their data^{1} also
fail to support the memoryless search hypothesis. The RT x set-size slope for
target-*absent* trials is double the
one for target-present trials in the static condition, consistent with search
having memory^{ 3}. The termination of a target-absent search, and thus
RT, is not well-defined in the memoryless scenario. However, we know
empirically that in the random condition, a forced memoryless case, RT vs.
set-size slopes in target-absent trials are statistically indistinguishable
from those in target-present trials^{1}. This is clearly not what is
happening in the static case, suggesting search under static conditions is not
memoryless. In addition, the difference in RT x set-size slopes between static
(50±4 ms/item in experiment 1) and random (24±7 ms/item) conditions in
target-absent trials cannot be explained under the memoryless hypothesis;
memoryless search would do equally well in static and random conditions. This
difference, as well as the differences in absolute RTs and error rates between
static and random conditions, suggests that subjects may be using different
strategies for random and static trials, even when subjects do not spot the
target. This suggests that the random condition may be a poor model to
understand the workings of visual search under more natural conditions.

**Alex Bäcker**

Division of Biology, California Institute of Technology, MC 139-74, Pasadena, CA 91125, USA.

email: alex@caltech.edu

1.
Horowitz, T. S. and Wolfe, J. M. *Nature* 394, 575-577 (1998).

2.
Scheier, C., Khurana, B., Itti, L., Koch, C. & Shimojo, S.
*Vis. Res. Conf.* (1999).

3.
Treisman, A. & Gelade, G. *Cogn. Psychol*. **12**,
97-136 (1980).

Figure 1 - Bäcker, A.

** **

**Figure 1 (postscript file)** Predictions
of the model for the memory-driven scenario account for experimental reaction
times. Mean correct target-present reaction times (RTs) plotted against set
size for the random (circles) and static (squares) conditions from experiment 1
in ref. 1 (open symbols, black dashed lines) and prediction (filled symbols,
solid red lines) derived from the model assuming that visual search has memory.

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