When flanked by collinear Gabor patches, detection thresholds for a target Gabor patch improve by up to a factor of 2. This result has been interpreted as evidence for collinear facilitation. However, facilitation has been observed only for targets near detection threshold, where observers seem uncertain about the location and other properties of the stimulus. So the effect of the flankers may be to reduce this uncertainty. If this is true, then other cues to target location should produce a similar improvement in thresholds. To test this hypothesis, we measured contrast detection thresholds for a Gabor target alone, and in the presence of either a faint circle surrounding the target location, or two high-energy flanking Gabor patches. We also used an adaptive procedure to measure the slope of the psychometric function to determine whether the slopes were considerably lower in the presence of location cues or flanking Gabors, as predicted by signal detection theory when uncertainty is reduced. As observed previously, the presence of collinear flankers improved detection thresholds by a factor of two. Yet, on average, the circle alone accounted for the most of the facilitation; for three of our five observers, it improved thresholds as much as the collinear flankers. Other cues that specified target location produced similar improvements in detection thresholds. The slopes of the psychometric functions were much shallower in the presence of these location cues or the collinear flankers compared to the target-alone condition. This change in the slopes indicates that the threshold improvement is largely due to a significant reduction in uncertainty.

*σ*=

*λ*/2) in which ∼1.5 periods of the sinusoidal pattern were visible (Figure 1). The Gabor could be slanted 45 deg. either right or left from the vertical. There were two types of location cues: (i) a dark circle centered on the target and (ii) four dark lines surrounding the target. The cues were 1 pixel (1.2 arcmin) wide and their contrast was 15%. The circle was 2.5

*λ*(0.83 deg) in diameter, the lines were 2

*λ*(0.67 deg) long. The lines had the same orientation as the target Gabor and were positioned 2.5

*λ*away from the target's center in a square fashion, as shown in Figure 1.

*λ*away from the target's center in both cases. The location cues were displayed on their own and in conjunction with the two Gabor patterns. Thus, for each cue we tested four configurations: (a) target alone; (b) target and the cue; (c) target, cue, and two parallel Gabors; and (d) target, cue, and two collinear Gabors. The four configurations are shown in Figure 1. In Experiment 1, all four conditions were randomly interleaved within each experimental session. In Experiment 2, only one condition was presented within each session. The two target orientations were randomly interleaved within each session in both experiments.

^{2}) and viewed through Wheatstone stereoscope on a pair of linearized Sony Trinitron G220 monitors. Viewing distance was 65 cm. The stereoscope was used for a series of studies on the spatial properties of surround effects, including disparity, but for this study, the binocular images were presented at zero disparity for all components. The video signal was rendered with nominal 8-bit precision, but an additional factor of 4 increase in precision was attained using an ordered 2 × 2 block pixel dithering (analogous to the newspaper halftone technique). The resulting 2 × 2 pixel size was 2.4 arcmin, whereas the dithering artifacts (0.8% contrast modulation at 22 cpd) were approximately 30 times below the detection threshold. The effective luminance resolution of the screen at the background level (after gamma-correction) was confirmed to be 0.2% (9 bits) by counting the number of gray levels in the stimulus screenshots.

*α*and steepness

*β*of psychometric functions. The 2IFC psychometric function of the target contrast

*c*was fitted by

*α*corresponds to 76% correct responses. Parameter

*β*describes the steepness (slope) of the psychometric function. For

*β*= 1,

*P*

_{correct}(

*c*) gives the signal detection theory prediction for a single linear detector with normally distributed additive noise characterized by standard deviation

*α*. Larger values of

*β*would signify either a nonlinear relationship between the stimulus contrast and the detector input or alternatively indicate multiple detectors and inherent uncertainty about which detector receives the signal (see 1).

*λ*diameter disk around each Gabor patch location. This calculation gives ∼1:16 ratio between the circle cue presented on its own and in conjunction with the two flanking Gabors.

*α*and steepness parameters

*β*(for definition, see Methods) as a correlation plot in Figure 4. For all five observers, the steepness increased as a function of threshold. As in Experiment 1, the two collinear Gabors positioned at the ends of the target produced the strongest facilitation compared to the target-alone condition, but they also produced the largest drop in steepness. Note that for three observers (YP, LM, and AMW), the facilitatory effect of the Gabor pattern was just slightly larger than the effect of the circle cue. The experimental results were fitted with the predictions of the Pelli (1985) uncertainty model. The model is based on signal detection theory and on the assumption of probability summation over multiple noisy detector outputs (see 1). Because the noise level and internal scaling of the contrast signal were unknown, the uncertainty model fits were carried out with one free parameter representing the unknown signal-to-noise factor for each observer. In all cases, the uncertainty model gave a good fit to the observed threshold–steepness correlation.

*λ*away from the target Gabor lowered detection threshold by almost a factor of two, whereas the same Gabors positioned at the sides of the target produced a smaller degree of facilitation. However, we discovered that a comparable degree of facilitation can be induced by a faint circle, or a set of four faint lines surrounding the target. Such low-energy patterns can cue an observer to the target location or to both its location and orientation, respectively. We also showed that the improved performance is accompanied by a significant decrease in the slope of the psychometric functions both for flanking high-energy Gabors and low-energy cues.

*λ*).

*λ*diameter circle as the location cue. Other circle parameters were the same as before. The results for three observers (YP, PV, and LM) are shown in Figure 4 with open squares. The 10

*λ*circle produced as much facilitation as the 2.5

*λ*circle, which supports the uncertainty explanation. This is reminiscent of the studies of Kovacs, Feher, and Julesz (1998) and Kovacs and Julesz (1994), which showed that contrast sensitivity was enhanced when a Gabor probe was positioned at symmetrical points (medial axis) of the enclosing boundary, even for large distances between the boundary and the target. They interpreted this as evidence for “skeletal” representation of objects, but our results suggest that uncertainty reduction would be a more natural explanation for the effect.

*M*in each interval. We also assume that a physical value of contrast

*c*is linearly translated into a response

*kc*plus noise, where

*k*refers to the gain of each detector, that is, the proportionality constant between contrast and number of spikes. The gain parameter

*k*is related to the psychometric threshold (i.e., the horizontal position of the psychometric curve) whereas the uncertainty parameter

*M*is related to the steepness of the curve. All

*M*detectors have the same gain

*k*and each detector produces an independent noisy response from a Gaussian distribution. The observer finds the largest of these responses in each interval and then chooses the interval with the larger response. Errors arise when the interval without the increment produces a larger response and the probability of error increases with the number of detectors that the observer monitors. This formulation is based on Pelli's (1985) uncertainty model. For our two-interval forced choice task, the probability of a correct response is given by the probability that the interval with the signal produces the larger response. Alternately, the probability of a correct response is one minus probability that the blank interval produces the larger response:

*c*is the contrast of the signal,

*f*(

*x*) is Gaussian probability density function, and

*N*(

*x*) is the cumulative function for the Gaussian distribution.

*M*detectors in this interval has a value

*x*and all the other detectors have a value less than

*x*. These other detectors include a total of 2

*M*− 2 detectors that see no contrast (the remaining

*M*− 1 from the blank interval, and

*M*− 1 from the signal interval), and the one detector that sees the signal contrast

*c*. The probability that a detector that does not see a signal produces a response

*x*is given by the Gaussian density

*f*(

*x*). The probability that a detector that sees signal produces a response

*x*is

*f*(

*x − kc*), where

*k*is the gain parameter and

*c*is the signal contrast. The probability that all the other detectors will produce a contrast less than

*x*is the product of all their cumulative distributions, that is,

*N*(

*x*)

^{2M − 2}

*N*(

*x − kc*), where the first term is due to the 2

*M*− 2 detectors that see no contrast and the second term is from the one detector in the signal interval that sees the signal. The expression is multiplied by

*M*because any one of the

*M*detectors in the nonincrement interval can produce the largest response. The integral calculates the probability of an incorrect response over all values of

*x*.