Predicting the future course of a moving target is invaluable for planning actions. We used trajectory detection in noise to investigate this predictive capability. Using a contrast probe technique, we showed that in noise, contrast increments are more easily seen at the end of the trajectory than at the beginning. Analyses of the contrast data revealed that the improvement at the end of the trajectory was due to a substantial reduction in the number of detectors monitored, as well as to an increase in the gain of detectors responding to the increment. It appears that the first segment of the trajectory acts as an automatic cue that draws attention to subsequent segments of the trajectory, leading to enhanced detectability for predictable motion trajectories.

*k*represents the scaling factor between the physical contrast and its internal representation. Changes in this parameter reflect changes in gain (Figure 2c). The other free parameter

*M*is uncertainty, or the number of detectors monitored (Figure 2d). We used an iterative procedure to find the best-fitting values of

*k*and

*M*for a given set of data.

^{2}. Each stimulus dot subtended 2 arc min at a viewing distance of 1 m. The signal dot had a contrast of 54%. In the contrast discrimination experiments, the contrast of the noise dots was one of 5 values centered about 54%, in steps of 2

^{1/4}(0.075 log units). These 5 values corresponded to Michelson contrasts of 35.6, 44.9, 54.4, 66.9, and 82.7%. This range of noise values was used so that the contrast increment could not be identified as the brightest dot in the display. We were restricted in the range of contrast increments that could be added to our signal, which limited the highest proportion correct in the added noise conditions to values below 0.9. The display area was a circular region 12.6° in diameter. The number of dots in this area determined the dot density. For the noise experiments, the number of dots was either 190 or 380, corresponding to noise densities of 1.5 or 3 dots/deg

^{2}, respectively.

*M*in each interval. The detectors have a sensitivity

*k*, and each detector produces a noisy response. 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 uncertainty model (Pelli, 1985). For our 2-interval forced choice task, the probability of choosing the interval with the contrast increment is given by where

*c*is the contrast of the trajectory, Δ

*c*is the contrast increment

*f*(

*x*) is Gaussian probablity density function

*F*(

*x*) is the cumulative Gaussian ∫

^{x}

_{−∞}

*f*(

*x*′)

*dx*′

*k*is a sensitivity parameter

*M*is the uncertainty parameter.

*c*±

*Δc*, whereas the responses to non-increment contrasts are samples from a distribution centered at

*c*. The variance of this distribution does not represent the variability in response to a single contrast value, but rather the pooled variance across all five noise contrasts. The observer monitors the output of

*M*detectors in each interval and makes a correct choice when the largest response from the increment interval exceeds the largest response from the non-increment interval. There are two components to this correct choice. The first term on the right hand side is the probability that the largest response comes from the detector that sees the contrast increment. This is the probability that a sample from a distribution centered at

*c*±

*Δc*is larger than 2

*M*-1 samples from a distribution centered at

*c*. As the observer monitors

*M*detectors in each temporal interval, there is a total of 2

*M*-1 detectors that see a contrast centered about

*c*,

*M*-1 from the interval with the increment, and

*M*from the other interval. The second term is the probability that the largest response comes from the interval with the increment, but from a detector that does not see the increment. It is the probability that one of the non-increment detectors in the increment interval has the largest response.

*k*and

*M*in two ways. The errors associated with the fit were obtained from the covariance matrix where the diagonal terms specify the variance of

*k*and

*M*. We also measured the standard deviation of the fits across repeated measurements of the psychometric function. Typically the errors estimated from repeated measurements are much smaller than the errors estimated from the fitting procedure. There is an overall tendency for the sensitivity term

*k*to decrease with noise level, probably due to contrast normalization. Because the parameter

*M*occurs as an exponent in the equation above, very small changes in the steepness of the psychometric function can produce dramatic changes in

*M*. For values of

*M*of the order of 10, the lower and upper bounds on

*M*could be within a factor of 3 (

*M*could range from 3.3 to 30). For values

*M*of the order of 100, the lower and upper bounds could be within a factor of 7. Therefore, we are only interested in an order of magnitude for this parameter.

*find*the trajectory. By design, the trajectory motion resembles the motion of the noise dots on a frame-by-frame basis; the only difference is that the trajectory moves in the same direction on every frame, whereas the noise dots change direction on every frame. During the initial 20 to 30 ms of the display, there is only a small difference between the responses generated in a motion mechanism by the trajectory dot and by the noise dots. The observer has no way of knowing which moving dot is the true trajectory, and so must monitor all directions and locations within the 2° region surrounding fixation. For observer N.K., the higher noise level appears to offset the benefit of a fixed trajectory location; even though only the direction of the trajectory is randomized, her uncertainty estimate for increments at the beginning of the trajectory indicates that she acts as if uncertain of the location of the trajectory. As the trajectory continues on its straight path, it generates a motion response that becomes increasingly larger than the responses generated by most of the noise dots (Verghese et al., 1999). The robust motion response generated by the first 100-ms segment is an effective cue to the location and direction of the subsequent parts of the trajectory, thereby producing the marked improvement in detecting contrast increments at the end of the trajectory.

*k*, perhaps amounting to about a factor of 1.5 for end increments relative to beginning increments. However, there is a huge change, by more than a factor of 100, in the uncertainty parameter

*M*. Two other observers participated in these experiments (see Figure 4). They also found detection of contrast increments in noise to be easier at the end of the trajectory than at the beginning. While one of these observers showed the same large change in uncertainty with little change in sensitivity, the other observer showed a large change in sensitivity (factor of 3) with little change in the uncertainty parameter. Figure 4 provides a comparison of the gain and uncertainty values associated with increments at the beginning and at the end of the trajectory for all four observers. The error bars represent the standard deviation associated with two repetitions of the experiment. This experimental variability is typically smaller than the upper and lower bounds estimated from the fitting procedure (see “Methods”).

*if*the observer knows where to look (Verghese et al., 1999). However, the first 100-ms segment, which is supposed to be cueing subsequent parts of the trajectory, is detected on only 55% to 65% of trials when it is presented in 380 noise dots at a randomly chosen location. Why is this strong local motion response so poorly detected when the observer is uncertain about its location and direction? Our simulations with motion energy detectors indicate that two things happen at higher noise levels that reduce the visibility of the first part of the trajectory: First, the motion response to the trajectory becomes more variable because the local motion detector now has many noise dots within its receptive field, and second, the number of effective noise competitors increases with noise level. Observers detect a 100-ms trajectory in dense noise in only about 60% of the trials because at least one noise competitor produces a larger response in the noise interval on the remaining trials. In short, some noise configurations may act as competing cues to other locations and motion directions. Nevertheless, the 100-ms trajectory can still act as an effective cue because only a few noise competitors at the end of 100 ms have a comparable motion response.

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