Crowding, the difficult identification of peripherally viewed targets amidst similar distractors, has been explained as a compulsory pooling of target and distractor features. The tilt illusion, in which the difference between two adjacent gratings’ orientations is exaggerated, has also been explained by pooling (of Mexican-hat-shaped population responses). In an attempt to establish both phenomena with the same stimuli—and account for them with the same model—we asked observers to identify (as clockwise or anticlockwise of vertical) slightly tilted targets surrounded by tilted distractors. Our results are inconsistent with the feature-pooling model: the ratio of assimilation (the tendency to perceive vertical targets as tilted in the same direction as slightly tilted distractors) to repulsion (the tendency to perceive vertical targets as tilted away from more oblique distractors) was too small. Instead, a general model of modulatory lateral interaction can better fit our results.

*λ*= 0.28° and

*σ*= 0.19°, respectively) were presented in one of four configurations, identified as 3, 6, 9, or 12 o’clock, for 100 ms. Figure 2 shows the 9 o’clock configuration.

*θ*was 167.7° in the 9 o’clock configuration of Phase 2 (Figure 2). Target-center azimuths in the 12, 3, and 6 o’clock configurations were 77.7, 347.7, and 257.7°, respectively. In all configurations of Phase 2, the azimuths of distractor centers were

*θ*± 12.7°. In Phase 1,

*θ*was 0.3, 90.3, 180.3, or 270.3°. The center of each target and distractor was separated from a fixation cross by 3.7 deg of visual angle.

*t*is the target tilt. Figure 3 shows CG’s data from the 3 and 9 o’clock configurations, with 45° distractors. The parameters reflect two aspects of performance, bias −

*µ*and sensitivity 1/

*σ*.

*p*< .025 level.

*f*(

*θ*;

*θ*denote the response of the population sensitive to a target with orientation

_{t}*θ*, in the absence of any lateral influences. Allowing modulatory influences

_{t}*g*and

*h*, from neurons sensitive to distractors with orientation

*θ*, the response of the population sensitive to the target takes the form

_{d}*θ*such that the (local) maximum in

_{t}*r*occurs at

*θ*= 0, there exists a set of parameter values that yields an essentially perfect fit to the measurements of bias summarized in Figure 6. However, to fit measurements of sensitivity, a model must produce psychometric response frequencies other than that used to determine bias (i.e., 0.5). If the population mode determines bias, then, for consistency, the population mode should determine all psychometric response frequencies. To make this concrete, we computed the frequency of anticlockwise responses using the formula where

*θ*is the orientation where

_{p}*r*has its peak,

*σ*is a free parameter, and Φ() is the standard normal distribution. Arbitrary response frequencies based on population modes could also be derived from Monte-Carlo simulations of noisy populations. The major advantage of a formula such as Equation 5 is that it can be solved analytically.

_{p}*r*represent the response of the neuron with preferred orientation

_{θ}*θ*. The frequency of anticlockwise responses can then be assigned the value where

*σ*is a free parameter and When the (Minkowski) exponent

_{o}*M*is large (e.g., >5), this decision rule will be dominated by the pair of oppositely oriented neurons whose responses are most different. Smaller values of

*M*give larger weight to less informative opponent-pairs.

*β*was fixed at 0.

_{g}*d*can be described with four parameters: If

*d*(

*θ*;

*θ*,

_{t}*α*,

*β*,

_{c}*β*) describes the response of the population sensitive to a target with orientation

_{s}*θ*and

_{t}*d*(

*θ*;

*θ*,

_{d}*α*,

*β*,

_{c}*β*) describes the response of each population sensitive to a distractor with orientation

_{s}*θ*, then will describe the pooled population response. The parameter

_{d}*γ*may take any value between 0 and 1 to allow the target’s population a preferential contribution to the pool.

*r*closest to 0, then bias can be computed by finding the

*θ*such that the local maximum in

_{t}*r*occurs at

*θ*=0.

*α*> 1 neurons would be implausibly inhibited by stimuli having their “preferred” orientations (i.e.,

*θ*

_{0}). Therefore, for the fit shown in Figure 6,

*α*was not allowed to exceed the value that would produce a balanced population response. That is, we forced