**Size and aspect ratio are ecologically important visual attributes. Relative size confers depth, and aspect ratio is a size-invariant cue to object identity. The mechanisms of their analyses by the visual system are uncertain. In a series of three psychophysical experiments we show that adaptation causes perceptual repulsion in these properties. Experiment 1 shows that adaptation to a square causes a subsequently viewed smaller (larger) test square to appear smaller (larger) still. Experiment 2 reveals that a test rectangle with an aspect ratio (height/width) of two appears more slender after adaptation to rectangles with aspect ratios less than two, while the same test stimulus appears more squat after adaptation to a rectangle with an aspect ratio greater than two. Significantly, aftereffect magnitudes peak and then decline as the sizes or aspect ratios of adaptor and test diverge. Experiment 3 uses the results of Experiments 1 and 2 to show that the changes in perceived aspect ratio are due to adaptation to aspect ratio rather than adaptation to the height and width of the stimuli. The results are consistent with the operation of distinct banks of information channels tuned for different values of each property. The necessary channels have log-Gaussian sensitivity profiles, have equal widths when expressed as ratios, are labeled with their preferred magnitudes, and are distributed at exponentially increasing intervals. If an adapting stimulus reduces each channel's sensitivity in proportion to its activation then the displacement of the centroid of activity due to a subsequently experienced test stimulus predicts the measured size or aspect ratio aftereffect.**

- The data describing the logarithm of the size (aspect ratio) of test stimuli at the PSE versus the logarithm of size (aspect ratio) of the adaptor should conform to the D1 function predicted by the bank of channels model.
- The point of inflection on the D1 function should occur where the magnitudes of the adaptor and test pattern are the same.
- The aspect ratio of a test stimulus at the PSE should depend on the aspect ratio of the adaptor and be independent of the relative sizes of adaptor and test.

^{2}and minimum near zero. Observers viewed the monitor from a position, stabilized by a chinrest, 115 cm along the normal to the center of the screen. At this distance each pixel subtended 1′ of visual angle. Observer responses were recorded using two buttons on a CRS CB3 button box.

*σ*= 1 minute of visual angle) and stimuli matched for luminance energy (the contrast of the stimuli was scaled in inverse proportion to their area). The jittering of the positions of the stimuli ensured that the boundaries of the boundary-defined stimuli were typically not spatially coincident across trials preventing the buildup of afterimages. In the case of the stimuli matched for luminance energy, differences in the magnitudes of boundary repulsion might be expected since light scatter will be larger with higher luminance. Across the three stimulus types, however, the magnitudes of the aftereffects were consistent with being equal, engendering confidence that the aftereffects observed in this study would constitute geometrical aftereffects rather than boundary repulsion whichever of the three stimulus types we chose. For simplicity we chose the filled stimuli. Figure A1 of 1 illustrates the stimuli used and Figure A2 presents the aftereffects measured.

^{2}. The boundaries of the stimuli were smoothed to background luminance using a one-sided Gaussian function with a standard deviation of 1 minute of visual angle to allow the sizes and aspect ratios to be specified on a continuous range rather than being quantized by pixel size. Square and rectangular stimuli were preferred to circular and elliptical stimuli because successively presented elliptical stimuli would have a range of local orientation differences and would, therefore, suffer from confounding aftereffects of adaptation to local orientation. Successively presented rectangular stimuli can only differ locally in their boundary orientation by 90°, which would not induce tilt aftereffects (Clifford et al., 2000).

*,*

^{n}*n*= {−4, −3, −2, −1, 0, 1, 2, 3, 4} degrees of visual angle. The two test stimuli in each trial had reciprocal linear dimensions. For example, if the left hand stimulus subtended 1.05

^{3}degrees of visual angle vertically and horizontally then the right hand stimulus subtended 1.05

^{−3}degrees. The areas of the test stimuli were, therefore, 1.05

^{2}

*,*

^{n}*n*= {−4, −3, −2, −1, 0, 1, 2, 3, 4}.

^{½}× 1.02

*and 2*

^{n}^{−½}× 1.02

^{−}

*,*

^{n}*n*= {−4, −3, −2, −1, 0, 1, 2, 3, 4}, respectively. The aspect ratios of the test stimuli were, therefore, 2 × 1.02

^{2}

*,*

^{n}*n*= {−4, −3, −2, −1, 0, 1, 2, 3, 4}. Again the aspect ratios of the left and right test stimuli were modified by reciprocal ratios. For example if the left stimulus had an aspect ratio of 2 × 1.02

^{4}then the right hand test stimulus had an aspect ratio of 2 × 1.02

^{−4}.

*p*(left), was determined for each adapting condition and a cumulative Gaussian distribution fitted to the data describing that probability as a function of the logarithm of the area of the left test stimulus. When the left hand test stimulus was at its largest the observers typically reported it as largest at a probability of 1 and when at its smallest a probability of 0 and so no lapse rate was incorporated in the fit. The fitted function is shown as Equation 1 below with

*X*representing the area of the left test stimulus.

*μ*in Equation 1 and the anti-log yielded the reported size of the left stimulus at the PSE. The function

*erf*is the error function and

*σ*is the standard deviation. The R

^{2}values for the fits to the size adaptation data are presented in Table B1 of 2.

*X*in Equation 1) and the PSE determined. The logarithm of the aspect ratio of the left hand test pattern at the PSE was then determined from the fitted function and the aspect ratio provided by the anti-log. The R

^{2}values for the fits to the aspect ratio adaptation data are presented in Table B2 of 2. The specific conditions of adaptation differed across experiments and are reported within the sections describing those experiments.

*A, σ, X*

_{0}, and

*Y*

_{0}. Parameter

*A*determines the amplitude of the D1 function,

*σ*the width,

*X*

_{0}the magnitude of the independent variable when the aftereffect is zero and

*Y*

_{0}the magnitude of the dependent variable when the aftereffect is zero. The aftereffect at a particular point on the function is given by the ratio between the dependent variable at that point and the value of

*Y*

_{0}.

^{2}values for the fits are 0.973, 0.988, 0.997, and 0.993 for observers ED, SM, KT, and KS respectively). The free parameters

*Y*

_{0}and

*X*

_{0}in the fit specify the position of the point of inflection of the D1. Values of 1 for

*Y*

_{0}and

*X*

_{0}would indicate that the size of the left test stimulus at the PSE was 1 square degree after prior exposure to an adapting stimulus of 1 square degree. The geometric mean (and 95% confidence intervals) of the free parameter

*Y*

_{0}in the fit across the four observers is 1.00 (0.94 lower 95% CI, 1.06 upper 95% CI). For parameter

*X*

_{0}the geometric mean is 1.04 (0.91 lower 95% CI, 1.18 upper 95% CI). This result is consistent with the test stimulus being perceived as having its true size when the adapting and test stimuli are the same size. The free parameters

*σ*and

*A*pertain to the form of the D1. The geometric mean of

*σ*in the fits to the data of the four observers is 1.95 (1.63 lower 95% CI, 2.33 upper 95% CI). The value of

*σ*determines the positions of the points of maximum amplitude on the D1 function. The derivative of Equation 2, the second derivative of the Gaussian, is zero when ln(

*X*/

*X*

_{0}) is equal to ±

*σ*. If we assume

*X*

_{0}to be 1, then the maximum amplitudes, calculated from the geometric mean of

*σ*across the observers, are at adaptor sizes of 7.0 (5.3 lower 95% CI, 10.3 upper 95% CI) and 0.14 (0.10 lower 95% CI, 0.19 upper 95% CI). These values are reciprocally related and can be considered to indicate that the largest aftereffects are observed when the left hand adapting stimulus is 7.0 times and 1/7.0 times of the size of the test pattern. The geometric mean of the parameter

*A,*which determines the amplitude of the D1 function, across the observers was 0.47 (0.41 lower 95% CI, 0.55 upper 95% CI). Assuming the values of

*X*

_{0}and

*Y*

_{0}to be 1 and substituting the values of 7.0 and 0.14 for

*X*into Equation 2 we arrive at values for the size of the left test at the maximum amplitudes of 1.26 (1.20 lower 95% CI, 1.32 upper 95% CI) and 0.79 (0.76 lower 95% CI, 0.83 upper 95% CI).

*Y*

_{0}fitted in Figure 1 predicts the size of the left test stimulus when there is no effect of adaptation. Values other than 1 indicate a systematic bias in the perception of size of the test stimuli. The sizes of the left test stimuli at PSE for the single adaptor conditions were, therefore, divided by the value of

*Y*

_{0}for each of the four observers to remove each observer's bias. Following this the geometric mean of the sizes for the small adaptor, 0.93 (0.88 lower 95% CI, 0.98 upper 95% CI), did equate to the geometric mean of the reciprocals of the sizes for the large adaptor, 0.91 (0.88 lower 95% CI, 0.94 upper 95% CI) demonstrating that the aftereffects of adaptation to stimuli with one quarter and four times the area of the test stimuli are consistent with being equal in magnitude when expressed as ratios.

*Y*

_{0}and

*X*

_{0}in the fit specify the position of the point of inflection of the D1. In this case values of 2 for

*Y*

_{0}and

*X*

_{0}would indicate that the aspect ratio of the left test stimulus at the PSE was 2 after prior exposure to an adapting stimulus with an aspect ratio of 2. The geometric mean for the parameter

*Y*

_{0}across the four observers is 2.03 (1.97 lower 95% CI, 2.10 upper 95% CI) and for the parameter

*X*

_{0}it is 1.98 (1.45 lower 95% CI, 2.71 upper 95% CI). The result is, therefore, consistent with the test stimulus being perceived as having its true aspect ratio when the adapting and test stimuli have the same aspect ratio. The intersection of the x-axis and y-axis has been moved to point (2, 2) in Figure 2 to highlight this point. The geometric mean of

*σ*is 1.92 (1.61 lower 95% CI, 2.29 upper 95% CI), consistent with the result obtained for size adaptation. Again, the derivative of Equation 2 is zero when ln(

*X*/

*X*

_{0}) is equal to ±

*σ*. Here, if we assume

*X*

_{0}to be 2, then the maximum amplitudes, calculated from the geometric mean of

*σ*, are at adaptor aspect ratios of 13.6 (10.5 lower 95% CI, 19.7 upper 95% CI) and 0.29 (0.20 lower 95% CI, 0.40 upper 95% CI). As the aspect ratio of the test patterns was 2 these values are indicate that the largest aftereffects are observed when the adapting stimulus is 6.8 times and 1/6.8 times the aspect ratio of the test pattern. The geometric mean of parameter

*A*across the observers was 0.77 (0.73 lower 95% CI, 0.81 upper 95% CI). Assuming the values of

*X*

_{0}and

*Y*

_{0}to be 2 and substituting the values of 13.6 and 0.29 for

*X*into Equation 2 we arrive at values for the aspect ratio of the left test at the maximum amplitudes of 2.17 (2.14 lower 95% CI, 2.21 upper 95% CI) and 1.84 (1.81 lower 95% CI, 1.87 upper 95% CI).

^{2}values for the fits are 0.988, 0.989, 0.985, and 0.979 for observers ED, SM, KT, and KS, respectively). The magnitude of the aftereffect is seen to increase to a maximum and then decrease as the aspect ratios of the adapting and test stimuli diverge, supporting the prediction that aspect ratio is encoded in the population response of a bank of channels sensitive to specific aspect ratios and not two opposing pools of aspect ratio sensitive units. Moreover, there are no aftereffects of adaptation when the adapting and test stimuli have an aspect ratio of 2. A two-pool model might be expected to predict that there would be no adaptation for an adaptor with an aspect ratio of 1 (Regan & Hamstra, 1992) and that a substantial aftereffect for an aspect ratio of 2 would be observed, but these predictions are not supported by the data. The average position of the point of inflection of the D1 functions across the observers is consistent with being at the point (2, 2) providing further evidence for a bank of channels model for the encoding of aspect ratio.

*Y*

_{0}and

*X*

_{0}so that the point of inflection of the D1 function was at an aspect ratio of 1, the geometric mean of the aspect ratios of the test stimuli. The individual data for the observers is rendered using the same symbols as previously employed. The error bars represent 95% confidence intervals in the mean. The predictions were calculated for each observer individually and the mean and 95% confidence intervals plotted for comparison with the data.

*X*is the stimulus size or aspect ratio,

*X*is the preferred magnitude of channel

_{i}*i, a*is the activity in channel

_{i}*I*, and

*X*is the perceived size or aspect ratio. The standard deviation,

_{p}*σ,*is distinct from the standard deviation of the fitted D1 function. In Panel (c) of Figure 5 it is evident that the centroid of activation in the channels that respond to the test stimulus with a magnitude of 1 is displaced toward smaller magnitudes because of the reduction of sensitivity of the channels that were activated by the adaptor.

*A*and

*σ*in the D1 functions fitted to the size adaptation data were 0.47 and 1.95, respectively. A D1 with parameter values of 2.13 (the reciprocal of 0.47 to account for the inversion of the D1 function) and 1.95 was predicted by the model if the gain applied to the channel maximally sensitive to the adaptor was 0.58 and the channel bandwidth was a factor of 32.25 at full width half maximum. For aspect ratio adaptation the geometric means of the fitted parameters

*A*and

*σ*were 0.77 and 1.92, respectively. The reciprocal of the value of

*A*is 1.3. The adaptor was, however, only present on the left and the aspect ratios of the test stimuli were constrained to have a geometric mean of 2 meaning that the aspect ratio of the left hand test stimulus at the PSE was only responsible for nulling half of the aftereffect. The modeled value for

*A*was, therefore, 1.69, the square of 1.3. These values for

*A*and

*σ*were predicted by the model if the gain applied to the channel maximally sensitive to the adaptor was 0.68 and the channel bandwidth was a factor of 28.66.

*Th*is the aspect ratio discrimination threshold,

*C*is a constant multiplier,

*H*is the height of the rectangle and

*W*the width (

*H*and

*W*are reciprocally related).

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