Thus, the most common surface slant at all azimuths is 0°. Said another way, gaze-normal surfaces project to larger retinal images than steeply slanted surfaces. If the distribution in the world is uniform, the probability of observing a particular slant at the retina will be proportional to the cosine of that slant because of the perspective projection of the eye. The distribution of surface slants in the world is presumably uniform, at least for tilts near 0° (the distribution is non-uniform for tilts near 90° because the ground plane is often visible Potetz & Lee, 2003).
IMAGE OF UNEQUAL PUPIL SIZE PATCH
A gaze-normal surface (slant = 0°) is the most likely to stimulate a patch of retina (Hillis, Watt, Landy, & Banks, 2004). We are not aware of measurements of the probability distributions for different head-centric positions, but there is good evidence concerning the most probable surface orientation. From the figure, we cannot determine how commonplace various size ratios are because the probability of a given ratio depends on the probability of surfaces being presented at different positions relative to the head and on the probability of different surface orientations. 1, 2įigure 1 shows the size ratios that occur with gaze-normal surfaces at different positions relative to the head. Specifically, dichoptic images of different shapes, but the same retinal size appeared to differ in size when the eyes were in eccentric gaze (Ames, Ogle, & Gliddon, 1932 Herzau & Ogle, 1937 Ogle, 1939). Ogle presented experimental evidence that the hypothesized neural magnification occurs and that the trigger for the magnification is an extra-retinal, eye-position signal. As a consequence, one would predict that the deterioration of stereopsis that accompanies large differences in image size would not occur when the size differences are compatible with eye position. We reasoned that if the hypothesized neural magnification occurred before the stage of disparity estimation (i.e., before correlating the two eyes' images), it would reduce the difference in the sizes of the represented images and thereby increase the reliability of disparity estimates. Ogle made no claim about where in visual processing the neural magnification occurs. Ogle proposed that when the eyes are fixating eccentrically, the retinal image in the nasally turned eye (the eye receiving the smaller retinal image) is magnified “psychologically” relative to the other eye's image such magnification would be the reciprocal of the magnification in Equation 2. (2)where R l and R r are the horizontal rotation angles of the left and right eye, respectively. She performed best when the presented images were roughly the same size, indicating that she has compensated for the persistent image-size difference. Finally, we looked for compensation in an observer who has constantly different image sizes due to differing eye lengths. We also found that a local cross-correlation model for disparity estimation performs like humans in the same task, suggesting that the decrease in stereo performance due to image-size differences is a byproduct of the disparity-estimation method. This shows that no neural compensation for image-size differences accompanies eye-position changes, at least prior to disparity estimation. The worsening was determined only by relative image size and not by eye position. Magnifications of 10–15% caused a clear worsening of stereo performance. We did so for different gaze directions, some compatible with the image-size difference and some not. Does this mean that stereopsis exhibits deficits for such stimuli? Or does the visual system compensate for the predictable image-size differences? To answer this, we measured discrimination of a disparity-defined shape for different relative image sizes. Near, eccentric objects naturally create retinal images of different sizes.
With the eyes in forward gaze, stereo performance worsens when one eye's image is larger than the other's.
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