Disparity averaging mechanisms in stereopsis

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Biomedical and Chemical Engineering


Disparity averaging, Channel interaction, Stereopsis, Computer modeling, Depth perception

Subject Categories

Biomedical Engineering and Bioengineering | Engineering | Life Sciences | Neuroscience and Neurobiology


Under ideal conditions, human stereoacuity is quite high: Observers can discriminate disparity differences of less than 5 arcsec (Berry, 1948; Westheimer & McKee, 1978), smaller than the width of single foveal cone photoreceptors (Curcio et al ., 1987). How do we achieve such a high precision in stereopsis? Disparity averaging may provide a solution. Although all SF components in a broadband stimulus (e.g., a thin line) have the same physical disparity, different SF channels may register a slightly different disparity due to noise in the stimulus (external noise) and noise in the neural pathway (internal noise). Averaging of these slightly different disparities across SF channels can reduce the noise and enhance the signal and therefore improve our precision in depth discrimination.

This dissertation investigates the disparity-averaging mechanism. In particular, it tests the hypothesis that the overall disparity is computed as a weighted average of the various disparity estimates generated by different SF channels. In order to test this hypothesis, compound sinewave gratings with two component gratings placed at different disparities were employed as stimuli. The research of this dissertation consisted of three parts. In the first two parts, psychophysical data on disparity averaging were collected. These data were then used to modify Tsai and Victor's (2003) model, a well-respected stereoscopic model, in order to simulate the underlying disparity-averaging mechanisms.

Experiment 1 tests the hypothesis that both SF and contrast are significant factors in determining the averaged disparity. To test this hypothesis, perceived depths for artificial objects, compound gratings, were measured. The SF components in each compound grating were pulled apart and placed at different disparities whereas the percept of the overall compound grating remained to be a single surface. Component SFs and contrasts were manipulated independently and systematically. The results confirm that SF and contrast are indeed significant factors in disparity averaging and they interact with each other. In addition, at equal component contrast, the perceived depth is biased towards the disparity of the higher-frequency component. When the relative contrast between components is varied, the perceived depth moves towards the disparity of the component with higher relative contrast. The rate of this change in perceived depth with respect to contrast differs for different SFs. The perceived depth as a function of contrast (the depth-contrast function) is systematically ordered with respect to ratios between the component SFs (SF ratios), independent of their absolute values. The greater the SF ratio, the greater the bias in perceived depth towards the higher SF.

Experiment 2 tests the hypothesis that disparity averaging also occurs at stereothreshold or increment threshold from 0 disparity (i.e., the smallest noticeable change in depth from the fixation plane). The results from previous studies suggest that SF channels are independent of each other at stereothreshold. The implication is that for a broadband surface, when only one of the components appears behind the fixation plane, the whole surface would move along with it in depth. But this seems unlikely because the percept of a surface should not be determined completely by only parts of the surface. Experiment 2 was designed to test the hypothesis that SF channels interact with each other at stereothreshold (increment threshold from 0 disparity) and the interaction is due to disparity averaging. The results suggest that this is indeed the case: (1) The stereothreshold for a single grating is elevated in the presence of a second grating at the fixation plane. This result suggests that instead of being independent of each other, SF channels interact at stereothreshold. (2) The amount of this elevation can be predicted using the corresponding perceived depth results. The results obtained in this experiment indicate that both stereothresholds and perceived depths are governed by the same disparity-averaging mechanism.

The purpose of the third part is to test and expand Tsai and Victor's (2003) stereoscopic model (the T&V model) in order to simulate the underlying disparity-averaging mechanisms. This was accomplished using the perceived depth data obtained in Experiment 1. The T&V model was chosen to be the basic model because it is a general model that utilizes responses from a whole population of binocular neurons and can account for a variety of psychophysical phenomena. There are some qualitative similarities between the empirical results and the predictions of the original T&V model, but there are also important differences. Both qualitative and quantitative discrepancies were found between the original T&V model's predictions and the empirical data. (Abstract shortened by UMI.)


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