The effects of spatial frequency on binocular fusion: from elementary to complex images

Impact of monocular vs. binocular contrast and blur on the range of functional stereopsis

Stereopsis depends on the smallest stereo threshold (lower limit) and the upper fusion limit. While studies have shown that the lower limit worsens with reduced contrast and blur, more strongly in monocular than in binocular conditions, the effect on the upper limit remains uncertain. Here, we assess the impact of contrast and blur on the range of the disparity sensitivity function (DSF) in a stereo letter recognition task. Subjects had to identify the stereo letters embedded in a random dot stereogram, and adaptive staircases were used to estimate the two limits. Five subjects performed the experiment at baseline contrast (100%), with different contrast (32% and 10%) and blur (+0.75DS and +1.25DS) in monocular and binocular degradation. We proposed three possible outcomes: 1) the range collapses in both directions 2) the lower limit threshold reduces, but the upper limit is not affected 3) the threshold for both limits increases and the range remains the same. We found that the curve for both limits was lowpass in shape, resulting in a smaller range at higher SFs. The results were similar to the first prediction, where the threshold for the lower limit increased while the upper limit was reduced at lower contrast and higher blur. The shrinkage of DSF is significant in monocular conditions. However, with blur, there was inter-subject variability. A simple cross-correlation stereo-matching algorithm was used to quantify the effect of contrast and blur. The results were consistent with the behavioral result that the range of DSF decreases with image degradation.

The vergence horopter

The horopter is defined by the criterion with which it is measured; these include the apparent frontoparallel plane, the region of binocular single vision, and identical visual direction. Another criterion is one that "the positions of the points are such that none provides a stimulus for fusional movement of the eyes". Measuring the horopter using this criterion is the aim of the current paper. Based on previous research investigating corresponding points, we predicted the vergence horopter should trace an arc similar to the empirical horizontal horopter. We further predicted based on the characteristics of vergence eye movements in the periphery, that the range of horizontal disparities that do not elicit a vergence movement would increase with eccentricity. In experiment 1 we conducted the first measurements of the vergence horopter along the horizontal plane of regard and sagittal planes. We found that the vergence horopter consists of a stable range of disparities that do not increase with eccentricity. In experiment 2, we measured Panum's fusional range for the same eccentricities and elevations to determine the placement of the vergence horopter within the fusional ranges. In the horizontal plane, the vergence horopter sits centrally within Panum's fusional range. In the vertical plane, the data are suggestive that the vergence horopter is less slanted than the corresponding fusional range.

The Effect of Stimulus Size on Stereoscopic Fusion Limits and Response Criteria

The stereoscopic fusion limit denotes the largest binocular disparity for which a single fused image is perceived. Several criteria can be employed when judging whether or not a stereoscopic display is fused, and this may be a factor contributing to a discrepancy in the literature. Schor, Wood, and Ogawa (1984 Vision Research, 24, 661–665) reported that fusion limits did not change as a function of bar width, while Roumes, Plantier, Menu, and Thorpe (1997 Human Factors, 39, 359–373) reported higher fusion limits for larger stimuli than for smaller stimuli. Our investigation suggests that differing criteria between the studies could contribute to this discrepancy. In experiment 1 we measured horizontal and vertical disparity fusion limits for thin bars and for the edge of an extended surface, allowing observers to use the criterion of either diplopia or rivalry when evaluating fusion for all stimuli. Fusion limits were equal for thin bars and extended surfaces in both horizontal and vertical disparity conditions. We next measured fusion limits for a range of bar widths and instructed observers to indicate which criterion they employed on each trial. Fusion limits were constant across all stimulus widths. However, there was a sharp change in criterion from diplopia to rivalry when the angular extent of the bar width exceeded about twice the fusion limit, expressed in angular terms. We conclude that stereoscopic fusion limits do not depend on stimulus size in this context, but the criterion for fusion does. Therefore, the criterion for fusion should be clearly defined in any study measuring stereoscopic fusion limits.

Surface edges mitigate the disparity gradient constraint on binocular fusion and visual direction

One function of the visual system is to combine the different views of the two eyes so that each object appears in a single direction. Using pairs of isolated dots, previous studies have found that binocular fusion gives way to diplopia if the disparity gradient between the dots is steep. This paper evaluates whether fusion is possible in the presence of steep disparity gradients if those gradients occur between the edges of two surfaces, not isolated dots. Two target squares with a steep disparity gradient were presented alone, or were incorporated into separate surfaces - one foreground, the other background. The addition of surfaces, or support texture, restored fusion, overcoming the disparity gradient constraint on fusion. Visual direction was the average of the monocular views in the presence of support texture, indicating that single vision arose from fusion rather than a local suppression of one eye's view. The results suggest a close relationship between the disparity gradient constraint on fusion and the mitigating influence of support texture, because both effects decline dramatically over the same small range of element separations and both effects are reduced by differences in contrast polarity.