Academic journal article Human Factors

The Effects of Spatial Frequency on Binocular Fusion: From Elementary to Complex Images

Academic journal article Human Factors

The Effects of Spatial Frequency on Binocular Fusion: From Elementary to Complex Images

Article excerpt


Stereoscopic displays are becoming an increasingly common feature of human-machine interfaces, and display technology has improved dramatically over the last few years (Patterson, Moe, & Hewitt, 1992; Sollenberger & Milgram, 1993; Wann, Rushton, & Mon-Williams, 1995). Such systems make use of the fact that the human visual system interprets the horizontal disparity between corresponding points in the left and right images as indicating depth relative to the fixation plane (for a review, see Howard & Rogers, 1995). Thus objects located in front of the fixation plane generate crossed disparities, whereas objects behind the fixation plane result in uncrossed disparities. Accurate stereoscopic judgments are limited by the ability of the observer to fuse the left and right eye images, so it is important to understand the factors that influence the fusion limit - that is, the maximum disparity that is compatible with fusion.

A number of factors are known to influence the fusion limit. One such factor is the spatial frequency content of the stimulus. It has been repeatedly shown that with stimuli containing high spatial frequencies the fusion limit is relatively small, whereas the limit is considerably larger in the case of low spatial frequency stimuli. Such results have been reported using various types of spatial frequency-tuned stimuli, including vertically oriented sinusoidal gratings (Felton, Richards, & Smith, 1972), one-dimensional difference of Gaussian profiles (1D-DOGs; Schor, Wood, & Ogawa, 1984), and Cauchy functions (Schor, Heckmann, & Tyler, 1989). With 1D-DOGs, the fusion limit increases from 10 min of arc for stimuli centered on 2.6 cycles per degree to more than 100 min of arc for a stimulus at 0.15 cycles per degree (Schor et al., 1984). However, the effects of combining stimuli with different spatial frequencies are paradoxical, because when the test stimuli are vertically oriented bars (containing a wide range of spatial frequencies), the fusion limit appears to be limited to that of the highest spatial frequency components.

Why is the visual system apparently unable to extend the fusion limits to higher values in such cases? The present study addresses this issue by using a different type of test stimulus, one that has a two-dimensional difference of Gaussian (2D-DOG) profile. We find that under such conditions, the fusion limit can indeed be extended to values typical of the low spatial frequency components.

A second factor that has a major effect on the fusion limit is related to the experimental procedure. In most previous studies the fusion limit was determined by progressively increasing disparity until diplopia occured. However, as Fender and Julesz (1967) demonstrated, there is a strong effect of hysteresis in such conditions: If the disparity is increased progressively, fusion can be maintained with much larger disparities than if the disparity is progressively decreased from a large initial value. This effect can result in the fusion limit being extended by a factor of as much as 20. However, in a number of normal viewing conditions, such as looking at the environment after closing one's eyelids for a while, the visual system cannot take advantage of such a phenomenon. Thus another of our motivations in the present study was to examine fusion limits under conditions in which the disparity changes in a step-wise manner, thus avoiding hysteresis-related effects.

A third, related, factor influencing the fusion limit is the possibility of vergence eye movements. In the vast majority of psychophysical experiments, such effects have been minimized by requiring the observer to fixate a reference point with zero disparity throughout the measurement period. However, under natural viewing conditions, an observer can use vergence movements to increase the range over which fusion is possible. Although voluntary vergence could in principle be used to fuse stimuli with very large disparities (at least 25 [degrees] in the case of crossed disparities when initial fixation is at infinity), there is also evidence that a reflex vergence mechanism operates over a smaller range of values, even if the observer is instructed to avoid voluntary vergence movements. …

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