Chapter 2 Principles of Stereoscopic Depth Perception and ...

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2. Principles of Stereoscopic Depth Perception and Reproduction Figure 2.2: Different perspectives from the left and right eye onto an object. separated (on average approximately 6.5 cm) which provides each eye with a unique viewpoint unto the world (see Figure 2.2). This horizontal separation causes an interocular difference in the relative projections of monocular images onto the left and right retina. When points from one eye’s view are matched to corresponding points in the other eye’s view, the retinal point to point disparity variation across the image provides information about the relative distances of objects to the observer and the depth structure of objects and environments. The line that can be drawn through all points in space that stimulate corresponding retinal points for a given degree of convergence is called the horopter (see Figure 2.3). The theoretical horopter is a circle, known as the Vieth-Müller circle, which passes through the fixation point and the nodal points of both eyes. Experimental work has shown that the empirical horopter lies slightly behind the theoretical horopter, although no satisfactory explanation has yet been provided to account for this fact. However, differences between the theoretical and the empirically measured horopter are small and can usually be ignored for practical purposes (Palmer 1999). Points which are not on the horopter will have a retinal disparity. Disparities in front of the horopter are crossed and disparities behind the horopter are uncrossed. As long as the disparities do not exceed a certain magnitude, the two separate viewpoints are merged into a single percept (i.e., fusion). The small region around the horopter within which disparities are fused is called Panum’s fusional area. Although Figure 2.3 seems to suggest that Panum’s area is a fixed property of a given retinal region, this is only done for schematic purposes. The actual size and shape of Panum’s area vary with the spatial and temporal characteristics of the stimulus, as well as the procedures used to measure it. If disparity is large the images will not fuse and double images will be 54
2.2. Human depth perception seen, a phenomenon that is known as diplopia. A simple demonstration of this is to hold one finger up at arm’s length and another finger at half arm’s length. Fixating with both eyes on the farthest finger will make the closest one appear double, and vice versa. The largest disparity at which fusion can occur is dependent on a number of factors. Duwaer & van den Brink (1981) showed that the diplopia threshold is dependent on the subject tested, the amount of training a subject received, the criterion used for diplopia (unequivocal ’singleness’ of vision vs. unequivocal ’doubleness’ of vision), and the conspicuity of the disparity. Although limits vary somewhat across studies, some representative disparity limits for binocular fusion can be given. For small sized stimuli (i.e., smaller than 15 minutes of arc) the range of disparity for the foveal area is about +/-10 minutes of arc, while at 6 degrees eccentricity the range increases to around +/-20 minutes of arc. For large stimuli (1.0 - 6.6 degrees) the range for the foveal region is about +/-20 minutes of arc, that is, two times the range for smaller stimuli (Patterson & Martin 1992). However, most individuals have an appreciation of depth beyond the diplopia threshold, the region where single vision has been lost. Up to 2 degrees of overall disparity between two images is tolerated before the sensation of depth is lost (Howard & Rogers 1995). Stereoscopic vision greatly enhances our ability to discriminate differences in depth, particularly at close distances. Estimates of the effective range of stereopsis vary across the literature, but it is clear that stereoscopic information becomes less effective as distance increases and retinal disparities become smaller. For distances beyond 30 meters disparities become negligible. Stereoscopic vision is also necessarily limited to the central region of the visual field where the two retinal images overlap, the binocular visual field. With both eyes open the maximum width of the total visual field is approximately 200 degrees. The binocular field is about 120 degrees wide, flanked on either side by uniocular fields of approximately 40 degrees each. Stereoscopic sensitivity is remarkably good at regions close to the horopter: people can detect a disparity of just a few seconds of arc. Better stereo-acuity performance is reported for crossed than for uncrossed disparities (Woo & Sillanpaa 1979). The only monocular cue that provides a similar degree of depth resolution is motion parallax created by moving the head from side to side (Howard & Rogers 1995). In fact, monocular motion parallax and binocular disparity are closely related, since temporally separated successive views of an environment can in principle 55
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