The Stroboscopic Pulfrich Effect Is Not Evidence for the Joint Encoding of Motion and Depth
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Journal of Vision (2005) 5, 417-434 http://journalofvision.org/5/5/3/ 417 The stroboscopic Pulfrich effect is not evidence for the joint encoding of motion and depth Laboratory of Sensorimotor Research, National Eye Institute, Jenny C. A. Read National Institutes of Health, Bethesda, MD Laboratory of Sensorimotor Research, National Eye Institute, Bruce G. Cumming National Institutes of Health, Bethesda, MD In the Pulfrich effect, an illusion of depth is produced by introducing differences in the times at which a moving object is presented to the two eyes. In the classic form of the illusion, there is a simple explanation for the depth percept: the interocular delay introduces a spatial disparity into the stimulus. However, when the moving object is viewed stroboscopically, this simple explanation no longer holds. In recent years, depth perception in the stroboscopic Pulfrich effect has been explained by invoking neurons that are sensitive both to stereo disparity and to direction of motion. With such joint motion/disparity encoders, interocular delay causes a perception of depth by causing a shift in each neuron’s preferred disparity. This model has been implemented by N. Qian and R. A. Andersen (1997). Here we show that this model's predictions for perceived disparity are quantitatively at odds with psychophysical measures. The joint-encoding model predicts that the perceived disparity is the virtual disparity implied by the apparent motion; in fact, the perceived disparity is smaller. We show that the percept can be quantitatively explained on the basis of spatial disparities present in the stimulus, which could be extracted from pure disparity sensors. These results suggest that joint encoding of motion and depth is not the dominant neuronal basis of depth perception in this stimulus. Keywords: binocular vision, interocular delay, Pulfrich effect, psychophysics, computational modeling ated: The target appears first in front of, then behind, the Introduction fixation plane, depending on its direction of motion. The detection of image motion on the retina and the It was pointed out many years ago (Pulfrich, 1922) that detection of binocular disparities present similar computa- there is a simple geometrical explanation for this: A moving tional problems: Object motion gives rise to images that object changes its position over time, so interocular delay occupy different retinal locations at different times; in bin- gives rise to a real spatial disparity on the retina. Suppose ocular viewing, the images occupy different retinal loca- the image reaching the left eye is delayed relative to the tions in the two eyes. The most famous demonstration of a right eye, and that the object, moving at speed v, has posi- link between the processing of motion and stereoscopic tion x when it is first seen by the right eye. By the time this depth is the Pulfrich effect (Burr & Ross, 1979; Lee, 1970a, same image reaches the left eye, the image in the right eye 1970b; Morgan, 1976; Morgan & Thompson, 1975; Pul- will have moved to a new position, x + v∆t. At this mo- frich, 1922). This is a depth illusion, created when the im- ment, the left eye’s image is at x, while the right eye’s image age from one eye reaches the brain later than from the is at x + v∆t, so there is a spatial disparity, ∆x = v∆t, which other. The delay may arise clinically (e.g., in multiple scle- is interpreted as depth in the usual way. Thus, the illusion rosis if optic nerve damage slows transmission of the image of depth in the classic Pulfrich effect is a consequence of from one eye; Rushton, 1975) or can be introduced artifi- the stimulus and – while confirming that spatial disparity cially. Before the advent of electronic stimuli, this was done results in a percept of depth – does not inform us further by placing a neutral density filter over one eye to dim the about the neuronal mechanisms of depth perception. image; dim images require more retinal processing time However, this geometrical explanation does not hold than bright images, so the image from the filtered eye for the stroboscopic version of the Pulfrich effect (Burr & reaches the brain later (Julesz & White, 1969; Ross & Ross, 1979; Lee, 1970b; Morgan, 1975, 1976, 1979; Mor- Hogben, 1975). Nowadays, computer-generated stimuli can gan & Thompson, 1975), in which the moving target is be presented with a real interocular delay between the illuminated only intermittently. A space-time diagram of times at which the images are presented to the two eyes, this stimulus is shown in Figure 1. The squares represent allowing the interocular delay to be precisely controlled, appearances of the target; blue indicates its appearances in and its effect studied without confounding effects due to the right eye, and red those in the left. The horizontal axis luminance differences. If images of a target moving hori- represents the time of each appearance; the vertical axis is zontally back and forth in the frontoparallel plane are position. Note that the two eyes never receive simultaneous viewed with interocular delay, an illusion of depth is cre- images of the target. If the strobe flashes at time t, both eyes doi:10.1167/5.5.3 Received October 27, 2004; published May 17, 2005 ISSN 1534-7362 © 2005 ARVO Journal of Vision (2005) 5, 417-434 Read & Cumming 418 see an image of the target in the position it occupied at therefore hailed them as the physiological substrate under- time t, but the right eye sees this image immediately, while lying depth perception in these stimuli. the left eye does not see this image until time t + ∆t. The However, while plausible, this model has never been difference between this and the classic stimulus is that here thoroughly tested. A detailed comparison between the pre- the right eye is not presented with an image at time t + ∆t. dictions of this model and psychophysical data has been The brain must therefore “remember” the right eye’s image hampered by the conflicting reports concerning disparity from time t to match it with the image that occurs later in perception in the strobe Pulfrich effect. Lee (1970b) re- the left eye. This stimulus does have the potential to inform ported that depth in the stroboscopic Pulfrich effect was us about the neuronal mechanisms involved. For example, considerably smaller than in the classic case, and did not the perception of depth in this stimulus depends on the classify it as a “true” Pulfrich effect at all. In contrast, Burr temporal integration period over which stereo matches are and Ross (1979) reported that the amount of depth per- possible (Lee, 1970a; Morgan, 1979). ceived was exactly the same as for the “classic” Pulfrich ef- The early literature on Pulfrich-like stimuli contained fect where the object is continuously visible: The object is two major explanations for depth perception in Pulfrich- seen at the virtual disparity implied by its apparent motion like stimuli. Ross (Ross, 1974, 1976; Ross & Hogben, (see Figure 1). Morgan and colleagues (Morgan, 1979; Mor- 1974) suggested that interocular delay might per se produce gan & Thompson, 1975) found that the amount of depth a perception of depth, given that moving objects with non- depended on the time separating successive appearances of zero disparity stimulate corresponding points on the two the stroboscope. When this inter-flash interval was short retinas at different times. Tyler (1974, 1977) and Morgan (10 ms), the perception was indeed that of the virtual dis- (1979) suggested that spatial disparities physically present in parity. However, at the longer inter-flash interval used by the stimulus, after temporal filtering by the visual system, Burr and Ross (50 ms), Morgan found that – while depth might suffice to explain the depth percept. In recent years, was still perceived – the perceived disparity was less than these two explanations have merged. Depth perception is the virtual disparity. now assumed to depend on neuronal mechanisms that ap- ply joint spatiotemporal filtering, making them sensitive to direction of motion as well as to disparity (Anzai, Ohzawa, & Freeman, 2001; Carney, Paradiso, & Freeman, 1989; virtual disparity vt∆ Morgan & Castet, 1995; Morgan & Fahle, 2000; Morgan position & Tyler, 1995; Pack, Born, & Livingstone, 2003; Qian, 1997; Qian & Andersen, 1997). These joint mo- tion/disparity sensors are characterized by receptive field profiles that are tilted relative to the space-time axes ∆t (“space/time-inseparable”) (Adelson & Bergen, 1985; DeAngelis, Ohzawa, & Freeman, 1995), so their preferred t t +∆t time disparity changes as a function of interocular delay. Joint motion/disparity sensors "cannot distinguish an interocular Figure 1. Space-time diagram of stroboscopic Pulfrich stimulus. time delay from a binocular disparity" (Qian & Andersen, The squares represent appearances of the stroboscopically illu- 1997), so they represent a modern version of Ross’s sugges- minated target in the two eyes: blue for appearances in the right tion that interocular delay directly causes a depth percept. eye and red for those in the left eye. The target appears at the To see how they explain depth perception in the strobo- same position in each eye, but there is an interocular delay such scopic Pulfrich stimulus, note that the flashed stimuli de- that the target appears a time ∆t later in the left eye than it does fine an apparent motion in both eyes. The interocular delay in the right. The dotted lines indicate the trajectory implied by the means that the trajectory of this apparent motion has a dis- apparent motion. The "virtual disparity" v∆t is defined to be the parity, even when the individual flashed images do not. spatial separation between these two lines (Burr & Ross, 1979). Filters that encode disparity and motion simultaneously would be sensitive to the virtual disparity defined by these apparent motion paths.