Ординатура / Офтальмология / Английские материалы / Seeing_De Valois_2000

224Clifton Schor

D. Relative Disparity

Stereopsis is our ability to detect relative depth between two objects, and relative depth could be computed in several ways. Each eye has an image of the two objects, and relative disparity could be computed as the di erence in the image separations formed in the two eyes. Alternatively, each of the compared objects subtends an absolute disparity at the horopter, and relative depth could be computed from the di erence in these absolute disparities. It has been argued that relative disparities for stereo-perception are computed from di erences in absolute disparity rather than from comparisons of spatial o sets of the two monocular images (Westheimer & McKee, 1979). Although absolute disparity provides only a vague sense of depth, which is supplemented by oculomoter convergence (Foley, 1980) and monocular depth cues, depth could be discriminated with hyperresolution by comparing activity of two separate detectors of absolute disparity (Regan, 1982).

E. Stereo-Depth Contrast

Veridical space perception requires that the visual system does not confuse a disparity generated by object surfaces in our environment and disparities produced by errors of viewpoint caused, for example, by body sway or errors of gaze direction or eye alignment (Enright, 1990). For example, errors of cyclovergence and of gaze direction would produce disparity maps that would correspond to inclination and slant of real surfaces in space. Fortunately, the visual system is relatively insensitive to whole field disparity gradients (uniform and shear) (Gillam, Flag, & Findley, 1984; Mitchison & Westheimer, 1984, 1990; Shipley & Hyson, 1972; Stevens & Brookes, 1987, 1988; van Ee & Erkelens, 1996). This avoids confusion between real surface depth variations and surface slant distortions caused by viewpoint errors. In part, our insensitivity to whole field disparity gradients results from a global process that normalizes continuous variations of disparity (disparity gradients) so that an abrupt depth variation between a small surface within a background disparity gradient is perceived as a depth change relative to a normalized fronto-parallel background.The result is that the small object within a background composed of a disparity gradient will appear as though it were on a zero-disparity or fronto-parallel background field.

Depth contrast (Werner, 1937, 1938) is a specific class of a general category of percepts referred to as simultaneous contrast. Examples of simultaneous contrast in other visual-sensory modalities include luminance contrast (Helmholtz, 1909), induced motion such as the moon and moving cloud illusion (Duncker, 1929), color contrast (Kirschmann, 1890), tilt or orientation contrast as seen in the rod-and-frame illusion (Gibson, 1937), spatial frequency and size contrast (MacKay, 1973) and curvature contrast (Gibson, 1937). These various forms of simultaneous contrast allow a constancy of space perception in the presence of luminance and spectral changes in overall lighting, optical distortion caused by atmospheric thermals or optical aberrations of the eye, and motion caused by passive movements of the body and eyes. Figures 30 and 31 are illustrations of brightness and depth contrast illusions produced

226 Clifton Schor

interactions between individual nearby disparities. Simultaneous depth contrast also operates globally over long ranges or large separations (Fahle & Westheimer, 1988). The global e ect describes the referencing of all depth variations to the overall background disparity that has been normalized to appear as the fronto-parallel plane. The local e ects are relative depth contrasts between adjacent objects or surfaces, all of which are seen with respect to the normalized background disparity. The magnitude of long-range global interactions varies with background disparity, contrast, and size (Kumar & Glaser, 1991). Local or short-range simultaneous contrast between two disparity gradients is greater when they are separated along a common slant axis (van Ee & Erkelens, 1996).These e ects are enhanced by short exposure durations (10 ms) (Werner, 1937) and are dramatically reduced with several seconds of exposure (Kumar & Glaser, 1992).

F. Position and Phase Limits

As with sensory fusion, stereo-acuity depends upon spatial scale. When tested with a narrow-band luminance stimulus (1.75 octaves) such as produced by a di erence of Gaussians (DOG), stereo-threshold becomes elevated when tested with spatial frequencies below 2.5 cycles/deg (Schor & Wood, 1983; Schor et al., 1984b; Smallman

&MacLeod, 1994). The luminance spatial frequency dependence of stereopsis and fusion suggest that disparity is processed early in the visual system within a broad range of linear channels with band-limited tuning for luminance spatial frequency. Interocular di erences in spatial frequency also influence sensitivity to binocular disparity (Schor et al., 1984b). Figure 32 illustrates that sensitivity to depth of a small patch, composed, for example, by DOG or Gabor patches with moderate bandwidths (1.75 octaves), is reduced when the patch is tilted about its vertical axis. Tilt is produced by horizontal disparities between patches of unequal size and spatial frequency. Stereosensitivity becomes reduced when center spatial frequencies of the patches di er by more than three octaves over a frequency range from 0.075 to 2 cpd. At higher spatial frequencies (2–19 cpd), stereoscopic depth thresholds of tilted patches remain acute over a much wider range of interocular di erences in target width and corresponding spatial frequencies.The broad range of interocular di erences in spatial frequency that support stereopsis suggest that disparity can also be encoded from disparities subtended by contrast features defined by the edges of the stimulus (envelope). Pattern size and location could be encoded from a nonlinear extraction of the overall contrast envelope that defines the spatial extent (overall size) of the target, independent of its luminance spatial frequency content (surface texture) (Wilcox

&Hess, 1995; Schor et al., 1998; Edwards, Pope, & Schor, 1999).

Variations of fusion limits and stereo-threshold with luminance spatial frequency (Figure 10) may be related to the position and phase limits for disparity processing described previously for binocular sensory fusion. Physiologically, binocular receptive fields have two fundamental organizational properties. The receptive fields that represent binocular disparity can be o set from a point of zero retinal correspon-

Static and dynamic stereo-spatial tuning functions. Spatial tuning functions are shown for static (top) and dynamic (bottom) stereopsis measured with seven standard width di erence of Gaussian functions (DOGS), whose center spatial frequencies are indicated by the arrows along the upper edge of the figure. Bandwidths are greater for spatial functions tuned about high than low spatial frequencies. The dashed line is a maximum sensitivity envelope that describes stereo-sensitivity measure with equal width DOGS presented to the two eyes. The slopes of the sensitivity envelope di er for static and dynamic stereopsis. Numbers above arrows along the top margin of the figure quantify the increase of the spatial frequency range of tuning functions (in octaves) for dynamic compared with static stereopsis. The luminance profile of the DOG function is inset at the upper left side of the graph. (Reprinted from Vision Research, 24, Schor, C. M., Wood, I. C., & Ogawa, J. Spatial tuning of static and dynamic local stereopsis, pp. 573–578, Copyright © 1984, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom.)

dence (position disparity). They can also have zero positional disparity combined with a quadrature organization in which there is a 90 phase shift of the areas of excitation and inhibition in one eye’s receptive field compared to the other (phase disparity) (Figure 24) (DeAngelis et al., 1995). The position limit at high spatial

retinal eccentricity along the horopter or fixation plane. Thus the stereo-threshold is lower at an eccentricity of 5 than it is with a disparity pedestal of only 80 arc min centered in the midsagittal plane (Krekling, 1974). Di erences between stereoand vernier acuity described above are highlighted when tested in the retinal periphery. Stereo-acuity remains constant with horizontal retinal eccentricities of up to 40 arc min, whereas vernier acuity rises by nearly an order of magnitude over the same range of retinal eccentricities (Schor & Badcock, 1985). Stereo-thresholds are elevated slightly with equivalent retinal eccentricities along the vertical meridian (McKee, 1983). At larger horizontal eccentricities, stereo-thresholds increase gradually up to 6 at a retinal eccentricity of 8 (Rawlings & Shipley, 1969).

H. Spatial Interactions

Stereo-sensitivity can either be enhanced or reduced by nearby targets. The threshold for detecting depth corrugations of a surface such as the folds in a hanging curtain decreases with depth-modulation frequency (reciprocal of spacing between the folds) up to 0.3 cycles per degree where it is lowest (Tyler, 1975). At depth-modu- lation frequencies lower than 0.3 cpd, the threshold for stereopsis is elevated and appears to be limited by a disparity gradient or minimal rate of change of depth/ degree of target separation. At depth-modulation frequencies higher than 0.3 cpd, stereo-threshold is elevated as a result of depth averaging. Similar e ects are seen with separations between point stimuli for depth (Westheimer & McKee, 1979; Westheimer, 1986; Westheimer & Levi, 1987).

When a few isolated targets are viewed foveally, changes in the binocular disparity of one introduces suprathreshold depth changes or biases in others when their separation is less than 4 min arc. This depth attraction illustrates a pooling of disparity signals. When targets are separated by more than 4–6 arc min, the bias is in the opposite direction, and features appear to repel one another in depth. Attraction and repulsion also occurs with cyclopean targets (Stevenson, Cormack, & Schor, 1991), showing that they are not based simply on positional e ects at the monocular level.The enhancement of depth di erences by repulsion might be considered a depth-contrast phenomenon that is analogous to Mach bands in the luminance domain that are thought to result form lateral inhibitory interactions. Depth distortions that are analogous to Mach bands have been demonstrated with horizontal disparity variations between vertically displaced contours (Lunn & Morgan, 1996), demonstrating analogous spatial interactions in the horizontal disparity domain and the luminance-contrast domain.

I. The Contrast Paradox

The luminance-contrast of targets also influences stereo-acuity. Cormack, Stevenson, and Schor (1991) demonstrated that both correlation thresholds and stereoacuity were degraded as contrast was reduced below 16%. Both thresholds were proportional to the square of the contrast reduction (e.g., reducing the contrast by a

232 Clifton Schor

factor of two caused a fourfold elevation of the thresholds). This marked reduction of disparity sensitivity results from intrinsic noise in the disparity-processing mechanism that exceeds the noise in low-contrast stimuli caused by spurious matches.

Curiously, when the contrast of the two eye’s stimuli is reduced unequally, stereo-acuity is reduced more than if the contrast of both targets is reduced equally (Cormack, Stevenson, & Landers, 1997; Halpern & Blake, 1988; Legge & Gu, 1989; Lit, 1959; Rady & Ishak, 1955; Schor & Heckman, 1989). Stereo-acuity is reduced twice as much by lowering contrast in one eye than by lowering contrast in both eyes. This contrast paradox only occurs for stereopsis and is not observed for other disparity-based phenomenon, including correlation-detection thresholds (Cormack, Stevenson, & Landers, 1997), Panum’s fusional limits (Schor & Heckman, 1989), or transient disparity-induced vergence (Schor et al., 1998). The contrast paradox occurs mainly with low spatial frequency stimuli ( 2.0 cycles/degree) (Cormack et al., 1997; Halpern & Blake, 1988; Schor & Heckman, 1989). Several factors could account for this contrast tuning, including di erent amplitude noise sources in the two monocular signals that was uncancelled (Legge & Gu, 1989), an interocular inhibitory process (Kontsevich & Tyler, 1994; Schor & Heckman, 1989), or a temporal asynchrony between the transmission times for the two eyes signals to the visual cortex (Howard & Rogers, 1995). Contrast tuning might serve to reduce the possibility of false matches of o -horopter targets subtending large visual angles (Cormack et al., 1997).

J. Temporal Constraints

The duration and synchronization of monocular components of disparity signals greatly influence our stereo-sensitivity. Although depth in a stereogram may be perceived with just a spark of illumination (Dove, 1841), stereo-depth detection threshold decreases with exposure durations longer than 100 ms up to 3 sec with line (Langlands, 1926) and random dot (Harwerth & Rawlings, 1977) patterns. Critical duration for perceiving depth in random-dot stereograms can take several seconds in some individuals, whereas depth perception is almost immediate with line stereograms for the same individuals. The prolonged exposures needed for random-dot stereograms can be shortened by presenting monocular cues that guide vergence eye alignment to the depth plane of the stereogram (Kidd, Frisby, & Mayhew, 1979). This suggests that the extra time needed for perception of depth in the RDS results from the inability of the binocular system to resolve ambiguous matches for disparities exceeding 1 (Stevenson, Cormack, & Schor, 1994). In e ect, vergence must search blindly until the disparity of the correct match is reduced to 1 , within the operating range of the binocular cross-correlation process.

Depending upon the luminance spatial frequency of a target, stereo-threshold also varies with target velocity. Stereosensitivity for dynamic or moving targets is greater than with static targets composed of low spatial frequencies (Schor et al.,

1984b; Morgan & Castet, 1995). Comparison of stereo-thresholds in Figure 32 illustrates that stereo-thresholds for target spatial frequencies lower than 2.4 cycles/ deg were five times more sensitive with dynamic than static targets, whereas the thresholds were very similar for static and dynamic stimuli at higher spatial frequencies (Schor et al., 1984b). Sensitivity to dynamic depth is limited in part to sensitivity to interocular time delays. Sensing the depth of moving targets requires both spatial and temporal tuning. A nonzero binocular disparity stimulated by a target that is moving at a constant velocity parallel to the horopter is equivalent to a zero disparity of a target moving along the horopter, with a time delay to corresponding retinal points. The more sensitive the temporal resolution of a binocular neuron the better is its sensitivity to binocular disparity or interocular spatial phase shifts of the two ocular images.The minimum detectable spatial phase di erence between the eyes for dynamic targets is about 5 and an interocular temporal delay as small as 450 s (Morgan & Castet, 1995). These results suggest that stereopsis for moving targets is accomplished by neurons having a spatial-temporal phase shift in their receptive fields between the eyes.

Stereo-acuity is optimal with simultaneous presentation of both eyes’ stimuli. It remains high with interocular delays shorter than 25 ms (Ogle, 1964) or as long as visual persistence allows some overlap of the two monocular stimuli (Engel, 1970). Optimal stereo-acuity with thresholds of 3 arc sec also requires simultaneous presentation of at least two targets that define the stereo-depth interval. When foveally viewed targets of di erent depth are presented sequentially, with no time gap between them, stereo-threshold can be elevated by an order of magnitude (22–52 arc sec) (Westheimer, 1979). When time gaps are introduced between the two successive views that exceed 100 ms, the stereo-threshold increases dramatically to 0.5 , presumably because of noise in the vergence system and a loss of memory of the vergence position of the first stimulus (Foley, 1976). Interestingly, sequential stereopsis is approximately the same for wide spatial separations (10 ) between sequentially foveally fixated targets and narrow ones (Enright, 1991; Wright, 1951). This is surprising because the wide separation target requires saccades between the first and second target, and these introduce a small time interval between the two targets equal to the duration of the saccade (approximately 50 ms). One would also expect that vergence errors introduced by saccades would introduce a noise source that would elevate the sequential stereo-threshold. Enright reports that eye movements are also unstable with sequential stereo-measures between adjacent stimuli and perhaps they are as variable as the disconjugacy of large saccades to widely spaced stimuli. It is also clear that eye movements are not entirely responsible for the reduction of sequential stereo-acuity (Enright, 1991) and that perhaps temporal masking may contribute to the elevated sequential-stereo threshold. The small interval during the saccade between sequential stimuli might diminish the temporal masking between widely separated sequential stimuli compared to that associated with no time delay between adjacent sequential stimuli.