Movement parallax: an asymptotic function of amplitude and velocity of head motion.

Three experiments providing a two-object display with monocular movement parallax acting as the only effective cue to depth were carried out with ten observers. The matched width of the variable (rear) object, i.e. the amount of constancy, was taken as a measure of the effectiveness of movement parallax under the condition under question. Experiment I showed that successively disparate images (position parallax) are not sufficient to produce the impression of depth as compared to movement parallax. In Experiment 2 and 3 velocity (1%) and amount (d) of head movement were varied. At values 5-10 times threshold, depth perception by movement parallax reached half of its maximal effectiveness, It was virtually independent of L‘ and d when these values exceeded 20 times threshold level. Kq wortfs-movement parallax; monocular depth perception Although monocular movement parallax has been investigated intermittently since Bourdon’s experiment (1898), there still exist studies questioning its role as a cue to depth. Observers perceived motion rather than depth in one study (Gibson et al., 1959) or simply separation in depth, relative distance being indeterminate in another (Smith and Smith, 1963). Gogel and Tietz (1974) have also reported apparent object motion concomitant with head motion, when the object’s depth is not perceived correctly. And Eriksson (1972) found that in some cases even a reversal of apparent order in depth of two luminous objects occurred when viewed in total darkness. Nevertheless movement parallax is widely acknowledged as a cue to relative or even absolute (Ferris, 1972; Johansson, 1973) depth. But though most authors agree thar it works, few suggestions have been offered to explain how it does. The results of electrophysiology suggest a possible approach to the explanation of the effectiveness of movement parallax in depth perception. There exists strong evidence for the existence of cells in the visual system that respond to the direction and velocity of a moving stimulus (Barlow and Hill 1963a, 1963b, 1964; Bridgeman, 1972) and a hypothesis to explain space perception on that basis has been put forward (Nakayama and Loomis, 1974). The involvement of the motion detecting cells in the depth analysing process, in the case of retinal motions occurring with head motions (relative movement parallax), would be confirmed if it could be shown that successively disparate images (position parallax) are not sufficient for depth perception, but that motion flow over the retina is required. This will be investigated in Experiment 1. The most concrete and often cited definition of movement parallax has been presented by Graham (1965, p. 504): “When a subject’s eyes move with respect to the environment, or when the environment moves with respect to a subject’s eyes, a differential angular velocity exists between a line of sight to a fixated object and the line of sight to any other object in the visual field.” It can be shown (Appendix 1) that for small head movements and the line of sight being roughly perpendicular to the direction of head movement where a, b are the object distances, I: and d velocity and amplitude of head movement, Q the differential angular velocity, and dy the variation of the angle y between the two iines of sight (see Fig. 5). If we consider o the critical value for movement parallax, as Graham’s definition seems to imply, the effectiveness of movement parallax is enhanced by a greater velocity of relative movement of the observer and the objects. This is apparently true for threshold conditions (Graham et al., 1948; Zegers, 19483, but in supra-th~hold con~tions normal life experience teHs us that depth perception by monocular movement parallax should not depend on either the amplitude or the velocity of head movement over a considerably wide range, and the expression w/u = l/a l/b that depends only on object distances seems to be a better representation of what is going on in depth perception by movement parallax. This can be tested by experiments in which monocular movement parallax is the only cue to depth and the assumptions underlying the derivation of (1) are valid. There are only limited data on the influence of velocity (u) and amplitude (d) of head movement. Although Zegers reports that the threshold angular velocity for a motionless observer to perceive the depth difference of two needles moving along a horizontal path “increase(s) with an increase in basic rate of stimuius movement up to a limiting rate” (Zegers, 1948% p. 4971, no attempt has been made to vary c systematically under conditions of active head movement of the observer.