Influence of Depth Cues on Velocity of 3-D Apparent Motion

Michael K. McBeath

ABSTRACT

A new objective technique called the method of motion handedness was used to measure the influence of depth cues on perspective velocity of 3-D apparent motion. Subjects discriminated between tilted, maximally-fast clockwise and counterclockwise stimulus sequences, producing a space/time (or experienced velocity) function. In the first study, apparent motion was tilted back at four different angles. Results indicated that temporal variance was better accounted for by 3-D spatial separation than by 2-D retinal separation. In the second study, consistency of the four depth cues was varied. Results indicated that influence of each depth cue was additive. When all cues specified tilt in depth, velocity of apparent motion remained relatively constant over separation in 3-D space.

Method of Motion Handedness
Four elements are presented cyclically in either the clockwise or counterclockwise order. Arrows represent experienced trajectory when stimuli are presented clockwise at various rates.
When presentation rate is very slow, experienced trajectory is diamond shaped. When presentation rate is just above threshold, experienced trajectory curves into a circle When presentation rate is just below threshold, direction of presentation is indiscernible. When presentation rate is very rapid, no motion is experienced. (just occasional blinking).
drawing of four presentation rates and their perceived motion
Drawing of tilt planes Results of Experiment 4 with best fitting linear model. Averages of all 12 subjects combined.
^^The diamond-shaped stimulus configuration was tilted in depth through a horizontal axis by one of four angles. Angles were chosen so that spatial separation increased from one to two in equal increments. (secant(0.0)=1.00. secant(41.4)=1.33, secant(53.1)=1.67, secant(60)=2.00). Stimuli are shown for the 0.0 tilt condition.
>> Figure 14. Results of Experiment 4 with best fitting linear model. Averages of all 12 subjects combined. (Each point is a mean of 144 staircase turn values.
Experimental Parameters Varied in Study 3 <Light shades indicate left eye view.

<Dark shades indicate right eye view.

 Results of Experiment 5
Figure 15. Experimental Parameters Varied in Study 3

All combinations of four depth cues were varied: disparity, relative size, perspective, and depth-luminance covariance. When a cue remained constant, it specified no tilt in depth. When cue varied, it specified a 60 degree tilt in depth

 Figure 16. Results of Experiment 5: Influence of Each Depth Cue

Contribution to critical stimulus separation due to each depth cue. Stimulus configuation is elliptical and tilted in depth. Each cue is set to specify a configuration tilt of either 0 or 60 degrees. All four cues influence critical stimulus separation is the direction predicted for 3-D velocity constancy, though only depth-luminance covariance and disparity had stastically significant influence.
Influence of Each Combination of Depth Cues Figure 17. Influence of Each Combination of Depth Cues

Contribution to critical stimulus separation due to each combination of three depth cues. Stimulus configuration is elliptical and tilted in depth. Each cue is set to specify a configuration tilt of either 0 or 60 degrees. The monotonically increasing staircase pattern indicates that critical separation is a near additive function of the three depth cues shown. All combinations of change in cue specification influence critical separation in the direction predicted for 3-D constancy.

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