Modeling depth from motion parallax with the motion/pursuit ratio.

The perception of unambiguous scaled depth from motion parallax relies on both retinal image motion and an extra-retinal pursuit eye movement signal. The motion/pursuit ratio represents a dynamic geometric model linking these two proximal cues to the ratio of depth to viewing distance. An important step in understanding the visual mechanisms serving the perception of depth from motion parallax is to determine the relationship between these stimulus parameters and empirically determined perceived depth magnitude. Observers compared perceived depth magnitude of dynamic motion parallax stimuli to static binocular disparity comparison stimuli at three different viewing distances, in both head-moving and head-stationary conditions. A stereo-viewing system provided ocular separation for stereo stimuli and monocular viewing of parallax stimuli. For each motion parallax stimulus, a point of subjective equality (PSE) was estimated for the amount of binocular disparity that generates the equivalent magnitude of perceived depth from motion parallax. Similar to previous results, perceived depth from motion parallax had significant foreshortening. Head-moving conditions produced even greater foreshortening due to the differences in the compensatory eye movement signal. An empirical version of the motion/pursuit law, termed the empirical motion/pursuit ratio, which models perceived depth magnitude from these stimulus parameters, is proposed.

Integration time for the perception of depth from motion parallax.

The perception of depth from relative motion is believed to be a slow process that "builds-up" over a period of observation. However, in the case of motion parallax, the potential accuracy of the depth estimate suffers as the observer translates during the viewing period. Our recent quantitative model for the perception of depth from motion parallax proposes that relative object depth (d) can be determined from retinal image motion (dθ/dt), pursuit eye movement (dα/dt), and fixation distance (f) by the formula: d/f≈dθ/dα. Given the model's dynamics, it is important to know the integration time required by the visual system to recover dα and dθ, and then estimate d. Knowing the minimum integration time reveals the incumbent error in this process. A depth-phase discrimination task was used to determine the time necessary to perceive depth-sign from motion parallax. Observers remained stationary and viewed a briefly translating random-dot motion parallax stimulus. Stimulus duration varied between trials. Fixation on the translating stimulus was monitored and enforced with an eye-tracker. The study found that relative depth discrimination can be performed with presentations as brief as 16.6 ms, with only two stimulus frames providing both retinal image motion and the stimulus window motion for pursuit (mean range=16.6-33.2 ms). This was found for conditions in which, prior to stimulus presentation, the eye was engaged in ongoing pursuit or the eye was stationary. A large high-contrast masking stimulus disrupted depth-discrimination for stimulus presentations less than 70-75 ms in both pursuit and stationary conditions. This interval might be linked to ocular-following response eye-movement latencies. We conclude that neural mechanisms serving depth from motion parallax generate a depth estimate much more quickly than previously believed. We propose that additional sluggishness might be due to the visual system's attempt to determine the maximum dθ/dα ratio for a selection of points on a complicated stimulus.

Visual depth from motion parallax and eye pursuit.

A translating observer viewing a rigid environment experiences "motion parallax", the relative movement upon the observer's retina of variously positioned objects in the scene. This retinal movement of images provides a cue to the relative depth of objects in the environment, however retinal motion alone cannot mathematically determine relative depth of the objects. Visual perception of depth from lateral observer translation uses both retinal image motion and eye movement. In Nawrot and Stroyan (Vision Res 49:1969-1978, 2009) we showed mathematically that the ratio of the rate of retinal motion over the rate of smooth eye pursuit mathematically determines depth relative to the fixation point in central vision. We also reported on psychophysical experiments indicating that this ratio is the important quantity for perception. Here we analyze the motion/pursuit cue for the more general, and more complicated, case when objects are distributed across the horizontal viewing plane beyond central vision. We show how the mathematical motion/pursuit cue varies with different points across the plane and with time as an observer translates. If the time varying retinal motion and smooth eye pursuit are the only signals used for this visual process, it is important to know what is mathematically possible to derive about depth and structure. Our analysis shows that the motion/pursuit ratio determines an excellent description of depth and structure in these broader stimulus conditions, provides a detailed quantitative hypothesis of these visual processes for the perception of depth and structure from motion parallax, and provides a computational foundation to analyze the dynamic geometry of future experiments.

The motion/pursuit law for visual depth perception from motion parallax.

One of vision's most important functions is specification of the layout of objects in the 3D world. While the static optical geometry of retinal disparity explains the perception of depth from binocular stereopsis, we propose a new formula to link the pertinent dynamic geometry to the computation of depth from motion parallax. Mathematically, the ratio of retinal image motion (motion) and smooth pursuit of the eye (pursuit) provides the necessary information for the computation of relative depth from motion parallax. We show that this could have been obtained with the approaches of Nakayama and Loomis [Nakayama, K., & Loomis, J. M. (1974). Optical velocity patterns, velocity-sensitive neurons, and space perception: A hypothesis. Perception, 3, 63-80] or Longuet-Higgens and Prazdny [Longuet-Higgens, H. C., & Prazdny, K. (1980). The interpretation of a moving retinal image. Proceedings of the Royal Society of London Series B, 208, 385-397] by adding pursuit to their treatments. Results of a psychophysical experiment show that changes in the motion/pursuit ratio have a much better relationship to changes in the perception of depth from motion parallax than do changes in motion or pursuit alone. The theoretical framework provided by the motion/pursuit law provides the quantitative foundation necessary to study this fundamental visual depth perception ability.