Optical magnification as event information

Abstract

The geometrical optics of approach events is delineated. It is shown that optical magnification provides information about distance and time until collision. An experiment is described in which two objects--white styropor spheres 10 cm in diameter, seen against a white plaster wall--were moved simultaneously at equal, constant speed along straight, converging paths at eye level towards a human observer and towards a common, virtual point of collision which either coincided with the observer's station point or was placed in front of, or behind, that point. Approach events differed with regard to trajectories, distances, velocities, and times-to-collision involved. Events were observed monocularly fixating and binocularly non-fixating, without head movements. The objects always stopped before colliding, and subjects had to respond to the virtual collisions. Most responses were too early, especially for impending collisions at, or behind the observers' station point. Responses for impending collisions in front of the observers tended to be too late, especially for larger total amounts of optical magnification and higher velocities, which together imply shorter times-to-collision. Relative errors were comparatively larger for very short and very long times-to-collision throughout, where events of the first kind were overshot, the latter ones undershot. Results are interpreted with reference to biological theories and the constraints imposed by geometrical optics. Special attention is focused on the issue of unavoidable, necessary confounding of variables in time-to-collision studies.

Accuracy of judging time to arrival: Effects of modality, trajectory, and gender.

“…Results of Experiment 4 showed substantial underestimation for trajectories 45° from transverse, and unpublished data (Schiff, 1988) have also shown intermediate amounts of judgment error for trajectories only 10° elevated from the scalar eye height of the top of approaching autos. Kebeck and Landwehr (1988) found phenomena very similar to those reported here by using objects (model trains) approaching observers or each other at eccentric angles in real 3-D space, implying that our findings are not restricted to filmed space. Head-on T a estimates are for the most part underestimates, that is, conservative constant errors.…”

Image velocity, not tau, explains arrival-time judgments from global optical flow.

“…In addition to the demonstrated insufficiency of tau, TTA judgments are known to be mediated by several variables that are not related to tau, such as the absolute amount of optical magnification (Kebeck & Landwehr, 1993), changing target vergence (Heuer, 1993), and perceived velocity (Smeets, Brenner, Trébuchet, & Mestre, 1996). Furthermore, DeLucia (1991; DeLucia & Warren, 1994) showed that relative size as a static depth cue supersedes motion-based depth information for objects on a collision trajectory.…”

Visual discrimination thresholds for time to arrival

“…For head-1 As has also been noted by others (e.g., Bootsma & Craig, 2002, p. 918, note 6), in Todd's (1981) experiment, approach was not head-on in the sense of the two objects' midpoints traveling on converging trajectories toward the observer (cf. Kebeck & Landwehr, 1992, for such a scenario); rather, the two objects were set side by side, so that the two abutting lateral edges traveled on a collision course along the observer's cyclopean line of gaze. centered, straight trajectories, the optic flow field's focus of expansion coincides with the object's or the observer's direction of travel and gaze (Warren, 1998), and global τ, at this point, is undefined (or zero).…”