George J. Andersen

Induced self-motion in central vision.

Previous research on visually induced self-motion found that stimulation of the central visual field (up to 30 degrees in diameter) results in perceived object motion while self-motion requires peripheral stimulation. In the present study, perceived self-motion was induced with a radially expanding pattern simulating observer motion through a space filled with dots, with visual angles of 7.5 degrees, 10.6 degrees, 15 degrees, and 21.2 degrees. Speed and texture density were also varied. The duration of reported self-motion (a) decreased with increased speed, (b) failed to increase with increased visual angle, and (c) decreased with visual angle at the highest speed level. In a second experiment, subjects rated the perceived depth of the displays. The speed and speed/area interaction effects on judged depth matched those found for induced self-motion. These results suggest an extension of the focal/ambient theory: In addition to a more primitive ambient processing mode that requires peripheral vision, there is a higher level system concerned with ambient processing that functions in the central visual field and uses more complex stimulus information, such as internal depth represented in a radially expanding pattern.

Focused attention in three-dimensional space

The size offocused attention was assessed within a three-dimensional display. Subjects viewed random-dot stereogram displays in which they responded differentially to vertical and horizontal bars. Adjacent noise elements either were identical to the response target or specified the opposite response. The position of the noise elements was varied in depth according to binocular disparity. Interference by incompatible noise elements decreased with depth separation between the noise elements and response target. In addition, interference was greater for noise elements that were more distant from the observer than from the response target than it was for noise elements that were closer to the observer than to the response target. The implications of these results for a viewer-centered representation of focused attention in depth are discussed.

Velocity gradients and relative depth perception

The effectiveness of velocity gradients in providing relative depth information was assessed using random dot patterns translating horizontally. The gradients simulated two planes meeting at a horizontal line at the center, and subjects judged whether the center was the nearest or farthest part of the display. Accuracy increased with maximum dot speed, exceeding 90% in conditions combining the highest speed (10.4o/sec) and longer of two display durations (10 sec) with unrestricted fixation. Separate experiments examined a rotational component perceived in the motion of the planes and the latency in reporting a rigid organization of the displays. Possible reasons for the chance accuracy found by Farber and McConkie (1979) and alternative explanations of the effect of maximum dot speed on accuracy are discussed. A model is presented that accounts for the effects of dot speed and display duration on the accuracy of relative depth judgments.

Recovering viewer-centered depth from disparity, occlusion, and velocity gradients

Two experiments were conducted to assess the effects of corresponding and conflicting binocular and monocular information on the recovery of depth order (signed depth). Subjects viewed displays in which the same or opposite depth orders were indicated by disparity and occlusion, in one experiment, or by disparity and velocity gradients, in a second experiment. The same 36 subjects, 17 who had failed a Random Dot E test and 19 who had passed, were run in both experiments. When binocular and monocular information indicated conflicting depth orders, most subjects responded in accordance with the monocular information on some trials in both experiments. This was true even for a subgroup who always responded in accordance with the stereoscopic information on control trials that did not provide monocular information for depth order. For this subgroup, the impact of conflicting monocular information in the velocity gradient task correlated with performance on the uncrossed version of the Random Dot E test. We also found that some subjects who failed static tests of stereoscopic depth perception could respond accurately to continuously changing disparities.

Spatial orientation from optic flow in the central visual field

Previous research has shown that stimulation of the central visual field with radial flow patterns (produced by forward motion) can induce perceived self-motion, but has failed to demon-strate effects on postural stability of either radial flow patterns or lamellar flow patterns (produced by horizontal translation) in the central visual field. The present study examined the effects of lamellar and radial flow on postural stability when stimulation was restricted to the central visual field. Displays simulating observer motion through a volume of randomly positioned points were observed binocularly through a window that limited the field of view to 15°. The velocity of each display varied according to the sum of four sine functions of prime frequencies. Changes in posture were used to measure changes in perceived spatial orientation. A frequency analysis of postural sway indicated that increased sway occurred at the frequencies of motion simulated in the display for both lamellar and radial flow. These results suggest that both radial and lamellar optic flow are effective for determining spatial orientation when stimulation is limited to the central visual field.

The use of occlusion to resolve ambiguity in parallel projections

Previous research has shown that the three-dimensional structure of an object usually can be perceived when viewing a parallel projection of the object rotating in depth. Accurate judgments of direction of rotation, however, have been found only with polar projections. The present study demonstrated that accurate direction judgments can occur with parallel projections if occlusion is included in the displays. The stimuli were parallel projections of pentagonal texture elements on the surface of a rotating sphere. In one condition, the elements were occluded as they rounded the edge of an opaque sphere. In another condition, elements on the far surface of a transparent sphere were occluded by elements on the near surface. Accuracy of direction judgments was consistently high in the first condition and increased monotonically with element size in the second condition, from chance to over 80% correct. The relationship of these results to the general issue of perceptually combining structure in depth information from one source with relative distance information from another source is discussed.

Dynamic occlusion in the perception of rotation in depth.

Occlusion of more distant texture elements by nearer elements can provide relative distance information in parallel projections of rotating objects, according to Braunstein, Andersen, and Riefer (1982). In that study, occlusion was present in static views in the form of contour interruptions or interposition. In the present study, all visible contours were eliminated. Dots were located within implicit pentagonal texture elements on a transparent sphere. The proportion of the sphere’s surface covered by pentagons and dot density within the pentagons was varied. Accuracy of direction of rotation judgments was significantly affected by area, but not by dot density. Accuracy levels with purely kinetic occlusion were as high as in the earlier study, which included static interposition. Judgments of depth and shape were not affected significantly by occlusion, suggesting that occlusion is a specialized source of information for depth order. Levels of texture and the separability of depth and relative distance judgments are discussed.

Minimum Points and Views for the Recovery of Three-Dimensional Structure

Mathematical analyses of motion perception have established minimum combinations of points and distinct views that are sufficient to recover three-dimensional (3D) structure from two-dimensional (2D) images, using such regularities as rigid motion, fixed axis of rotation, and constant angular velocity. To determine whether human subjects could recover 3D information at these theoretical levels, we presented subjects with pairs of displays and asked them to determine whether they represented the same or different 3D structures. Number of points was varied between two and five; number of views was varied between two and six; and the motion was fixed axis with constant angular velocity, fixed axis with variable velocity, or variable axis with variable velocity. Accuracy increased with views, decreased with points, and was greater with fixed-axis motion. Subjects performed above chance levels even when motion was eliminated, indicating that they exploited regularities in addition to those in the theoretical analyses.

Perception of three-dimensional structure from optic flow without locally smooth velocity

A common assumption in several analyses of optic flow is that the velocity field must be locally smooth in order to recover relative depth and the structure of surfaces in the environment. This study investigated the appropriateness of this constraint to human perception. In the first experiment, subjects were asked to identify the number of planes present in a display simulating one, two, three, four, or five overlapping, transparent planes. Subjects were able to detect the presence of up to three planes accurately for both horizontal and depth translations. In the second experiment, subjects judgments of the depth separation of two transparent, overlapping planes increased with the simulated separation. In Experiment 3, subjects were able to determine accurately the sign of depth for two overlapping, transparent surfaces. These results suggest that a smoothness constraint is not required for the analysis of optic flow by human observers. Alternative approaches to the analysis of optic flow are discussed.

A counterexample to the rigidity assumption in the visual perception of structure from motion.

It has been proposed that the human visual system prefers perceptions of objects that are rigid or undergo minimum form change. A counterexample is presented in which a rigid two-dimensional figure rotating in the frontal plane is perceived as a distorting three-dimensional shape. It is argued that this perception results from the stimulation of automatic processes for perceiving size change, and that these processes are not subject to a general rigidity assumption.