In the present study an alternative analysis to tau was considered that was based on perceived speed and size and that assumed constant deceleration for the detection of collision events. Observers were presented with displays simulating a 3-D environment with obstacles in the path of observer motion. During the trial, observer motion decelerated at a constant rate and was followed by a blackout prior to the end of the display. Observers had to detect which trials resulted in a collision. The results indicate that collision detection varied as a function of the size of the obstacles, observer speed, and edge rate--findings not predicted by an analysis of tau. The results suggest that observers use an analysis based on speed and size information. A model that assumes constant deceleration is proposed for braking control.

Three experiments were conducted to test Hoffman and Richards's (1984) hypothesis that, for purposes of visual recognition, the human visual system divides three-dimensional shapes into parts at negative minima of curvature. In the first two experiments, subjects observed a simulated object (surface of revolution) rotating about a vertical axis, followed by a display of four alternative parts. They were asked to select a part that was from the object. Two of the four parts were divided at negative minima of curvature and two at positive maxima. When both a minima part and a maxima part from the object were presented on each trial (experiment 1), most of the correct responses were minima parts (101 versus 55). When only one part from the object--either a minima part or a maxima part--was shown on each trial (experiment 2), accuracy on trials with correct minima parts and correct maxima parts did not differ significantly. However, some subjects indicated that they reversed figure and ground, thereby changing maxima parts into minima parts. In experiment 3, subjects marked apparent part boundaries. 81% of these marks indicated minima parts, 10% of the marks indicated maxima parts, and 9% of the marks were at other positions. These results provide converging evidence, from two different methods, which supports Hoffman and Richard's minima rule.

Observers were presented with displays simulating a 3-D environment with obstacles in the path of motion. During the trial, observer motion decelerated at a constant rate and was followed by a blackout prior to the end of the display. On some trials the rate of deceleration resulted in stopping before the collision, whereas on other trials the rate of deceleration resulted in a collision with the obstacles. The observer's task was to detect which trials simulated an impending collision. Proportion of collision judgments was greater for older as compared with younger observers when a collision was not simulated. Older observers showed less sensitivity to detect collisions than younger observers did, particularly at high speeds. The age-dependent results are discussed in terms of analyses based on tau and constant deceleration. The results suggest that increased accident rates for older drivers may be due to an inability to detect collisions at high speeds.

The perception of depth and slant in three-dimensional scenes specified by texture was investigated in five experiments. Subjects were presented with computer-generated scenes of a ground and ceiling plane receding in depth. Compression, convergence, and grid textures were examined. The effect of the presence or absence of a gap in the center of the display was also assessed. Under some conditions perceived slant and depth from compression were greater than those found with convergence. The relative effectiveness of compression in specifying surface slant was greater for surfaces closer to ground planes (80 degrees slant) than for surfaces closer to frontal parallel planes (40 degrees slant). The usefulness of compression was also observed with single-plane displays and with displays with surfaces oriented to reduce information regarding the horizon.

This study examined whether the perception of heading is determined by spatially pooling velocity information. Observers were presented displays simulating observer motion through a volume of 3-D objects. To test the importance of spatial pooling, the authors systematically varied the nonrigidity of the flow field using two types of object motion: adding a unique rotation or translation to each object. Calculations of the signal-to-noise (observer velocity-to-object motion) ratio indicated no decrements in performance when the ratio was .39 for object rotation and .45 for object translation. Performance also increased with the number of objects in the scene. These results suggest that heading is determined by mechanisms that use spatial pooling over large regions.

We investigated surface interpolation in displays of structure from motion (SFM). To do so, we introduced a new method for measuring surface perception in dynamic displays-the SFM probe. An SFM probe is a dot that moves rigidly with the dots on a simulated surface, and whose distance from that surface can be adjusted with a joystick or similar control. The displays we studied were random-dot cylinders containing a vertical strip devoid offeature points (the gap). Subjects adjusted an SFM probe, presented in the gap, until the probe dot appeared to be on the surface. Variability in probe-dot placement decreased with increasing texture density on the cylinder and increased with increasing gap width. Subjects showed a consistent bias to place the probe dot outside the cylinder. This bias increased with increasing texture density for the SFM displays. (The opposite bias was found in a static two-dimensional interpolation task with an arc whose curvature matched that of the cylinder: Subjects placed the probe dot inside the arc.) This outside bias is inconsistent with several theoretical approaches to surface interpolation.In a typical structure-from-motion (SFM) display, several dots move about on a computer-driven display. The dots move, of course, in the plane of the display. However, for certain motions of the dots, subjects report that the dots appear to move in three dimensions, not in the plane of the display (Braunstein, 1962(Braunstein, , 1976Green, 1961;Ullman, 1979; see also Wallach & O'Connell, 1953). Moreover, subjects often report that the dots move together rigidly. In some cases, primarily when there are few dots, subjects may report that the dots appear to be connected by imaginary lines. In other cases, primarily when there are many dots, subjects may report seeing a surface in three dimensions (such as a sphere, a cylinder, or some other shape-see, e.g., Braunstein & Andersen, 1984), with the dots appearing to be little lights attached to the surface. The impression of a surface can be quite compelling, particularly if the display is composed of light dots against a dark background and the display is viewed monocularly in a darkened room. The surface is, nonetheless, not physically present in the display, suggesting that subjects interpolate a "subjective surface" between visible feature points in an SFM display.There have been many psychophysical studies of the perception of SFM. Most have investigated the minimal conditions (i.e., the minimal numbers of points or views) for structure to be perceived, and how the perceived structure varies as one varies the numbers of points and views (Braunstein, Hoffman, & Pollick, 1990 Perfetto, 1984;Lappin, Doner, & Kottas, 1980;Petersik, 1987;Todd, Akerstrom, Reichel, & Hayes, 1988;Treue, Husain, & Andersen, 1991). No psychophysical studies have investigated the interpolation of surfaces in regions of a display devoid of feature points. To help fill this gap, the experiments described here provide quantitative data on surface interpolation for a particular co...

Interpolation across orientation discontinuities in simulated three-dimensional (3-D) surfaces was studied in three experiments with the use of structure-from-motion (SFM) displays. The displays depicted dots on two slanted planes with a region devoid of dots (a gap) between them. If extended through the gap at constant slope, the planes would meet at a dihedral edge. Subjects were required to place an SFM probe dot, located within the gap, on the perceived surface. Probe dot placements indicated that subjects perceived a smooth surface connecting the planes rather than a surface with a discontinuity. Probe dot placements varied with slope of the planes, density of the dots, and gap size, but not with orientation (horizontal or vertical) of the dihedral edge or of the axis of rotation. Smoothing was consistent with models of 2-D interpolation proposed by Ullman (1976) and Kellman and Shipley (1991) and with a model of 3-D interpolation proposed by Grimson (1981). Wallach and O'Connell (1953) demonstrated that if subjects are shown the two-dimensional (2-D) shadow cast by a clear glass sphere that has small opaque dots on its surface and rotates about a vertical axis, then subjects perceive a spherical surface. A similar perception is commonly reported for computer-generated displays in which dots move about on a computer screen in a manner consistent with their being projections of dots on a rotating sphere (see, e.g., Braunstein, 1966;Braunstein & Andersen, 1984). Apparently human vision is adept at inferring 3-D structure from the 2-D motions of projected features. This process of inferring 3-D structure from 2-D motions, referred to as structure from motion (SFM) after Ullman (1979), has been studied extensively since the advent of computer-generated displays. (For reviews, see Braunstein, 1978Braunstein, , 1983Braunstein, , 1988 In many displays of SFM in which dots alone are projected on the computer screen, observers report seeing more than just a 3-D structure for the dots. They report, in addition, that they perceive a continuous surface in 3-D passing through, or near, the dots. Such perceptions of "subjective surfaces" on the basis of sparse collections of dots are not limited to SFM displays. Subjective surfaces have also been reported,

An important task during driving is the maintenance of headway during car following. The visual information available to a driver for successful car following was examined. A model of car following that used the visual angle and change in visual angle of a lead vehicle was developed. The study examined whether information from the surrounding scene (e.g., the roadway and buildings) influenced car-following performance. Licensed drivers were presented with a car-following task in a driving simulator. The simulator display consisted of a roadway scene with a lead vehicle that varied speed according to a sine wave. To evaluate the role of scene information, car-following performance was examined when the surrounding scene was present or absent. Two frequencies and three amplitudes of speed variation were also examined. The results indicated that control gain was greater when the scene was absent, with near unity gain when the scene was present. These findings indicated more accurate control during car following when the surrounding scene information was present. These results suggest that drivers also use other sources of information (e.g., absolute distance information from height in the visual field relative to the horizon and edge rate information specifying observer speed) to maintain headway. The implications of this research to nighttime accident rates and intelligent highway systems are discussed.