Judging the time to collision with a simulated textured object: Effect of mismatching rate of expansion of object size and of texture element size

We measured the accuracy with which subjects estimated the time to collision with a simulated textured object approaching at constant speed along the line of sight. The independent variable was the ratioR, whereR = (rate of dilation of the texture elements that covered the simulated object) / (rate of dilation of object size). When matching was perfect (i.e.,R = 1.0), the mean of 12 settings was close to the nominal value of 2,000 msec for both subjects. In addition, the standard error of 12 settings was only 25 and 52 msec in 2,000 msec for the 2 subjects. Discrimination threshold for time to collision was not significantly affected byR over the range investigated betweenR = 0 andR = 2.0. However, the accuracy of estimating time to collision was significantly affected byR. Estimated time to collision was a monotonic function ofR. For example, when the mismatch was only 10% (i.e.,R = 0.9) subjects judged time to collision would occur 178 msec later than the true time to collision of 2,000 msec.     

Interpolation in structure from motion.

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 of feature 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.     

Interpolation in structure from motion

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—theSFM 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 of feature points (thegap). 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.     

Memory for locations within regions: Spatial biases and visual hemifield differences

Memory for location of a dot inside a circle was investigated with the circle in the center of a computer screen (Experiment 1) or with the circle presented in either the left or the right visual field (Experiment 2). In both experiments, as in Huttenlocher, Hedges, and Duncan’s (1991) study, the task was to relocate the dot by marking the remembered location. When errors in angular and radial estimates were considered separately, it was found that, in both experiments, the angular locations of estimates of the dots’ positions regressed toward different locations inside each quadrant of the circle; the radial locations of the estimates of dots’ positions tended to regress toward locations near the circumference. These variations in the direction of bias appeared to reflect a general shift of estimates toward the upper left arc of the circle. The second experiment replicated the preceding effects but also revealed that the regressions within quadrants of angular values were stronger after right visual field than after left visual field presentations. We interpret the dissociation between visual fields as evidence that memory for categorical spatial relations (Kosslyn, 1987) is more dependent on left-hemisphere than on right-hemisphere processing.     

Perceived curvature of arcs and dot patterns as a function of curvature, arc length, and instructions

Arcs of circles, with six arc lengths and four radii of curvature, and an equivalent set of figures composed of three dots were used as stimuli. Subjects in Group I imagined the circle from which an arc or dot triplet was taken and indicated the centre of the circle. Group II subjects estimated the location of the point that was equidistant from the middle and ends of an arc, or equidistant from the three dots of a triplet. The results from arcs showed, in Group I, an underestimation of curvature that decreased as a function on the length of the arc. In Group II, however, overestimation of the curvature of most arcs occurred, indicating a strong influence of the difference in the perceptual task on the results. The effect of instructions was similar with the dot figures but, in general, more errors resembling overestimation of curvature occurred with these figures.     

Aging and the detection of observer and moving object collisions

The authors examined age-related differences in the detection of collision events. Older and younger observers were presented with displays simulating approaching objects that would either collide or pass by the observer. In 4 experiments, the authors found that older observers, as compared with younger observers, had less sensitivity in detecting collisions with an increase in speed, at shorter display durations, and with longer time-to-contact conditions. Older observers also had greater difficulty when the scenario simulated observer motion, suggesting that older observers have difficulty discriminating object motion expansion from background expansion from observer motion. The results of these studies support the expansion sensitivity hypothesis-that age-related decrements in detecting collision events involving moving objects are the result of a decreased sensitivity to recover expansion information.     

Do rotation coordinates provide the substrate for a mental protractor?

In previous studies, we have found that the accuracy in judging collinearity of lines or dots varies considerably from one subject to another as a function of the relative angle of the stimulus elements. A model of errors generally shows large excursions across several subranges of angular position. These do not appear to be motor errors, at least not ones that are well separated from perceptual mechanisms. The errors are most likely generated at primary visual cortex, or beyond. We examined and modeled accuracy in judging collinearity of dot pairs, varying the angular position of the dots through 360 degrees, the distance between the dots (stimulus span), and the distance at which the subject was required to respond (response span). Subjects manifested idiosyncratic profiles of error across angular positions, as reported previously. But across the tested range of spans, from 4 to 8 deg, the errors tended to be the same, irrespective of stimulus or response span. This suggests that the judgments are based on a radial (angular) measure of spatial position. We discuss these results in the context of proposals that the brain maps spatial position using rotation coordinates. These new data are consistent with the hypothesis that subjects use the z-axis coordinates as a mental protractor for judging angular position and collinearity.     

Do monocular time-to-collision estimates necessarily involve perceived distance?

Motivated by the debate between indirect and direct theories of perception, a large number of researchers have attempted to determine whether judgments of time to collision are based on the ratio of perceived distance to perceived speed or on the ratio theta/(d theta/dt), i.e. tau. Despite the considerable research effort devoted to this question there seems to be no clear resolution. We used a staircase tracking procedure to estimate errors in estimating time to collision for a simulated approaching object. To investigate the role of perceived distance in the judgment of time to collision, we asked observers to alternate between two viewing distances (100 and 500 cm). For the 500 cm viewing distance, we magnified the visual display by a factor of five so that the retinal images [and the values of theta/(d theta/dt) through time] were identical for the two viewing distances. All visual cues to distance were available. There were no significant differences between estimates of time to collision made at the two viewing distances. We conclude that our observers ignored perceived distance when estimating time to collision and based their responses on theta/(d theta/dt). We concur with recent proposals that, in the future, time-to-collision research should move away from the either/or analysis of different information sources that has dominated previous studies towards investigations of how different information sources are integrated.     

Infants' timing strategies to optical collisions: a longitudinal study

Blinking is a good indication of awareness to optical collisions in early infancy. In the current longitudinal study, infants were presented with the image of a looming virtual object approaching on a collision course under different constant velocities and constant accelerations. The aim was to investigate which timing strategies the infants used to determine when to make the defensive blink. Blinking when the virtual object reaches a threshold visual angle (angle-strategy) or angular velocity would result in difficulties with accelerating approaches, while blinking when the object is a certain time away (time-strategy) would enable successful responses to all approaches. Eleven infants were tested longitudinally at 22, 26, and 30 weeks. Five infants switched from an angle- to a time-strategy, while one infant switched from using angular velocity to a time-strategy. Five infants used a time-strategy already at 22 weeks. These findings show that with age there is an attunement in the perceptual systems of infants which makes them switch to better specifying variables, enabling them to successfully time their defensive blinking to impending optical collisions.     

Effects of texture and shape on perceived time to passage: Knowing “what” influences judging “when”

In the present study, we examined whether it is easier to judge when an object will pass one’s head if the object’s surface is textured. There are three reasons to suspect that this might be so: First, the additional (local) optic flow may help one judge the rate of expansion and the angular velocity more reliably. Second, local deformations related to the change in angle between the object and the observer could help track the object’s position along its path. Third, more reliable judgments of the object’s shape could help separate global expansion caused by changes in distance from expansion due to changes in the angle between the object and the observer. We can distinguish among these three reasons by comparing performance for textured and uniform spheres and disks. Moving objects were displayed for 0.5–0.7 sec. Subjects had to decide whether the object would pass them before or after a beep that was presented 1 sec after the object started moving. Subjects were not more precise with textured objects. When the disk rotated in order to compensate for the orientation-related contraction that its image would otherwise undergo during its motion, it appeared to arrive later, despite the fact that this strategy increases the global rate of expansion. We argue that this is because the expected deformation of the object’s image during its motion is considered when time to passage is judged. Therefore, the most important role for texture in everyday judgments of time to passage is probably that it helps one judge the object’s shape and thereby estimate how its image will deform as it moves.     

Reduced spatial sensitization on nonuniform backgrounds.

Spatial sensitivity (Westheimer) functions, when measured on nonuniform backgrounds made up of light dots of 12 min arc, were found to differ in shape, depending on the polarity of the central area on which the test spot was placed. When thresholds were measured on the dark centre between light dots, ie on the adapting-field illumination, the resulting curve was similar to the control curve, measured on a uniform background equated for flux. In comparison, thresholds measured on a central light dot, serving as a pedestal, peaked at larger background diameters and showed much less sensitization compared to the control function.     

Time-to-contact judgments of an approaching object that is partially concealed by an occluder

Prior studies of time-to-contact (TTC) focused on judgments of unoccluded approaching objects. P. R. DeLucia, M. K. Kaiser, J. M. Bush, L. E. Meyer, and B. T. Sweet (2003) showed that partial occlusion decreases an object's optical size and expansion rate and that the value of tau derived from the reduced optical size (relative rate of accretion; RRA) does not necessarily correspond to TTC. In the present study, a computer-generated object approached the observer while unoccluded or partially concealed by a stationary or moving occluder. In some scenes, the occluder's motion nullified the object's optical expansion. Results indicated that stationary and moving occluders affected TTC judgments. RRA predicted directional changes in TTC judgments but predicted larger changes in such judgments than were observed. Tau did not predict effects of occlusion. When developing models of perceived collision, it is important to consider effects of partial occlusion on optical TTC information and on TTC judgments.     

Looming Responses to Obstacles and Apertures: The Role of Accretion and Deletion of Background Texture

Successful navigation in the world requires differentiating an obstacle in one's path from an aperture through which one could pass. An approaching obstacle is specified by texture expansion within the obstacle's contour and the deletion of background texture outside the object. In contrast, an approaching aperture contains texture expansion within the aperture's frame and accretion of background texture within the aperture's contour. This study investigated 3- to 5-month-old infants' discrimination of obstacles from apertures, examining eyeblink responses to the movement of both kinds of objects against backgrounds varying in salience. Obstacles produced stronger looming reactions than apertures, and the salience of the background influenced responses to apertures but not obstacles. These findings imply that infants differentiate obstacles from apertures based on their relative patterns of accretion versus deletion of background texture, and suggest that infants recognize the functional consequences of contact with these objects.     

Development of sensitivity to information for impending collision

Infants were tested in three experiments to study the development of sensitivity to information for impending collision and to investigate the hypothesis that postural changes of very young infants in response to an approaching object are of a tracking rather than of a defensive nature. Experiment 1 involved the presentation of three types of shadow projection displays, specifying (1) collision, (2) noncollision, and (3) a nonexpanding rising contour, to infants from 1 to 9 months of age. Avoidance of collision appears to be absent in 1- to 2-month-olds, begins to develop in 4- to 6-month-olds, and is present in 8- to 9-month-old infants. In Experiment 2, 1- to 2-month-old infants were presented with optical expansion patterns which specified collision and noncollision. The top contour of these displays stayed at eye level. No significant difference was observed between reaction to the collision and the noncollision displays, suggesting that the young infants were tracking the displays and not attempting to avoid collision. Experiment 3 was designed to determine whether an approaching real object might elicit an avoidance response in infants not sensitive to an optical display specifying collision. No evidence of avoidance behavior was observed in the 1- to 2-month-olds; however, avoidance, as indexed by blinking, does appear to be present at 4 months of age.     

Shape discrimination for motion-defined and contrast-defined form: squareness in special.

Shape discrimination was measured for: (i) two-dimensional rectangular targets that were perfectly camouflaged within a stationary pattern of random dots and rendered visible by relative motion of the dots, and (ii) similar dotted rectangles that were rendered visible by luminance contrast. Shape discrimination was disconfounded from size discrimination by requiring subjects to discriminate the aspect ratios of rectangles whose areas were altered independently of aspect ratio. When dot speed and contrast were both high, the aspect-ratio discrimination threshold was as acute for motion-defined (MD) rectangles as for contrast-defined (CD) rectangles and, at 2-3%, corresponded to a change of side length of about 24 s arc compared to a mean dot separation of 360 s arc. Discrimination of MD rectangles collapsed at low dot speeds and could not be measured at speeds less than about 0.03-0.08 deg s-1, but discrimination of CD rectangles was almost unaffected by dot speed. The aspect-ratio discrimination threshold was lowest for a square and progressively increased as the rectangle became more asymmetric. It is suggested that the visual system contains a mechanism that compares the separations of pairs of contours along different azimuths, and that, during visual development, this shape-discrimination processing of MD and CD targets is driven by the same environmental and behavioural pressures towards a common end point. The human equivalent of a pathway that includes the cortical area MT is thought to be important for shape discrimination of MD forms.     

Interpolation across surface discontinuities in structure from motion Asad Satdpour

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).     

Effects of texture and shape on perceived time to passage: knowing "what" influences judging "when"

In the present study, we examined whether it is easier to judge when an object will pass one's head if the object's surface is textured. There are three reasons to suspect that this might be so: First, the additional (local) optic flow may help one judge the rate of expansion and the angular velocity more reliably. Second, local deformations related to the change in angle between the object and the observer could help track the object's position along its path. Third, more reliable judgments of the object's shape could help separate global expansioncaused by changes in distance from expansion due to changes in the angle between the object and the observer. We can distinguish among these three reasons by comparing performance for textured and uniform spheres and disks. Moving objects were displayed for 0.5-0.7 sec. Subjects had to decide whether the object would pass them before or after a beep that was presented 1 sec after the object started moving. Subjects were not more precise with textured objects. When the disk rotated in order to compensate for the orientation-related contraction that its image would otherwise undergo during its motion, it appeared to arrive later, despite the fact that this strategy increases the global rate of expansion. We argue that this is because the expected deformation of the object's image during its motion is considered when time to passage is judged. Therefore, the most important role for texture in everyday judgments of time to passage is probably that it helps one judge the object's shape and thereby estimate how its image will deform as it moves.     

The interaction of oculomotor cues and stimulus size in stereoscopic death constancy.

In the natural world, observers perceive an object to have a relatively fixed size and depth over a wide range of distances. Retinal image size and binocular disparity are to some extent scaled with distance to give observers a measure of size constancy. The angle of convergence of the two eyes and their accommodative states are one source of scaling information, but even at close range this must be supplemented by other cues. We have investigated how angular size and oculomotor state interact in the perception of size and depth at different distances. Computer-generated images of planar and stereoscopically simulated 3-D surfaces covered with an irregular blobby texture were viewed on a computer monitor. The monitor rested on a movable sled running on rails within a darkened tunnel. An observer looking into the tunnel could see nothing but the simulated surface so that oculomotor signals provided the major potential cues to the distance of the image. Observers estimated the height of the surface, their distance from it, or the stereoscopically simulated depth within it over viewing distances which ranged from 45 cm to 130 cm. The angular width of the images lay between 2 deg and 10 deg. Estimates of the magnitude of a constant simulated depth dropped with increasing viewing distance when surfaces were of constant angular size. But with surfaces of constant physical size, estimates were more nearly independent of viewing distance. At any one distance, depths appeared to be greater, the smaller the angular size of the image. With most observers, the influence of angular size on perceived depth grew with increasing viewing distance. These findings suggest that there are two components to scaling. One is independent of angular size and related to viewing distance. The second component is related to angular size, and the weighting accorded to it grows with viewing distance. Control experiments indicate that in the tunnel, oculomotor state provides the principal cue to viewing distance. Thus, the contribution of oculomotor signals to depth scaling is gradually supplanted by other cues as viewing distance grows. Binocular estimates of the heights and distances of planar surfaces of different sizes revealed that angular size and viewing distance interact in a similar way to determine perceived size and perceived distance.     

Discriminating direction of motion trajectories from angular speed and background information

The effects of a background scene on the perception of the trajectory of an approaching object and its relation to changes in angular speed and angular size were examined in five experiments. Observers judged the direction (upward or downward) of two sequentially presented motion trajectories simulating a sphere traveling toward the observer at a constant 3-D speed from a fixed distance. In Experiments 1–4, we examined the effects of changes in angular speed and the presence of a scene background, with changes in angular size based either on the trajectories being discriminated or on an intermediate trajectory. In Experiment 5, we examined the effects of changes in angular speed and scene background, with angular size either constant or consistent with an intermediate 3-D trajectory. Overall, we found that (1) observers were able to judge the direction of object motion trajectories from angular speed changes; (2) observers were more accurate with a 3-D scene background, as compared with a uniform background, suggesting that scene information is important for recovering object motion trajectories; and (3) observers were more accurate in judging motion trajectories based on angular speed when the angular size function was consistent with motion in depth than when the angular size was constant.     

Vernier acuity as affected by target length and separation

Vernier acuity was measured for vertical lines of different lengths; the threshold (about 4 sec of arc) was almost as good for the shortest stimuli (1 min 20 sec squares) as for the longest (21 min 20 sec × 1 min 20 sec rectangles) and did not change when two round dots were shown in positions corresponding to the squares. The threshold for the two dots measured in terms of minimum detectable lateral offset increased when the vertical separation between the dots increased, but, when replotted in terms of the angle of tilt between them with respect to vertical, the threshold improved with dot separation; moreover, at asymptote, the threshold was comparable to that obtained for detecting that an actual line was tilted out of vertical. Our data suggest that, in performing the vernier task, Ss do not extrapolate the edges of the vernier elements; instead, they judge the deviation of the inner ends of the stimuli from verticality. This hypothesis explains the effect of increasing separation between vernier elements and also accounts for other types of acuity, such as the detection of curvature.