Perception of Displayed Information
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Second, speed information indicating the same curvatures as the size information contributes directly to the accuracy of the discriminations. The evidence for this is that accuracy is greater with speed information that is relevant to the discrimination than with speed information that indicates curvature but is not relevant to the discrimination because it indicates the same intermediate curvature for both displays in a pair.
The method was the same as that in Experiment 3a , except that the sphere moved in a concave arc. All met the same visual acuity requirement and received extra credit for participating.
The smaller effects found with concave trajectories probably reflect the generally lower accuracy found with these trajectories. In Experiment 1, we found that speed information presented with size information resulted in increased accuracy of judgments of the relative curvature magnitude of motion trajectories. In this experiment, we examined whether displays with both size and speed information would provide more accurate judgments of the sign of curvature than would displays with only one type of information available.
The stimuli differed from those in Experiments 1 and 2 in the following way.
The Doors of Perception
In Experiments 1 and 2, both displays in a pair were based on the same direction of curvature but differed in the magnitude of curvature. In the present experiment, both displays were based on the same magnitude of curvature but differed in the sign of curvature.
That is, the sphere moved in a convex trajectory in one display and moved in a concave trajectory in the other. The order of presentation was counterbalanced. The simulated viewing distance and type of motion information were the same for both displays on each trial. The apparatus was the same as that in the previous experiments. Half of the observers were asked to indicate which of the two displays in a pair showed a convex trajectory, and half were asked to indicate which display showed a concave trajectory.
The 12 observers were undergraduate students at the University of California, Irvine, who received credit for participating.
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None had participated in any other experiment in this study. As in Experiment 1, there were 11 blocks of 27 trials, with the first block treated as a practice block. Proportions of correct sign of curvature judgments in Experiment 4. Although accuracy with speed information alone was at chance levels, angular speed was potentially informative about sign of curvature and could have contributed to accuracy when combined with size information. To further examine the role of speed information, the next experiment used speed functions based on parallel projections that carried no information about sign of curvature for the trajectories studied.
Experiments 1—3 found increased accuracy for relative curvature magnitude judgments for displays with both angular size and speed information at the greatest simulated distance. Experiment 2 showed that speed information from parallel projections increased the accuracy of curvature magnitude judgments when presented with size information.
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But even in parallel projections, there is speed information that may be relevant to judgments of relative curvature. There is no information in parallel projections, however, for judging sign of curvature. The speed information in parallel projections is identical for concave and convex trajectories. The present experiment investigated whether speed information from a parallel projection, when presented with size information from a perspective projection, can enhance judgments of the sign of curvature for trajectories in a horizontal plane at eye level.
The design and procedure were the same as those in Experiment 4 , except that in the combined size and speed information condition, the speed information was based on parallel projections rather than on the same simulated viewing distances as the size information. Ten observers participated in the experiments.
They were undergraduates students from UCI and received credit for the participating. None had participated in any other experiments in this study. Proportions of correct sign of curvature judgments in Experiment 5. For all the stimulus pairs in which size and speed information was combined, the speed information was based on a parallel projection and was the same for the convex and concave displays. This means that the speed information that was presented together with the size information could not be used to discriminate between convex and concave displays. The results, however, show that sign of curvature judgments, for the greatest simulated viewing distance, was more accurate when both size and speed information were present than when size information alone was present.
Overall, we found greater accuracy when curvature was indicated by changes in angular size only than when curvature was indicated by changes in angular speed only, for both judgments of relative curvature magnitude and judgments of sign of curvature. At the shortest simulated viewing distances highest perspective level , accuracy with curvature indicated by changes in angular size only was similar to accuracy with curvature indicated by changes in both angular size and angular speed.
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Accuracy with changes in angular speed only was near chance levels at all simulated viewing distances. Although we found high accuracy at near distances with variations in angular size indicating curvature and angular speed constant, we found near-chance performance with variations in angular speed indicating curvature and angular size constant.
Todd asked observers to judge where a free-falling projectile would hit the ground.
Perception of Displayed Information
The projectile was represented either by a single dot that did not change in size motion information only or by a configuration of dots that changed in size in the projection corresponding motion and size information. Observers were unable to make correct judgments on the basis of motion information only.
Gray and Regan had observers estimate the time to collision for patterns of circular dots approaching along the line of sight. The angular size of the dots was held constant during the motion. When the angular size of the dots was large enough exceeding 2. Although the types of motion were different in those two studies and in our study, the results of all three studies indicate that for an object moving in 3-D, observers are not accurate in judging object motion from speed information when the moving object maintains a constant angular size.
There are two explanations that might account for the near-chance judgments of curvature magnitude and sign of curvature when only speed information is presented. It is second-order motion information that would be most relevant to judgments of curvature magnitude or sign of curvature. Although observers might have compared speeds at different positions along the trajectories to estimate changes in speed, they could not have used maximum or minimum speeds to compare curvatures between displays in the present study, because the initial speed was randomly selected for each display.
A second explanation for the finding of near-chance accuracy with speed information alone is that the interpretation of a change in speed as resulting from a change in depth requires a perceptual constraint of constant 3-D speed. Without this constraint, the displays could be interpreted as motion along a straight path with varying 3-D speed. On the other hand, size information alone does provide high accuracy at the closer distances.
This is likely to be the result of a strong constant size constraint, with changes in the angular size of an object interpreted as changes in its position in depth Johansson, ; Sedgwick, At the greatest distance, due to reduced perspective effects, size changes were relatively small. The observer may have some tolerance for small changes in angular size and may not interpret small changes in angular size as resulting from changes in depth. This may account for the near chance performance with size information alone at the far distance.
Our finding of higher accuracy at the greatest viewing distance, with the speed function indicating a curved trajectory than with the speed constant and, thus, indicating a linear trajectory Experiments 3 and 5 , is consistent with the second explanation.
In these two experiments, size functions relevant to the discrimination were combined with two different speed functions that were not relevant to the discrimination because they were identical for both displays in a pair. Some display pairs in Experiment 3 had constant angular speeds; other pairs had speeds based on the same intermediate curvature. Accuracy was higher with a speed based on an intermediate curvature than with constant speed.
Some display pairs in Experiment 5 had constant angular speeds; others had speeds based on parallel projections, which have identical speed functions for convex and concave trajectories with the same curvature magnitude. Judgments of sign of curvature were more accurate with speed functions based on parallel projections than with constant speeds. The results of these two experiments suggest that speed information indicating that the path is curved in depth facilitates the perception of small changes in angular size as resulting from changes in distance.
The increase in discrimination accuracy when speed information that was not relevant to the discrimination was combined with relevant size information is not easily handled by cue combination theories. An increase in accuracy of judgments from a cue that is irrelevant to the discrimination, such as a velocity function based on a curvature intermediate to those being discriminated or based on a parallel projection when the task was to judge sign of curvature, suggest a different type of interaction between sources of information for judging curvature.
In different conditions in the present study, the velocity function could be relevant, if it was different for the two displays in a pair being discriminated, or ancillary, if it was not different or not discriminable in the two displays. To handle the present results, a cue combination model would have to allow the same cue to be either relevant to the discrimination or ancillary, for different display pairs.
Even with speed information not informative about degree of curvature or sign of curvature, that information could still indicate that the object was moving in a curved rather than in a straight trajectory. The visual system may have been constrained to find an interpretation of the size changes consistent with a curved trajectory, rejecting the alternative perception that the object was changing in size while moving along a straight path. The importance of the combination of angular size and speed information is also consistent with Craig et al. In any study using 2-D projections to study 3-D perception, the question can arise as to whether the judgments could have been based directly on 2-D variables rather than on a 3-D perception.
We used random initial sizes and speeds to prevent comparisons based on the maximum size or speed in a pair of displays. In debriefing, 56 of 98 observers indicated a strong 3-D impression in most displays, 27 indicated this for some displays, and 15 indicated that they did not have a strong 3-D impression. Our finding that in some conditions, accuracy from either angular size changes alone or angular speed chances alone dropped to near-chance level but accuracy based on a combination of these two sources of information was notably higher also seems inconsistent with observers basing their judgments directly on 2-D variables.
Overall, in this study, we examined the effects of angular size and speed on perceiving the trajectory of a single object moving in 3-D. The results demonstrated that 1 speed information alone does not result in accurate judgments of the magnitude or direction of a curved trajectory, 2 accuracy of judgments based on size information alone decreases sharply with increased distance, but 3 displays that include both speed and size information can provide high accuracy at a far distance even when the speed information is not directly relevant to the required judgment.
We would like to thank Brianna Phelps and Amy Vu for their assistance with this research and Adriane Seiffert and three anonymous reviewers for helpful comments. Skip to main content Skip to sections. Advertisement Hide. Download PDF. Effects of changes in size, speed, and distance on the perception of curved 3-D trajectories.