Camera-Monitor Systems as An Opportunity to Compensate for Perceptual Errors in Time-to-Contact Estimations

Abstract

For the safety of road traffic, it is crucial to accurately estimate the time it will take for a moving object to reach a specific location (time-to-contact estimation, TTC). Observers make more or less accurate TTC estimates of objects of average size that are moving at constant speeds. However, they make perceptual errors when judging objects which accelerate or which are unusually large or small. In the former case, for instance, when asked to extrapolate the motion of an accelerating object, observers tend to assume that the object continues to move with the speed it had before it went out of sight. In the latter case, the TTC of large objects is underestimated, whereas the TTC of small objects is overestimated, as if physical size is confounded with retinal size (the size-arrival effect). In normal viewing, these perceptual errors cannot be helped, but camera-monitor systems offer the unique opportunity to exploit the size-arrival effect to cancel out errors induced by the failure to respond to acceleration. To explore whether such error cancellation can work in principle, we conducted two experiments using a prediction-motion paradigm in which the size of the approaching vehicle was manipulated. The results demonstrate that altering the vehicle's size had the expected influence on the TTC estimation. This finding has practical implications for the implementation of camera-monitor systems.

Keywords: acceleration; camera–monitor systems; time-to-collision estimation.

Figure 1

The three different vehicle’s sizes in Experiment 1 are depicted at a distance of 38.88 m from the reference line. On the left, the vehicle is enlarged to three times its original size, in the middle, it is enlarged to 1.5 times its original size, and on the right, the vehicle at its original size.

Figure 2

The three different vehicle’s sizes in Experiment 2 are depicted at a distance of 30 m from the reference line. On the left, the vehicle is enlarged to three times its original size, in the middle, the vehicle is at its original size, and on the right, the vehicle is reduced to one-third of its original size.

Figure 3

The subjects initiated a trial by pressing the spacebar. A gray background was presented for 500 ms, followed by a white fixation cross in the center of the screen for 1 s before the stimulus video appeared. After the vehicle had disappeared, the subjects indicated their TTC estimation by pressing the spacebar. The trial ended with the TTC estimation, and the subjects initiated new trials at their own pace.

Figure 4

Mean TTC estimates as a function of the actual TTC values. Rows represent the acceleration level a, and columns indicate the velocity at occlusion v_occ. The gray dashed line represents a perfect estimation of the contact time. Colors represent the variations of vehicle’s size/size enhancement. Error bars indicate ±1 SE of the mean.

Figure 5

Actual and judged TTC values as a function of the occlusion distance for a comparison of the three acceleration conditions (decelerated a = −2.0 m/s² circles; constant speed a = 0 m/s² squares; and accelerated a = +2.0 m/s² triangles). Left panel: the performance of an ideal observer (ground truth, gray color). Middle panel: approaches of cars at their original size (orange color). Right panel: approaches with size enhancement/variation. The vehicles in the constant velocity trials were increased (blue color, solid line) or reduced in size (red color, solid line). Accelerating vehicles were increased (blue color, dashed line) and decelerating vehicles were reduced in size (red color, dashed line). Note that the line types and shapes in all three panels indicate the acceleration rate. Error bars represent ± 1 SE of the mean.

Figure 6

Mean estimated TTC as a function of the occlusion distance for constant-velocity trials. The gray dashed line represents the actual TTC (averaged across the different constant velocities). Error bars represent ± 1 SE of the mean.

Figure 7

Mean TTC estimation error (estimated TTC minus actual TTC) as a function of the occlusion distance for accelerated approaches. Each row indicates an occlusion velocity. Shapes indicate the acceleration rate. Error bars represent ± 1 SE of the mean.