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Theodore E Cohn, Tieuvi Nguyen, Jay E Barton; A visual factor in rear-end collisions?. Journal of Vision 2003;3(9):214. doi: https://doi.org/10.1167/3.9.214.
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In the US, over 20% of collisions between automobiles are rear-end collisions. But for transit buses, whose exposure and pattern of movement may be quite different, the number is significantly higher, being over 35%. If buses are more susceptible to this type of collision than automobiles, one wonders why. In this report we describe both a property of human vision that may relate to the answer plus a theory as to the link. Some formulations of the visual task inherent in avoiding such collisions suggest that an observer may utilize the angular width of an object ahead, divided by its time rate of change, to calculate a time to collision (TTC). Consider the initial act of perceiving closure with a vehicle ahead. If the quotient of angular width to its time derivative is what is used to initiate braking, then it must be done accurately. We have discovered that the time to react (RT) to a step increase in angular width is seen more slowly the larger the object. The stimulus contained only the 2D cue to closure and depth of field was unchanged at 1.5 m. Objects were light gray squares set in a dark gray surround. The size change started at a random time after a ready signal and was effected gradually, averaging close to a pixel per MSEC in 13.3 MSEC steps. Six normal observers were employed. Average reaction time (2 s.e.) were 284.5 (1.65) MSEC for 3.7 DEG, 294.2 (1.69) MSEC for 5.3 DEG, and 296.5 (1.80) MSEC for 7.6 DEG. The effect is small, about 10% of the estimated perceptual delay, but it is significant. Suppose that the computation of the time derivative of width, dw/dt, is thus distorted by an elevated dt. This lowers dw/dt and thus raises TTC. This finding accords with a conjecture by Leibowitz to explain collisions where trains strike vehicles. He suggested that larger objects appear to move more slowly, damaging the accuracy of the required TTC computation. His conjecture may also apply to collisions between automobiles.
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