Estimating the time-to-passage of visual self-motion: Is the second order motion information processed?

Previous work demonstrated that estimating time-to-contact (TTC) of moving objects towards an observer is based only on first-order information and does not take into account the acceleration information. We investigated whether smooth and continuous speed variations are considered in the extrapolation of linear self-motion towards a stationary target. The time-to-passage (TTP) estimation task consisted in presenting a simulated forward self-motion along a street at constant, increasing or decreasing velocity. After a while, the visual target appeared (e.g. a banner) before the visual stimulation ceased. Participants were then asked to imagine that the self-motion continued, and to press a button when they believed they reached the banner. The results showed that during accelerations, TTP estimates were closer to 2nd order than to 1st order predictions for the highest speed variations and the longest expected TTPs, but were between 1st and 2nd order predictions for other cases. On the contrary, during decelerations, TTP estimates were closer to 1st order predictions in most cases. This finding suggests that during accelerations, the processing of speed variations for the TTP estimation depends on the magnitude of the speed variations, whereas during decelerations, the extrapolation depends only on the final speed.