Dissociation of discrimination thresholds for time to contact and for rate of angular expansion

It is well known that, if a rigid sphere is moving at constant speed towards the eye along the line of sight then, for small values of theta, T = theta/theta, where T is the time to contact, theta is the instantaneous angular size and theta is the rate of increase of angular size. We describe a rationale and an experimental procedure for demonstrating empirically when subjects base discrimination of time to contact on trial-to-trial variations of (theta/theta) rather than on variations of theta or on variations of delta theta (the change of angular size during a presentation). Discrimination threshold for the ratio (theta/theta) was 0.070-0.13, and was independent of mean time to contact over a range of at least T = 1.0-4.0 sec. We conclude that the human visual pathway contains a mechanism that is sensitive to the ratio (theta/theta) rather independently of the values of theta and theta. Using a different procedure we demonstrated empirically that subjects based discriminations of rate of expansion on trial-to-trial variations of theta rather than variations of time to contact or on variations of delta theta. Discrimination threshold for rate of expansion was 0.85-0.14, and was independent of mean time to contact over a range of at least T = 1.0-4.0 sec. We conclude that the human visual pathway contains a mechanism that is sensitive to rate of expansion rather independently of time to contact or absolute change in size. When rate of expansion and time to contact were both available as cues, discrimination threshold was on average lower than when only one of the two cues was present. We conclude that there is some summation of the two cues. Our data can be explained by a small modification to a model previously put forward to account for data on threshold elevations and aftereffects caused by adapting to changing-size stimulation. This model incorporates a filter that is strongly activated by isotropic, homogeneous two-dimensional expansion of the retinal image and whose output is inversely proportional to time to contact (i.e. the more urgent the demand for evasive action, the stronger the output of the filter).