Unifying Time to Contact Estimation and Collision Avoidance across Species

The Formula: see text]-function and the Formula: see text]-function are phenomenological models that are widely used in the context of timing interceptive actions and collision avoidance, respectively. Both models were previously considered to be unrelated to each other: Formula: see text] is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, Formula: see text] has a maximum before ttc. Furthermore, it is not clear how both functions could be implemented at the neuronal level in a biophysically plausible fashion. Here we propose a new framework - the corrected modified Tau function - capable of predicting both Formula: see text]-type ("Formula: see text]") and Formula: see text]-type ("Formula: see text]") responses. The outstanding property of our new framework is its resilience to noise. We show that Formula: see text] can be derived from a firing rate equation, and, as Formula: see text], serves to describe the response curves of collision sensitive neurons. Furthermore, we show that Formula: see text] predicts the psychophysical performance of subjects determining ttc. Our new framework is thus validated successfully against published and novel experimental data. Within the framework, links between Formula: see text]-type and Formula: see text]-type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain.