Unifying time to contact estimation and collision avoidance across species

The τ-function and the η-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: τ is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, g 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 τ-type ("τ(cm)") and g-type ("t(mod)") responses. The outstanding property of our new framework is its resilience to noise. We show that t(mod) can be derived from a firing rate equation, and, as g, serves to describe the response curves of collision sensitive neurons. Furthermore, we show that tcm 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 τ-type and η-type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain.