Unifying Time to Contact Estimation and Collision Avoidance across Species

The -function and the -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: is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, 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 -type (“”) and -type (“”) responses. The outstanding property of our new framework is its resilience to noise. We show that can be derived from a firing rate equation, and, as , serves to describe the response curves of collision sensitive neurons. Furthermore, we show that 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 -type and -type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain. Author Summary: In 1957, Sir Fred Hoyle published a science fiction novel in which he described humanity's encounter with an extraterrestrial life form. It came in the shape of a huge black cloud which approached the earth. Hoyle proposed a formula (“”) for computing the remaining time until contact (“ttc”) of the cloud with the earth. Nowadays in real science, serves as a model for ttc -perception for animals and humans, although it is not entirely undisputed. For instance, seems to be incompatible with a collision-sensitive neuron in locusts (the Lobula Giant Movement Detector or LGMD neuron). LGMD neurons are instead better described by the -function, which differs from . Here we propose a generic model (“”) that contains and as special cases. The validity of the model was confirmed with a psychophysical experiment. Also, we fitted many published response curves of LGMD neurons with our new model and with the -function. Both models fit these response curves well, and we thus can conclude that and possibly result from a generic neuronal circuit template such as it is described by .