A neural computational model for animal’s time-to-collision estimation

The time-to-collision (TTC) is the time elapsed before a looming object hits the subject. An accurate estimation of TTC plays a critical role in the survival of animals in nature and acts as an important factor in artificial intelligence systems that depend on judging and avoiding potential dangers. The theoretic formula for TTC is 1/&tgr;≈&thgr;′/sin &thgr;, where &thgr; and &thgr;′ are the visual angle and its variation, respectively, and the widely used approximation computational model is &thgr;′/&thgr;. However, both of these measures are too complex to be implemented by a biological neuronal model. We propose a new simple computational model: 1/&tgr;≈M&thgr;–P/(&thgr;+Q)+N, where M, P, Q, and N are constants that depend on a predefined visual angle. This model, weighted summation of visual angle model (WSVAM), can achieve perfect implementation through a widely accepted biological neuronal model. WSVAM has additional merits, including a natural minimum consumption and simplicity. Thus, it yields a precise and neuronal-implemented estimation for TTC, which provides a simple and convenient implementation for artificial vision, and represents a potential visual brain mechanism.