We propose a bio-inspired approach to motion estimation based on recent neuroscience findings concerning the motion pathway. Our goal is to identify the key biological features in order to reach a good compromise between bio-inspiration and computational efficiency. Here we choose the neural field formalism which provides a sound mathematical framework to describe the model at a macroscopic scale. Within this framework we define the cortical activity as coupled integro-differential equations and we prove the well-posedness of the model. We show how our model performs on some classical computer vision videos, and we compare its behaviour against the visual system on a simple classical video used in psychophysics. As a whole, this article contributes to bring new ideas from computational neuroscience in the domain of computer vision, concerning modelling principles and mathematical formalism.