We derive curvature flows in the Heisenberg group by formal asymptotic expansion of a nonlocal mean-field equation under the anisotropic rescaling of the Heisenberg group. This is motivated by the aim of connecting mechanisms at a microscopic (i.e. cellular) level to macroscopic models of image processing through a multi-scale approach. The nonlocal equation, which is very similar to the Ermentrout-Cowan equation used in neurobiology, can be derived from an interacting particle model. As sub-Riemannian geometries play an important role in the Citti-Sarti-Petitot model of the visual cortex, this paper provides a mathematical framework for a rigorous upscaling of models for the visual cortex from the cell level via a mean field stage to curvature flows which are used in image processing.