A contact structure on an odd-dimensional manifold is the kernel of a 1-form $\alpha$ with $\alpha \wedge (d\alpha)^n \neq 0$ — the maximally non-integrable distribution. Petitot’s V1 model recasts the visual cortex as a contact 3-manifold $\mathrm{SE}(2)$ on which contour completion is a geodesic problem.