Before revision:  This, unfortunately, was not the case for the geometry processing community, where many visual recognition problems are defined on arbitrary surfaces(2D-manifolds). Technical difficulties hindering the generalization of CNNs to arbitrary-shaped manifold are rooted in the lacks of such key elements including the canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.
After revision:  This, unfortunately, was not the case for the geometry processing community, where many visual recognition problems are defined on curved surfaces, and the generalization of CNNs to arbitrary-shaped manifold are rooted in the lacks of such key elements including the canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.