Before revision:  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:  Technical difficulties hindering the generalization of CNNs to arbitrary-shaped manifold are rooted in the lack of key ingredients such as the canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.