Orientation-based representations (OBR) have many advantages. Three orientation-based differential geometric representations in computer vision literature are critically examined. The three representations are the extended Gaussian image (EGI),3 the support function based representation (SFBR),5 and the generalized Gaussian image (GGI).4 The scope of unique representation, invariant properties from matching considerations, computation and storage requirements, and relations between the three representations are analyzed. It is shown that an OBR using any combination of local descriptors is insufficient to uniquely characterize a surface. It must contain either global descriptors or connectivity information. The GGI as it was introduced4 requires the mapping of one principal vector onto the unit sphere. It is shown in this paper that this is unnecessary. This reduces the storage requirement of a GGI by half, therefore, making it a more attractive representation. It is also concluded that if the intention is to reconstruct surfaces from their representations, a SFBR should be used. If the intention is recognition, a truly orientation-based representation such as the GGI should be used.