We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications of these varieties in computer vision for triangulation of world features, we investigate when the associated projection map is generically injective; an essential requirement for successful triangulation. We give a complete characterization of this property and present it in two distinct forms, one of which is a direct generalization of previous work on the projection of points. As a consequence of our work, we acquire a formula for the dimension of multiview varieties. We further explore when the multiview variety is naturally isomorphic to its associated blowup. In the case of generic centers, we give a precise formula for when this occurs.