In this note we discuss how recognition can be achieved from a single 2D model view exploiting prior knowledge of an object's structure (e.g. symmetry). We prove that for any bilaterally symmetric 3D object one non- accidental 2D model view is sufficient for recognition. Symmetries of higher order allow the recovery of structure from one 2D view. Linear transformations can be learned exactly from a small set of examples in the case of "linear object classes" and used to produce new views of an object from a single view.