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According to the 1.5 views theorem (Poggio, 1990; Ullman and Basri, 1991) recognition of a specific 3D object (defined in terms of pointwise features) from a novel 2D view can be achieved from at least two 2D model views (in the data basis, for each object, for orthographic projection). In this note we discuss how recognition can be achieved from a single 2D model view. The basic idea is to exploit transformations that are specific for the object class corresponding to the object--and that may be known a priori or may be learned from views of other" prototypical" objects of the same class to generate new model views from the only one available. The paper is organized in two distinct parts. In the first part, we discuss how to exploit prior knowledge of an object's symmetry. We prove that for any bilaterally symmetric 3D object one non-accidental 2D model view is sufficient for recognition. We also prove that for bilaterally symmetric objects the correspondence of four points between two views determines the correspondence of all other points. Symmetries of higher order allow the recovery of structure from one 2D view. In the second part of the paper, we study a very simple type of object classes that we call linear object classes. 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. We also provide natural examples of linear object classes induced by symmetry properties of the objects. ¹