Symmetric 3D objects are an easy case for 2D object recognition

According to the 1.5-views theorem (Poggio, Technical Report #9005-03, IRST, Povo, 1990; Ullman and Basri, IEEE Trans. PAMI 13, 992-1006, 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 (for each object, for orthographic projection). This note considers how recognition can be achieved from a single 2D model view by exploiting prior knowledge of an object's symmetry. It is proved that, for any bilaterally symmetric 3D object, one non-accidental 2D model view is sufficient for recognition since it can be used to generate additional 'virtual' views. It is also proved 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 Euclidean structure from a single 2D view.