The paper proposes a novel approach to visual object recognition by representing a 3-D object as a linear combination of 2-D images of the object. The method handles rigid and non-rigid transformations, including scaling, and can be applied to objects with sharp or smooth boundaries. The authors demonstrate that the variety of views depicting the same object under different transformations can often be expressed as linear combinations of a small number of views. They show that for objects with sharp edges, an image obtained by rotation around the vertical axis can be expressed as a linear combination of two model images, and for objects with smooth boundaries, an image obtained by rotation can be expressed as a linear combination of five model images. The paper also discusses the use of two views to determine the alignment coefficients for general linear transformations, and provides a method to recover 3-D structure and motion from orthographic projections. The approach is implemented and tested on artificially created images and real images of 3-D objects, showing good agreement with the actual images.The paper proposes a novel approach to visual object recognition by representing a 3-D object as a linear combination of 2-D images of the object. The method handles rigid and non-rigid transformations, including scaling, and can be applied to objects with sharp or smooth boundaries. The authors demonstrate that the variety of views depicting the same object under different transformations can often be expressed as linear combinations of a small number of views. They show that for objects with sharp edges, an image obtained by rotation around the vertical axis can be expressed as a linear combination of two model images, and for objects with smooth boundaries, an image obtained by rotation can be expressed as a linear combination of five model images. The paper also discusses the use of two views to determine the alignment coefficients for general linear transformations, and provides a method to recover 3-D structure and motion from orthographic projections. The approach is implemented and tested on artificially created images and real images of 3-D objects, showing good agreement with the actual images.