Recognition by linear combinations of models

An approach to visual object recognition in which a 3D object is represented by the linear combination of 2D images of the object is proposed. It is shown that for objects with sharp edges as well as with smooth bounding contours, the set of possible images of a given object is embedded in a linear space spanned by a small number of views. For objects with sharp edges, the linear combination representation is exact. For objects with smooth boundaries, it is an approximation that often holds over a wide range of viewing angles. Rigid transformations (with or without scaling) can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations. Three alternative methods of determining the transformation that matches a model to a given image are proposed