Recognition by Linear Combinations of Models

Visual object recognition requires the matching of an image with a set of models stored in memory. In this paper, we propose an approach to recognition in which a 3-D object is represented by the linear combination of 2-D images of the object. IfJLk{M1,.” .Mk} is the set of pictures representing a given object and P is the 2-D image of an object to be recognized, then P is considered to be an instance of M if P= C~=,aiMi for some constants (pi. We show that this approach handles correctly rigid 3-D transformations of objects with sharp as well as smooth boundaries and can also handle nonrigid transformations. The paper is divided into two parts. In the first part, we show that the variety of views depicting the same object under different transformations can often be expressed as the linear combinations of a small number of views. In the second part, we suggest how this linear combination property may be used in the recognition process.