This paper studies an object recognition problem, that is, the problem of determining whether a given perspective image is obtained from a 3-D object to be recognized or not. As an extension of Ullman and Basri's approach, it is found that any perspective image of an object can be expressed as a certain type of nonlinear combination of four appropriate perspective images of the same object. We show that any image of an object with not only a rigid 3-D transformation but also a nonrigid transformation has this property. In order to recognize a 3- D object, we have only to store four perspective images and, whenever a new perspective image is given, determine whether it can be expressed as a combination of the four images. This implies that we no longer need to recover the 3-D information of an object explicitly under perspective projection. Our investigation shows that four perspective images have sufficient information to recognize a 3-D object.