The authors address the difficult problem of representing a three-dimensional object so that it can be efficiently recognized from any view (that is, without requiring a search through all possible views). The paper describes a representation based on the three-dimensional Fourier transform of the 3D object and an indexing technique to find the best match when given a 2D image. This technique is applied to the problem of face recognition and pose estimation (that is, whose face it is and which way the head is turned). Results are shown on a test dataset that has been used by other researchers. The technique does not eliminate the problem of searching through a number of views, with recognition requiring five minutes on moderate-sized datasets. The representation and matching scheme will also interest researchers in other problem domains where 3D models are available and the pose of the object is not given.