In this study, some issues on 3 - dimentional object recognition and pose determination are discussed. The method employs a laser projector which projects a cylindrical light beam on the plane object where it produces a bright ring pattern. The picture is then taken by a T.V camera. The ring pattern is mathmetically the ellipse of which the geometrical parameters have the 3 - dimentional feature of the object plane. This paper gives the mathematical aspects of 3 - dimentional recognition method and shows experimentally the variations of ellipse parameters as the spatial deviation of the plane object.