3D reconstruction of polyhedral objects from single perspective projections using cubic corner

This paper presents a direct method to recover the geometry of the 3D planar polyhedron depicted in a single perspective projection. It first finds the vanishing points and then the focal length, which establishes the linear relationship between a vertex on the image plane and its corresponding point on the object. The search for vanishing points produces three sets of parallel lines which are mutually orthogonal in 3D. These orthogonal lines enable the automatic identification of a cubic corner, from which the 3D coordinates of the three vertices connected to the corner are derived, thereby establishing the three planes meeting at the corner. After that, the faces and their connectivity, obtained from the line drawing automatically, are utilized to recover the whole 3D object. The algorithm recovers accurate 3D objects from accurate drawings. For inaccurate drawings, such as sketches, the algorithm can recover 3D objects conforming to human perception if the vanishing points and focal length can be established.