Location by involution

In this paper, we propose an iterative method of 3D location of 2D parallelogram or 3D parallelepiped shapes by monocular vision from a single image. The method we propose assumes that the camera is calibrated and that the size of the polygonal object is known. The 3D location is obtained in the following way. First we try to find the orientation of a geometric model of the object imaged such that they share the same vanishing points. This property known as "involution" in the 17th century insures that the model and the object have the same orientation. Moreover this property in invariant to translation. This greatly simplifies the location problem by allowing to decouple rotation and translation assessments. The method is illustrated and tested with real scene images.