3D location of circular and spherical features by monocular model-based vision

Mathematics is presented for using monocular model-based vision to find 3D positions of circular and spherical model features, and, for the circular case, orientations as well. Monocular model-based vision here refers to the use of a single projective image of modeled objects to solve for the 3D positions and orientations of the objects in the scene. A novel closed-formed solution for the 3D position and orientation of a circular features and the 3D position of a spherical feature is described. There are two general solutions for the circular feature bu there is only one solution when the surface normal of the circular feature passes through the center of projection. There is only one solution for the circular case. Advantages of this method are: (1) it handles spherical as well as circular features; (2) it has a closed-form solution; (3) it gives only the necessary number of solutions (no redundant solutions); (4) it uses simple mathematics involving 3D analytic geometry; and (5) it is geometrically intuitive