## Abstract

This paper addresses the mathematics for using monocular model-based vision to find the 3-D 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 3-D positions and orientations of the objects in the scene. The mathematics for solving 3-dimensional position and orientation of the object from matched model and image points/lines features are well known. However, no known paper addresses spherical features arid very few papers address the mathematics involving circular model features. This paper describes a novel closed-formed solution for the 3-D position and orientation of a circular features and the 3-D position of a spherical feature. The number of solutions for the circular case is found to be two in general, but 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) Handles spherical as well as circular features. (2) Closed-form solution. (3) Gives only the necessary number of solutions (no redundant solutions). (4) Simple mathematics involving 3-D analytic Geometry. (5) Geometrically intuitive.

## Date of this Version

3-1-1989