Pose determination of polyhedral objects from unconstrained 3D edge points

We present algorithms for locating polyhedral objects using three edge points. An edge point is a three-dimensional data point which lies on a known edge of an object. However, the precise position of an edge point on an edge is unconstrained. In general, with three edge points, we have to solve a system of nonlinear equations. However, there are special cases, where we can solve the location problems analytically. The special cases depend on the collinearity and coplanarity of the three edge points.