Computing stable poses of piecewise smooth objects

When a three dimensional object is known to be lying on a planar surface, its pose is restricted from six to three degrees of freedom. Computer vision algorithms can exploit the few stable poses of modelled objects to simplify scene interpretation and more accurately determine object location. The paper presents necessary and sufficient conditions for the pose of a piecewise smooth curved three dimensional object to be stable. For objects whose surfaces are represented by implicit algebraic equations, these conditions can be expressed as systems of polynomial equations that are readily solved by homotopy continuation. Examples from the implemented algorithm are presented