An algorithm for removal of extraneous Implicit polynomial curve

Implicit polynomial (IP) curves are used to describe data set, which are widely applied to many area due to their advantages. All the algorithms of fitting IP curve suffer from stability problems. That is, the fitting IP curves include extraneous curves component. This paper proposes the IP curve connectivity theorem, which provides the way to determine whether the fitting IP curves include the extraneous curves component. The examples of the IP curve connectivity detection are illustrated.