Robust determination of rotation-angles for closed regions using moments

In this paper we introduce a new moment based approach for determining the orientation of closed regions. It is widely in use to determine the orientation angle by the second order moments using the inertial ellipse. However, in these cases if the inertial ellipse degenerates to an inertial circle, then this method fails. In this paper we generalize that to the third and fourth order moments and show that the method is very robust in most cases. The method can be used for the rotation determination of closed regions and also for fitting of objects by geometrical primitives using the orientation of the object and of the primitive.