United moment invariants for shape discrimination

Shape discrimination occupied a very important place in pattern recognition and image manipulation. However, because of the affection of many factors, the geometric varieties of shape will happen. It is needed to find the invariant feature values in all kind of instances. So, this paper proposes some new formulas of moment invariants that are defined united moments. The rotation, translation and scaling can be discretely kept invariant to region, closed and unclosed boundary. And the experiments show the effectivity of the united moments.