Construction Method for Mirror Isometric Invariant and Its Applications

We present a method of constructing mirror isometric invariant.Firstly,we look for two intersecting geodesics on the orientable surface and two tangent vectors at the intersecting point.Then the cross product of two tangent vectors is calculated,and the direction of cross product is recorded.In the following step,the sign of the cross product is determined via the direction of cross product and the surface,and a new integral kernel is constructed through this cross product.Thus,the framework of isometric invariants is extended by this new kernel,and a new set of invariants can be obtained.All invariants are isometric,and can reflect the mirror relationship of the two objects as well.Several experiments are done on the human hand models.The results show that objects can be recognized and distinguished using these mirror isometric invariants with high efficiency.